A DETERMINATION OF THE APEX
•
OF THE
SOLAR MOTION
ACCORDING TO THE METHOD OF BRAVAIS
BY
H A. WEERSMA.
♦
GEBROEDERS HOITSEMA. — 1908. — GRONINGEN.















A DETERMINATION OF THE APEX
OF THE
SOLAR MOTION
ACCORDING TO THE METHOD OF BRAVA1S.







A DETERMINATION OF THE APEX
OF THE
SOLAR MOTION
ACCORDING TO THE METHOD OF BRAVAIS.
ACADEMISCH PROEFSCHRIFT
TER VERKRIJGING VAN DEN GRAAD VAN
DOCTOR IN DE WIS- EN STERREKUNDE
AAN DE RIJKSUNIVERSITEIT TE GRONINGEN
OP GEZAG VAN DEN RECTOR MAGNIFICUS
Dr. M. E. MULDER
HOOGLEERAAR IN DE FACULTEIT DER GENEESKUNDE TEGEN DE BEDENKINGEN DER FACULTEIT IN T OPENBAAR TE VERDEDIGEN
OP DONDERDAG 9 JULI 1908, DES NAMIDDAGS TE 3 UUR
DOOR
HERMAN ALBERTUS WEERSMA
GEBOREN TE GRONINGEN,
GEBROEDERS HOITSEMA. — 1906. — GRONINGEN.







Aan het eind van mijn academische studie gekomen, beschouw ik het als een aangename taak, U hoogleeraren in de faculteit der Wis- en Natuurkunde alsmede U Dr. De Sitter mijn welgemeenden dank te betuigen voor het genoten onderwijs. In het bijzonder gevoel ik mij gedrongen uiting te geven aan mijn gevoelens van dankbaarheid jegens U, hooggeleerde Kapteyn, niet alleen voor Uw leiding bij het samenstellen van mijn proefschrift, maar in het algemeen voor de vriendelijke en aanmoedigende belangstelling, die Ge steeds in mijn studie hebt getoond. Zeer zeker zullen mij steeds aangename herinneringen bijblijven aan den tijd, waarin ik onder Uw leiding mijn voorbereidende studie mocht voltooien.







TABLE OF CONTENTS.
Page.
Introduction 1
Chapter I. Discussion of the method of Bravais 3
Chapter II. The application of the method of Bravais to the present deter-
mination of the apex 16
Chapter III. Discussion of the results from zones of different declination 29
Chapter IV. Definitive results 50
Notes to Chapter I 58
Notes to Chapter II 60
Note to Chapter III 73
I. Tables i-xxxi.







INTRODUCTION.
Nearly all methods for the determination of the apex of the solar motion are based upon the hypothesis that the real proper motions of the stars have no predilection for any one direction. Recent investigations have shown that this hypothesis is no longer tenable. Both Kobold and Prof. Kapteyn ') have shown that there can be no doubt about the existence of strongly systematic deviations from a random-distribution. These led the latter to his theory of „starstreams", a theory which was subsequently confirmed by the investigations of Eddington and Dyson *), based on independent materials. It seems imperatively necessary therefore to have a new determination of the position of the apex by means of a method which is independent of this hypothesis of the randomdistribution of the proper motions.
It is this reason which led me to undertake such a determination by the method of Bravais. The method, published as early as 18438), is, in principle, quite free from any hypothesis. It is true that we cannot apply it rigorously owing to the fact that several ot the quantities contained in the equations, to which we are led, are still unknown. Still I think that, at the present moment
') Report of the British Association for the Advancement of Science 1905, pag. 257. ") Eddington: Monthly Notices of the Roy. Astron. Society 1906, page 34.
Dyson : Proceedings of the Roy. Society of Edinburgh, sess. 1907—'08, vol. XXVIII, part. III, no. 13.
The material used by Eddington has been treated in another way by Schwarzschild. 8) Journal de Mathématiques de Liouville, tome VIII, année 1843.



there is no other known method which is entitled to the same confidence Reasons for this greater confidence will be shown Chapter I.
Along with my aim
ist of determining the position of the apex as free as possible from any supposition about the proper motions
I had another aim in view, viz.:
2nd to find out whether the positions of the apex yielded by stars of different galactic latitude were the same or were decidedly different.



CHAPTER I.
DISCUSSION OF THE METHOD OF BRAVAIS.
Short explanation of the method.
Bravais considers the following problem: to determine the sun's motion relative to the centre of gravity of an arbitrary group of stars, the sun itself included. If the universe is assumed to be finite, we may imagine the group chosen in such a way that all the stars are contained in it; and we shall then get the sun's motion relative to the centre of gravity of the universe. Bravais has based the solution of his problem upon a principle of pure mechanics. As the origin of coordinates he takes the sun's position at the moment which is taken as the origin of time; the origin of coordinates is further supposed to be at rest relatively to the centre of gravity of the group. Through this point three fixed perpendicular axes are taken as axes of coordinates. If the components of the velocity of a star with respect to the adopted system of coordinates are called respectively dx, Jy and Jz and the mass m, then, as an immediate result from the choice of the origin, we have for all stars together:
(1) . . . . 2(mJx) = o. 2(mJy) = o. 2{mJz) = o.
Thèse equations form the basis of the method; after some simple mathematica! considerations they are reduced to three equations which are given on page 442 of the paper of Bravais. These express the components of the solar motion as a function of the spherical coordinates of the stars, their distances, masses, observed proper motions and radial peculiar velocities *).
Finally Bravais chooses the axes of coordinates in such a way that the positive axis of z points to the north pole, the positive axis of x to the point Aries and the positive axis of y to a point in the equator with a right-ascension of 6 hours. Let us call the rectangular components of the solar velocity |, rj and £; the right-ascension and declination of a star, « and 8; its distance from the sun, (>; the observed proper motion of the star in right-ascension and declination, expressed respectively in seconds of time and of are, f.ta and /us; its
') This name we shall give to the radial velocities relative to a fixed sun as origin.



radial peculiar velocity /up (taken positive if the motion is directed from the sun); the mass, m. If now we exclude the sun from the group of stars of which the centre of gravity is rigidly connected with the origin, the equations on page 442 quoted above may be easily reduced to the foliowing form.
2m{ 1 cos8£cos8a)|—2 m cos sin a cos a. tj — 2 m cos S sin S cos a. C = JT 15 sin a cos <S.sin £ cos a.,aa)— 2mcosdcosa
. . 2m( 1—cos8£sin8a)w — JE" 0/cos sin a cos a. £—J£wcos<5sin<5sina.C =
(2)
2M(j(— 15 cosacos J.^a + sin^sina.^) —2m cos8sina. /up.
2 nt cos 8$. £ — 2 m cos d sin S cos a. S — 2m cos 8 sin d sin a. r\ — 2 m(j(— cos Sjui) — 2 m sin d.
These equations are rigorous and therefore they determine, free from any hypothesis, the solar motion relative to the adopted origin as a function of the other quantities contained. In order to get his definitive equations *) Bravais introduced certain suppositions in regard to the masses, distances and radial velocities of the stars. By so doing he obtained a form somewhat simpler than the equations (2); but they are no longer a pure expression of the fundamental principle. For this reason we shall provisionally retain the equations in the form (2).
Objections to the method of Bravais.
Evidently the equations in the form (2) contain quantities which are unknown or known only to a small extent, viz:
1. the masses.
2. the distances.
3. the radial peculiar velocities.
Hence there are difficulties in the way of applying the method of Bravais to the determination of the apex. As we have said just now Bravais extricates himself from these by making certain simple suppositions. As in these suppositions lies Bravais' weak point, a just appreciation of the value of his method requires a thorough examination of the difficulties thus introduced. They may be expressed in the form of the two folio wing questions.
1. In how far can we meet these difficulties? On theanswerto thisquestion depends the absolute value of the method.
2. How do the difficulties compare with those arising from the other methods ? The masses and radial peculiar velocities do not enter into the equations furnished by the majority of other methods; the distances either do not appear in them or may be eliminated by a slight modification of the method. Hence, owing to the absence of these quantities, the other methods might seem to be
') Page 446 of the paper of Bravais.



superior to the one under discussion. But are these advantages really as great as they seem to be or, perhaps, do the same or equivalent difficulties — though somewhat masked — present themselves in the other methods? Evidently this question belongs under the second head, i. e. the relative value of the method of Bravais as compared with the other methods.
First question.
We shall treat separately the masses, distances and radial velocities.
a) The masses.
Bravais gives an application of his method to 61 stars with well determined proper motions. Here he takes all the masses to be equal, and they thus disappear from the equations. This supposition is equivalent to the adoption of a new origin of coordinates which is at rest relatively to what we may call the geometrie al centre of gravity *) instead of the mechanical one. For if we had started with the equations
(3) 2 Jx = 0 2 Jy = o 2 Jz = o
as a basis for the method instead of those of (1) we would have derived equations identical with those of (2), only all the factors m would be replaced by uniiy. Now the equations (3) are rigorous if we take as the origin of coordinates a point which is at rest relatively to the geometrical centre of gravity *); and therefore the modified equations obtained by replacing in the equations (2) all the factors m by unity are also rigorous in this case. Thus by putting all the masses equal to unity in the equations (2), wc get equations, which yield the correct values of the components of the solar motion, relative to the geometrical centre of gravity of all the stars3). If the stars move with uniform velocity in straight lines it is quite indifferent whether we get the sun's motion relative to the geometrical or to the mechanical centre of gravity. For in the present state of science, and presumably for many centuries to come, we have to consider the proper motions of the stars as uniform and rectilinear. With such a motion of the individual stars, the motion of the geometrical centre of gravity has the same property as that of the mechanical centre, viz that of being uniform and rectilinear and the two present exactly the same advantage for the present problem. No doubt if afterwards, in the very remote future, the curvature of the real orbits of the stars becomessensible, the mechanical centre of gravity will be preferable as an origin. In this case however the methods which are based on the hypothesis of a random-distribution are liable to the same objection because these also determine the sun's motion relative to the geometrical centre of gravity, as will be shown afterwards.
Howsoever this be, for the present at all events there can be no serious objection against the choice of the geometrical centre of gravity. The supposition
') For the exact definition of this point see Notes to Chapter I. 1).
*) See idem.
8) The axes of coordinates must be imagined to remain parallel to the directions originally chosen.



about the masses amounts to a change of origin and not to the introduction of a new hypothesis.
b) The distances.
The distances are also taken as equal by Bravais. This is equivalent to giving a preponderance to the stars nearest the solar system.
The magnitudes have often been taken as a criterion of the distances of the stars. But the criterion is a very imperfect one because the total quantities of light emitted are very different.
A better criterion is furnished b'y the proper motions. The distances might be taken to be in inverse ratio to the observed proper motions, though this proceeding may be considered liable to objection. Other things being equal, the observed proper motions will be smaller for the stars, which move in thé direction of the apex than for those which move in the opposite direction and as a consequence the distances derived for the first class of stars vvould systematically exceed those for the second class. This might cause an error in the determination of the apex in the case that the distribution of the peculiar proper motions is in some way systematic. For that reason a somewhat more refined proceedinoseems to be desirable We may avoid the difficulty in the following manner. *
By means of an approximate position of the apex we can determine for every star the angle p between the direction of the observed proper motion and the great circle towards the ant-apex. Denoting now the angular distance between the star and the apex by A; we may divide the stars into groups according to the value of sin A and these again into groups according to the value of p. For each of the so formed groups we may derive the mean value of the proper motions, which we will call JTXf p and divide this by
the mean value ^ of the proper motions of all the stars. Denoting by q
we shall have q = rp{A, ƒ). This function can therefore be determined empirically. We may, however, also determine it theoretically by making a simple supposition
with regard to the distribution of the peculiar proper motions. If we put f — —
q
and denote the observed proper motions of the stars by fi, then the quantities which we shall call the reduced proper motions, will be independent of the values and p and A. From these quantities p' we may thus consider the effect of the sun's motion on the distribution to have been eliminated. They will afford a better criterion for the distances than the directly observed quantities /li.
Finally in connection with these quantities the magnitudes may be used for the estimation of the distances. Tables have been derived empirically1) by Prof. Kapteyn , which give the mean parallax of stars of determined proper motion and magnitude. If now instead of the proper motions /u, we take the reduced proper motions ju' as the argument, we may take from these tables values
') Publ. 8 of the Astronomical Laboratory of Groningen.



for the parallaxes and hence for the distances, which, substitued in the equations of Bravais, are sufficiënt for a determination of the position of the apex
In this way the difficulties of the distances may be avoided to a great
ïxtent.
c) The radial velocities.
Of these quantities nothing was yet known in the time of Bravais. There thus was no other way but to neglect them altogether. Evidently this proceeiing is equivalent to the introduction of a hypothesis. Considering the origin rf coordinates to be at rest relatively to the geometrical centre of gravity so that the masses disappear from our equations we shall have (see equations 2):
2 cos 3 cos a . fip — o,
JS cos 3 sin a . fi? = o,
2 sin 3 fip =0,
in which the sums are extended over the whole material used for the determilation of the apex. These equations may be enunciated in the following way:
the sums of the projections of the radial peculiar velocities of all the stars ïpon the three axes of coordinates are zero, or:
the radial peculiar velocities of all the stars transferred to the geometrical :entre of gravity and treated as forces, will be in equilibrium.
We shall call this supposition the hypothesis of Bravais. Since at the )resent time with the aid of spectroscopy, soinething more of the radial /elocities has become known, it might seem possible to get rid of a part )f the uncertainty introduced by this hypothesis, introducing the values furlished by the spectroscope, The number of published spectroscopie velocities lowever is still too small at the present time for expecting an improvement by this. Moreover there exists another and more radical difficulty which is due to :he fact that what the spectroscope really determines is the radial motion of a star relative to the moving sun. From this relative motion the radial peculiar velocity might be obtained if we had some independant method of determining the sun's linear velocity. In fact, however, this linear velocity is itself derived from the spectroscopie observations on the hypothesis that the radial peculiar velocities are in equilibrium. But this hypothesis is identically the same as that af Bravais. Therefore by substituting in the formulae (2) for the radial peculiar velocities, the values derived from the observed spectroscopie velocities, no improvement is to be expected.
How this difficulty might be overcome will be shown later. For the present there seems to be no better way than simply to neglect the terms with up, thus adopting the hypothesis of Bravais. This hypothesis might introducé an error in the position derived for the apex if some such supposition as that of Herschel , who assumes a condensation of the stellar system, were correct, sspecially if the condensation were directed towards a point not too far distant from the Sun. But, as has been already remarked by Bravais even in such a case the error will vanish if opposite areas of the sky contain equal numbers of stars.



If the distribution of the stars selected for the determination of the apex does not quite fulfill the condition stated above, we may meet the difficulty by a suitable choice of the weights. For if we take care that the terms furnished by zones of the same area and equal but opposite declinations appear in the definitive equations with the same weights, the effect will be the same, with respect to the radial velocities, as if they contained an equal number of stars.
If this precaution be taken, then the hypothesis of Bravais will be satisfied not only in the case here considered of a condensation of the whole system but in a number of other cases besides.
It is satisfied certainly for a sufficiënt number of stars if the directions of the peculiar proper motions are supposed to be distributed at random. But other distributions of the velocities also are compatible with the hypothesis of Bravais.
If the theory of the star-streams referred to in the introduction gives a correct representation of the real distribution of cosmic velocities there must exist an equal preference for motions in two opposite directions. We shall suppose that an equal preference for both directions exists in every part of space, as will be the case if the two streams are well intermingled everywhere. If this condition is fulfilled the radial velocities will neutralize each other in every individual region. So the theory of the star-streams which may be considered the only supposition in regard to the distribution of the real velocities that is based directly on experience does not contradict the hypothesis of Bravais.
Schönfeld has investigated another distribution of the velocities. He has considered the question whether there is a systematic rotation about an axis perpendicular to the plane of the galaxy. If this were the case we might assume this axis to pass through the geometrical centre of gravity, as this is supposed to be at rest. This however can not lie far from the sun as a consequence of the adopted distribution of the stars; therefore the supposed rotation has no influence upon the radial velocities, and in this case also there will be a compensation of the terms neglected by Bravais.
If however the distribution of stellar velocities in space is such that the radial peculiar velocities of all the stars do not neutralize each other, no precaution whatever can prevent the apex determined from purely astronomical proper motions to differ from the true one. But even the introduction of the radial velocities derived from spectroscopie results will give no improvement as we have shown above.
However it will be shown at the end of this chapter that spectroscopie results may be combined in another way with astronomical ones to determine the apex free from any hypothesis about the radial velocities. This will require a fairly large number of suitable spectroscopic velocities.
Second question.
Difficulties arising from Bravais' method compared with those presented by the other methods.



a) The masses.
The masses appear in the equations when we adopt as origin a point rigidly connected with the mechanical centre of gravity. By taking as the origin a point holding the same relation to the geometrical centre of gravity they are eliminated. In the other methods generally it is not stated definitely which point is to be taken as the origin; but it may easily be proved that in the methods which are based on the hypothesis of the random-distribution as those of Airy, Argelander etc. the geometrical centre of gravity must really be considered as the origin.
We may assert that, if the hypothesis of the random-distribution is correct, this is only the case relatively to a point of which the motion is perfectly determined. For if we suppose it to be true relatively to a point P as origin, this will be no longer the case with reference to another point Q, which moves relatively to P. For to get the motions relatively to the new origin Q, we must form for every star the resultant of the original proper motion and a velocity equal and parallel to that of P relatively to Q. By doing so the randomdistribution will be destroyed. In adopting the hypothesis of the randomdistribution we must therefore take the point P or a point rigidly connected with P as origin. Now the origin P, as a consequence of the supposition made, has the property that all the proper motions transferred to it, will neutralize each other. But this is precisely a property of the geometrical centre of gravity and it is not possessed by any other point which moves relatively to it. The point P must therefore be rigidly connected with the geometrical centre of gravity.
We may therefore assert that the hypothesis of the random-distribution requires the assumption of the geometrical centre of gravity or a point rigidly connected with it as an origin. Therefore the methods which are based on this hypothesis can only determine the motion of the sun relative to the geometrical centre of gravity. The non-appearance of the masses in the equations to which these methods lead, cannot therefore be considered as a real advantage of these methods over that of Bravais.
In what follows we shall always suppose, unless the contrary is stated, that the origin is rigidly connected with the geometrical centre of gravity.
b) The distances.
Among the methods which rest on the hypothesis of the random-distribution , only that of Airy l) contains the distances in the equations. We may however transform this method in such a way that we get two sets of equations from one of which the distances disappear a). Also the method of Argelander 8) and that of Prof. Kapteyn 4) lead to equations from which the distances are
*) Memoirs of the Royal Astronomical Society of London, vol. XXVIII, page 143 etc. ") Astron. Nachr. No* 3721—'22, Meth. III, page 9.
8) Astron. Nachr. No. 363.
*) Proceedings of the meetings of the Akademy of Sciences at Amsterdam, Vol. II, page 353 etc.



absent. Indeed the hypothesis of the random distribution affords a principle by which it is possible to determine the position of the apex purely by means of considerations of symmetry without taking the distances into account. But another difficulty presents itself generally, namely that of assigning the weights with which the proper motions must be combined. As Prof. Kapteyn has shown this difficulty may be removed by grouping the stars according to the amount of the proper motions and combining the results obtained from the individual groups by weights in accordance with the mean errors in the results. This proceeding supposes that the values of the apex obtained from groups of stars at different distances from the solar system must be really identical, and this in its turn may be considered to be a consequence of the hypothesis of the random-distribution. We see therefore that in the derivation of the apex according to one of these methods this hypothesis plays a doublé part. The influence of it is a primary one, in so far as the equations used are themselves expressions of the hypothesis of the random distribution. It has a more subordinate secondary influence in the choice of the weights.
On the other hand we have seen that we may derive estimated values for the distances, which are sufficiënt for the determination of the position of the apex by the method of Bravais. These estimated distances are based for a large part on empirical data, though in deriving them we cannot entirely avoid introducing some hypothetical elements The hypothetical elements introduced in this way, however have only a secondary influence upon the position of the apex, an influence of the same order as the choice of the weights in the other methods.
c). The radial velocities.
As we mentioned already, Bravais, by neglecting the terms depending on the radial velocities introducés the following hypothesis:
Hypothesis B. The resultant of the radial peculiar velocities of all the stars relatively to the geometrical cenlre of gravity is zero.
We shall now compare this hypothesis with that underlying the other methods. For that purpose we shall denote the hypothesis of the random-distribution by H. As the methods which rest on the hypothesis H take into account only the tangential components of the peculiar velocities, we may here consider the hypothesis H to be relative to these components only. Now the hypothesis B may be expressed in a somewhat different form so that it is more easily
comparable with H.
Since the origin is at rest relatively to the geometrical centre of gravity,
we have rigorously:
the resultant of the total peculiar velocities of all the stars is zero.
Evidently we may put this in another way, viz:
the resultants of the tangential and of the radial peculiar proper motions are equal and oppositely directed.
Combining this property with the hypothesis of Bravais, we get:
(C) the resultant of the tangential proper motions of all the stars is zero.



Bravais' hypothesis thus may be put perfectly as well in the form (C) as in the form (B). In our comparison with other methods we will adopt the form (C).
The hypothesis H supposes that for every part of space or of the sky, which contains a sufficiënt number of stars, separately the condition expressed by (C) is fulfilled. But it involves more than this. It supposes that there is a radial symmetry in the distribution of the peculiar motions. We thus see that the hypothesis H really contains (C) as a part.
Among the methods, based on the hypothesis H, that of Prof. Kapteyn does not require the absolute correctness of the suppositions implied by the hypothesis H. For as it determines for every point of the sphere the direction of the apex as that of the resultant of the proper motions, it will not be necessary for the application of this method that a radial symmetry in the distribution of the proper motions exists. If for example there is an equal preference for two opposite directions in every part of the sky the position of the apex furnished by this method would still be correct. The other methods however which are based on the hypothesis H cannot be applied without reserve in this case. They presuppose that in the individual parts of the sky generally no large systematic deviations from the radial symmetry exist. For the method of Bravais it is quite indifferent whether they do exist or not, if only all the tangential peculiar proper motions transferred to a single point neutralize each other. This may be considered as a considerable advantage of the method of Bravais over the other methods.
The combination of the astronomical and spectroscopic velocities.
The method of Bravais would not lead to a correct result in the case that the tangential peculiar velocities have a resultant different from zero, consequently the radial peculiar velocities an equal resultant in the opposite direction. In this case however we could still obtain the true values for the components of the solar motion relative to the geometrical centre of gravity if only a sufficiënt number of spectroscopic velocities were available *). We would then have to combine in the proper way the results obtained from the astromical proper motions with those obtained from the radial velocities. — How the combination must be made will appear from the following consideration.
The equations of Bravais, definitively used for the determination of the apex, are of the following form (see the beginning of Chapter II):
2 (i — cosa 8 cosa a)| — 2 cos2 8 sin a cos a . r\ — 2 sin 8 cos 8 cos a . £ = = «2fy(i 5 cos 8 sin a . fia + sin 8 cos a . fis).
(4) 2 (1 — cosa 8 sin2 a)rj — 2 cosa 8 sin a cos a . § — 2 sin 8 cos 8 sin a . £ =
= 2(j(— 15 cos 8 cos et. [ia -\- sin 8 sin a . fis).
2 cos2 8 . £ — 2 sin 8 cos 8 cos a . § — 2 sin 8 cos 8 sin a . rj = 2y (— cos 8 . fit).
') Of course we will suppose here, that the distances would introducé no difficulty in the determination of the components of the solar velocity from the astronomical proper motions.



These equations may be obtained by starting from the fundamentalequations (3) '♦).
In developing the solution we have only to neglect the peculiar velocities.
Now, in order to get a system of equations analogous to these, which will determine the components |, 17 and £ from the observed spectroscopie proper motions v, we have to start from the same fundamental-equations, neglecting now the tangential peculiar proper motions. If we do so, we get the following set of equations a)
2 cosa£ cos' a . | + 2cosa 8 sina cosa .»? + 2sin£cos£cosa. £ = — Zvcosdcosa.
(5) 2 cosa 8 sina a . 17 + 2 cosa 8 sin a cos a . | + 2 sin d cos $sin « . £ = — sv cos 8 sin a.
2 sina 8 . £ -f 2 sin 8 cos 8 cos a . £ 2 sin 8 cos # sin a . rj = — 2 z/ sin
These equations are identical with the normal-equations belonging to the equations of condition used by Campbell for his preliminary determination of the solar motion from a group of 280 stars8).
If now we imagine the equations (4) and (5) to be relative to the same system of stars of which we denote the number by N, we get by adding the corresponding equations of the two systems:
N£ = 2L(>(i5cos£sina.,Mn-fsin5cosa./Ma) — v cos 8 cosa].
(6) N r] = 2[(>(— 15 cos 8 cos a. fia + sin 8 sin a. fis) — v cos 8 sin «].
N £ = 2[(> (— cos 8./us) — v sin £].
If we call the projections on the axes of x, y and z of the total linear velocities of the stars in space relative to the moving sun 8xt 8y and 8z, then the second members are precisely equal to the sums of these quantities with the negative sign. We may therefore write the equations in the form:
(7) ~L{8X +1) = o. z(8y + r/) = o. 2 (82 -f £)=o.
But these equations are identical with the equations (3), from which the rigorous equations of Bravais4) are derived. By adding therefore the equations (4) and (5) in the proper manner the exact equations for the determination of rj and £ are formed.
If therefore for a group of stars the spectroscopie as well as the astronomical proper motions were known, we could get from these the true values of the comcomponents of the solar motion relative to the geometrical centre of gravity of the group by adding the equations (4) and (5) or more simply by taking directly the equations (6). We will however consider the more general case that the astronomical proper motions are known for a group, which we call Mx, the spectroscopie proper motions for a group M2, which wholly or partially consists of other stars. Let us call the components of the solar motion as derived from the first
') See page 5.
*) For the proof see Note to Chapter I 2).
8) Astrophysical Journal, vol XIII, page 83 etc.
*) With respect of course to the geometrical centre of gravity.



group |t, hj and £j, those from the second group |a, rj2 and £3. By combimng these two groups of quantities we can derive the correct values for g, rj and C, only in the case that both groups Mx and Af9 may be considered to be fair samples of one and the same group Af. If this is not the case, the two sets of values will be relative to different points as origin. The relative motion of these two points will be unknown. The two sets of values cannot therefore be properly combined. At the present time spectroscopie proper motions are only known for a group of the brightest stars; astronomical proper motions for a much larger group containing a considerable number of much fainter ones. A combination of the components obtained from the two groups will not therefore be of any particular value at the present time unless we rest satisfied with a determination of the solar motion relative to the very bright stars only.
As soon however as the spectroscopie velocities will be known for a group M2 containing a sufficiënt number of stars among which the different magnitudes are represented nearly in the same proportion as they are in the group Mx, the case will be different.
The way in which the results obtained separately from the two groups must then be combined, in order to give the most reliable result, takes a particularly simple form if our stars are fairly evenly distributed over the sky. For the two groups M\ and M% may now be considered as fair samples of one and the same more extensive group M of which the stars are distributed evenly over the sky. For such a group the coefficients in the equations (4) and (5) will all vanish except that of § in the fïrst, rj in the second and £ in the third equation of each set. These coefficients may be easily found by a simple integration over the sky. Denoting the number of stars of the group M by Nthese coefficients become all equal to £ N in the equations (4) and equal to £iVin the equations (5).
If now we put:
*Lq (15 cos 8 sin « . fta + sin S cos a . fi$) =
2^ (— 15 cos d cos cc. /ua-\- sin 8 sin a . fi$) = Npy ( — cos S . pi) = Np»
£ — d cos S cos a — N^r
2 — v cos 8 sin a =
2 — v sin d =
then the two sets of equations (4) and (5) assume the following forms:
(4«) .... tN|, = N*Nn = Npy fN£, = NA
(5 a) .... |N£a = £Ni/a = |N£a = N?*
whereas the equations (6) which give the exact values of the components may be written:
(6a) . N£ = N(/* + qx) Nrj - N(p„ + qy)
N£ = N (/. + *)•



Eliminating now the quantities px, py, Pz, q*t qy and qz from these 9 equations we get:
( I = fl. + i& (8) 1 n = |i?i +
t l = K, + Et-
The assumed uniform distribution of the group M over the sky is not the most representative one. For if our data extend to magnitude m it centainly seems more satisfactory to get the sun's motion referr-ed to the geometrical centre of the whole of the stars down to that magnitude. In order to represent fairly the system of all the stars down to the magnitude mt the groups Mt and Ma (consequently also M), must satisfy the following condition: the number of stars of different magnitude and galactic latitude contained in our groups must be proportional to the corresponding numbers in the sky. They therefore must approximately satisfy the two conditions:
i°. The distribution must be symmetrical relatively to the plane of the
galaxy.
20. The stars must be distributed equally over the different galactic longitudes.
If the actual M| and M2 do not quite satisfy these conditions we may improve the results by a suitable choice of the weights.
If now we take the plane of the galaxy as plane of XY, the equations (4)» (5) and (6) will subsist, only the quantities 11 and £ will now represent galactic components. We will denote them by X, Y and Z. The coordinates a and 8 must be replaced by the galactic longitude and latitude l and b; ua and by the corresponding galactic components of proper motion. In the second members quantities which we will call P,- and Q, will take the place of the Pi and qi. As a consequence of the uniform distribution over the different galactic longitudes, all coefficients of X, Y and Z, except that of X in the first, Y in the second and Z in the third equation, will vanish. If again we denote by the index 1 the values of the components of the solar motion derived from the astronomical, by 2 those from the spectroscopie velocities and without an index those found from the total velocities of the stars of group M, we get the following equations (N = number of stars):
(4^) 2(i — cos2 b cos2 /) Xi = NPa, 2(1 — cos2 b sin2 /) Yi = NPy 2cos2 b. Z, = NPa.
(5^) 2 cos2 b cos2 /. Xi = NQa, 2 cos2 £ sin2/. Ya = NQy Ssin2^ . Za = NQ«. (6b) NX = N(P. + Q#). NY = N(Py + Qy) NZ = N(P. + Q,).
Eliminating now P«, Py, P«, Q*, Qy and Q« we get:
v 2(1 — cos2b cos2 /) v 2 cos2 b cos2 / v X = ^ X, + ^ 2'
v 2(1—cos2^sin2/) v 2cosa3sin2/
Y = N Y'+ N Y*
^ 2 cos2b v , 2 sin2^ ^
L — N N



As a consequence of the supposition of a uniform distribution over the galactic longitudes, the quantities / will disappear from the coefficients, for in any narrow zone of constant galactic latitude, we will have:
£ cos1 / = £ sina / = ^ number of stars.
Therefore the preceding equations take the torm:
As we know the numbers of stars up to the magnitude nt in the zones of different galactic latitude, the coefficients of X,, Y,, Z,, resp. X2, Ya, Z2 (z. e. the weights with which the galactic components from the groups of material Mj and Ma must be combined to get the exact galactic components) may be computed. To get the components §, rj and £ relative to the geometrical centre of all the stars down to the magnitude nt, we have thus to transform the quantities 12» £2 into corresponding galactic components Xi, Y», X2, Ya and Z2. Then we have to combine these in the manner explained above. The quantities X, Y and Z to once obtained may be transformed back to §, rj and £. It thus becomes clear that they may be derived free from any hypothesis about the distribution of the stellar velocities in space.
(9)



CHAPTER 11.
THE APPLICATION OF THE METHOD OF BRAVAIS TO THE PRESENT DETERNIINATION OF THE APEX.
The definitive formulae used.
In the present determination of the apex the example of Bravais with respect to the masses and radial peculiar velocities has been followed. The Jatter have been simply neglected; the former have been taken all equal to unity. We adopt therefore as origin of coordinates a point which is at rest relatively to the geometrical centre of gravity. With the distances, we have dealt in the way indicated in Chapter I. About this question a few remarks will be made presently.
The formulae definitively used thus get the following form:
i2 (i — cos *8 cos 2a) § — 2 cos *8 sin a cos a .— 2 sin S cos 8 cos a • £ =
2 ? (i 5 cos 8 sin a . fia + sin 8 cos a . m). 2(1 — cos *8 sin sa) rj — 2 cos88 sin a cos a . § — 2 sin 8 cos 8 sin « . £ =
2 q (— 15 cos 8 cos a . n* + sin 8 sin a . f*i)2 cos *8 . £ — 2 sin 8 cos 8 cos a . § — 2 sin 8 cos 8 sin a .r\ —
2 (> (— cos 8. ui).
These equations may be obtained from the normal-equations of Airy by combining those corresponding to the right-ascensions and those corresponding to the declinations in a suitable manner, after having given to every star a weight equal to (A Therefore the method of Airy applied in this manner must lead to the same results as that of Bravais.
The materials.
The stars used have been chosen in such a way that they are distributed fairly uniformly over the whole of the sky. They belong to the following groups:



1) The stars of Bradley from the north pole to declination —31° taken from Publ. 9 of the Astronomical Laboratory of Groningen. I have only rejected those stars between — 20° and — 310 which are also contained in Newcomb's catalogue of fundamental stars. There thus remain 2551 bradley-stars.
2) The fundamental stars of Newcomb ') between — 20° and — 40° of declination. In all 114 stars.
3) A number of 198 fainter stars of Taylor (nearly all magnitudes between 6 and 9), between — 20° and — 350 of deel., for which the proper motions have been derived by Prof. Kapteyn from the catalogue of Taylor-Downing (eq. 1835)") and that of Tucker (eq. 1900)8) (these proper motions have not as yet been published).
4) The fundamental stars of Newcomb between — 40° and — 520. In all 38 stars.
5) A number of 490 stars from the catalogue of astrographic standardstars by Sir David Gill (eq. 1900) *). The stars also contained in Newcomb's fundamental catalogue were excluded. Of the rest only the more reliable ones have been retained.
6) For the part of the sphere between — 520 and the south pole 225 stars of the „Fundamental-Catalog für die Zonenbeobachtungen am Südhimmel und südlicher Polar-Catalog für die Epoche 1900 von A. Auwers". 6)
The total number of stars is 3616.
The data required for the individual stars.
As may be seen from the formulae (4) it will be necessary to know for every star the following quantities:
a and 8, the right ascension and declination for a determined epoch, for which, in agreement with Publ. of the Lab. of Gron. n°. 9, we havechosen 1875; a and f*s, the proper motions in right-ascension and declination; (), the distance. lts estimation depends on the following quantities: m, the magnitude, reduced to the Potsdam scale;
(.i, the total proper motion in are of the great circle; ip, the angle of position of the total proper motion, taken in the sense, determined by the formulae on page 11 of Publ. 9;
A, the angular distance between the star and an approximate position of the apex which has been assumed in accordance with Publ. 9 «);
x) Catalogue of fundamental stars for the epochs 1875 an(* 1900 reduced to an absolute system by Simon Newcomb.
') General catalogue of principal fixed stars by Taylor, revised and edited by Downing, Edinburgh, 1901.
3) Catalogue of Southern Stars of Piazzi for the ep. 1900. Publications of the Lick-Observatory, vol. VI.
4) Gill, A catalogue of 8560 astrographic standard-stars between deel, —40° and — 520
for the eq. 1900, London 1906.
6) Astron. Nachr. n°. 3431—'32.
6) See page 8 of Gron. Publ. n°. 9.
3



/, the angle: North pole-Star-Antapex.
Finally
b, the galactic latitude, because it is our intention to include in our discussion , a separate treatment of zones of different galactic latitudes.
For the stars of Bradley all the required data have been taken from the catalogue in Publ. 9 of the Astron. Lab. at Groningen. The comparison with the proper motions in Newcomb's catalogue shows small systematic differences. They were not applied; it will be easy to take them into account in deriving our definitive results.
For the other groups of stars the value of the galactic latitude b and the quantities X and % were obtained by the aid of tables with the argument a and 8. The coordinates adopted for the pole of the Milky Way are those of Gould:
«1875 = l9°° 2°' ^1875 = + 27° 21'«
The quantities n and tfj were derived from the fia and n$ by means of another table with the doublé argument 15^ cos 8 and ns 1). As for the proper motions na and ns themselves and for the magnitudes m we have to consider the several groups separately.
Stars of Newcomb between — 20° and — 40° of declination.
The proper motions of these stars have been simply taken from Newcomb's Catalogue of fundamental-stars. As the magnitudes in this catalogue have been taken, wherever possible, from the Harvard Photometry2), a correction of _j_ om . 173) is necessary to reduce them to the scale of Potsdam. As the hundredths of magnitudes have been neglected, it has been rounded off to + om.2.
Stars of Taylor.
The proper motions of the faint stars derived from Taylor—Downing and Tucker 1900 have been reduced by Prof. Kapteyn to the system of Newcomb's fundamental-catalogue in the following way. As these faint stars were not contained in Newcomb's catalogue, it was necessary to derive first the systematic corrections for the bright stars of the same zone by comparing the proper motions of these with those of the stars contained in Newcomb's catalogue. Corrections were thus obtained for each hour of R. A. separately for the zones — 20° to — 30° and
30° to — 350. These were applied as a first correction for the faint stars.
The means of the proper motions in R. A. thus corrected were then formed for every hour. If there is no error depending on the magnitude we must expect
1) This table is the same as that which has been used for these quantities in Gron. Publ. no. 9 (see page 11). The quantities 15^ cos S were there simply denoted by
2) See page 243 of Newcomb's catalogue.
3) The value of -f- om. 17 for the correction Potsdam—Harvard has been adopted here and below in agreement with that applied in Publ. 8 (page 5 below).



the mean of the 24 average values thus obtained to be very nearly zero. As however in reality the value —0*0022 was obtained, it was assumed that the correction for the error in the proper motions in R. A. due to magnitude must be
-f o" 0022
on the average. This value was applied as a second correction. The values of the proper motions, obtained after the application of these corrections, have been provisionally adopted for the determination of the apex.
The magnitudes have been taken by Prof. Kapteyn from Harvard, vol. XLV, when given in this catalogue. If not observed at Harvard they have been taken from the Cordoba-Durchmusterung or Schönfeld's Südliche Durchmusterung. In this case corrections have been applied in order to reduce them to the scale of Harvard. To get them reduced to the scale of Potsdam I have added the correction + om. 17.
Stars of' Newcomb between — 40° and — 5 20 of declination
The proper motions have been taken from Newcomb's catalogue; to the quantities i5/uacosS however a correction of -f- 0".02Ó has been applied, as explained below (see stars of Gill).
The magnitudes have been treated in the same way as those of the stars in the zone between — 20° and — 40°.
Stars o f Gill
Only the proper motions depending on a sufficiënt number of authorities have been used. The positions according to the several authorities have been reduced by Sir David Gill to Newcomb's systems by applying constant correction both to the right-ascensions and to the declinations. To a few of them there have furthermore been applied periodic corrections.
A little difficulty was experienced for the proper motions in rightascension. It soon became obvious that they have a pronounced preference for negative values over nearly all the hours of R. A, Among 800 stars with rather well determined proper motions, depending nearly all upon the catalogues of Taylor 0835)» Gould (1875), Cape ((880) and Cape (1900), only 175 had apositive na, all the rest were negative.
In a paper, published in the Astron. Nachr. *), Sir David Gill treats the question of an apparent rotation of the brighter fixed stars as a whole with respect to the fainter stars as a whole for this zone. The same question has been treated also in the introduction to the catalogue of astrographic Standard stars.
In order to examine whether the interpretation of the discordances pointed out in these papers is confirmed by a direct comparison of the mean values of
') A. N. 3800.



Ha obtained from the brighter and fainter stars of the materials under discussion, I have taken the 800 stars just mentioned. After ha ving rejected three of them having exceptionally large proper motions, there remained 441 stars brighter than 70, 356 fainter than that magnitude. For each of the two groups I have derived the mean value of fia for each hour of R. A. Atter that, if for the two groups we take the mean of the 24 values ~jüa, we find:
for the brighter stars: ~~fïa = — o8. 0027 for the fainter stars: ~/Ta = — o8. 0030
These values do not confirm the supposition of a considerable systematic rotation of the brighter relative to the fainter stars.
Treating in the same way the proper motions furnished by Newcomb's fundamental-catalogue in this zone, only taking the limits of the zone somewhat wider, we found from 61 stars (excluding e Eridani with an exceptional large proper motion):
~jla = — O8 . 0024.
The number of stars of the last group is somewhat small for drawing any very reliable conclusion. Still it will be granted, that the three results, together, show no evidence of the existence of a rotation of the bright stars relative to the faint ones. They rather show a general preference of both the bright and faint stars for negative values of /*a. This must perhaps be ascribed to a systematic error in the system of Newcomb for this zone.
In trying to elucidate this point I made a comparison with Auwers. From 50 stars I get:
A /ua (Auw. — Newc ) = — o8.ooio.
If this difïference were applied as a correction the proper motions would become still more strongly negative. On the other hand however the amount of the difference shows that the uncertainty about the mean value of /ü~a, left by the two systems, is such, that at least a large part of the values found above may still be ascribed to systematic error. Taking into account the little a priori probability of a systematic rotation of all stars in this zone as a whole it seems that where we have to choose between the possibilities of a real systematic rotation and a systematic error, the latter must be the more probable.
For the determination of the apex, happily it is not of any considerable importance whether the anomaly is due to a property of the faint stars only or of the whole of bright and faint ones; nor whether the phenomenon is real or only the effect of systematic error. The effect may be eliminated from the results by taking care that opposite hour-groups get into the equations with the same weights. With this precaution it will be indifferent whether a correction is applied for the anomaly in question or not; with respect to the estimated distances however, which depend on the adopted values of the proper motions, it seemed preferable to apply a correction, by which the anomaly is removed.



For this reason we have applied to all values of 15 //a cos 8 both to the stars of Gill and to those of Newcomb in the same zone, a correction
J (15 /Ua COS S) — 4- 0*.02Ó.
For the rest the proper motions have been taken unaltered from the respective catalogues.
For the purpose of reducing the magnitudes of the stars of Gill to the scale of Potsdam, the magnitudes, as given in the catalogue, have been compared, as far as possible, with those given in Harvard '). In this way the following corrections for the reduction to Harvard, denoted by H — G have been derived for the different classes of magnitudes. They have been slightly smoothed by a curve. By further adding a correction of + om. 17, we got the reductions to the Potsdam scale, denoted by P — G.
m H-G P-G
m m
4.0 to 4.4 + 0.04 +0.21
4.4 to 4.9 —0.28 —O.II 5.0 to 5.4 — 0.40 — 0.23
5.5 to 5.9 —0.44 —0,27 6.0 to 6.4 — 0.46 — 0.29 6.5 to 6.9 — 0.47 —0.30 7.0 to 7.4 —0.41 —0.24 7.5 to 7.9 —0.27 --O.IO 8.0 to 8 4 — 0.14 4- 0.03 8.5 to 8.9 + 0.01 + 0.18 9.0 to 9.4 + 0.14 + 0.31 9.5 to 9.9 +0.21 -f- 0.38
As far as the magnitudes for the stars used were given in the Harvard catalogue, these have been taken, after ha ving added a correction of + om.i7. For the rest the correction P — G was applied to the magnitudes.
Stars of Auwers.
For these stars the proper motions as given in the catalogue of Auwers have been corrected for precession, adopting that of Newcomb. For this purpose values of km and A» have been used in accordance with those taken in Publ. 9 of the Astron. Lab. of Groningen (pag. 4) i. e.
') Annals of the astron. observatory of Harvard college, vol. XXXIV, which according to page 53 of this catalogue, has been joined as closely as possible to the Harvard Photometry (vol. XIV, Pickering I according to the Publ. of Potsdam).



km = -f o8.00035
= + os.ooo35 = + o//.oo53.
No other correction has been applied to the proper motions in the Catalogue of Auvvers. From a comparison of the proper motions given by this catalogue and those of Newcomb's fundamental catalogue, I found:
A^(Newc. — Auw.) = — o".ooi.
This value cannot exceed its uncertainty and it did not seem worth while to apply it. For the derivation of the periodic corrections there is hardly a sufficiënt number of stars common to Auwers and Newcomb. Such corrections have therefore not been applied. A constant correction A//a has not been applied as it could not be of influence upon the coordinates of the apex derived from the proper motions of this region of the sky. Moreover in our dejinitive solution all proper motions have been reduced to the system of Auwers , as will be explained in Chapter III, so that for the definitive results it is of no importance, whether reductions to Newcomb's system are or are not applied in this stage of our work.
The magnitudes of two variable stars, n». 184 and 367 of Auwers have been taken from Chandler's Catalogue x), adopting the values corresponding to the maximum of brightness. All the other magnitudes have been taken from Harvard *). These were reduced to Potsdam by a correction of + om. 17.
Catalogue containing the data for the individual stars.
The data for the different stars used for the determination of the apex, except for those of Bradley, have been given in Table I at the end of the present publication. For the bradley-stars they have been taken immediately from Gron. Publ. 9. In the first column of Table I the numbers of the stars have been given. In order to prevent any mistake the quantities 15 /ua cos S, which have been called simply fia in Publ. 9, have been denoted here by //„. The other notations, the same as those used above, are in perfect accordance with those of Publ. 9. The quantities fj, have been given in three decimals, but only the first two figures of the numbers may be considered to be calculated exactly. As for the rest the table explains itself.
The distances.
The distances have been estimated for the different stars in the way shortly explained in Chapter I It was therefore necessary to derive a table with the
arguments A and P — % — ip, giving the quantities f = —8) required for the reduc-
r . _ 9
tion of the total proper motions to quantities of which the amount will be inde-
') Astron Journ. 379.
2) Harv. XXXIV.
3) See page 6.



pendent in the mean of the angle % — ip. Referring to the Notes for details, we may sum up the derivation as follows. Let p represent the mean value of the total proper motions fi, belonging to a determinate value of sin X and p — % — V ')> t^ie mean value of all proper motions. Then in the fïrst place the quantities q, which are defined by the equation
('O) 1 = ^
i"
have been determined empirically from the stars of Bradley of Publ. 9. For that purpose the stars have been distributed into 4 groups according to the value of sin X, viz.:
a) 1.00 > sin X > 0.80 (1588 st.)
b) 0.80 > sin X > 0.60 (500 st.)
c) o 60 > sin X > 0.30 (427 st.) cl) 0.30 > sin X > 0.00 (110 st.)
Each of these groups of stars has been subdivided into 7 groups according to the values of p, viz.:
1) p betw. o° and + I5°
2) „ ± 15° T» ± 45°
3) * ± 45° „ ± 75°
4) » ± 75° * ±105°
5) * ±i°S° v ±135°
6) « ±^35° » ±165°
7) „ ± 165° „ + 1800
In each of the so formed groups a 1), a 2), . . . b 1) . . . etc. the mean value of n has been determined. The values thus obtained have been considered to represent the value of corresponding to values of sin X and p valid for the middle of the respective groups. Dividing these by the value ~ji (the mean of the proper motions of all the stars used) we get a set of empirically determined values of q, for the different values of sin X and p. As however these quantities run rather irregularly, mainly as a consequence of a few very large proper motions. I have smoothed them in various ways. In the first place a small number of exceedingly large proper motions, distributed over different values of p (6 proper motions in the zone 0.80 > sin X >0.60, 2 in the zone 0.60 > sin >,>0.30) have been excluded. In the second place each of the groups a 1), a 2) ... b 1) .... etc. has been subdivided into three equally numerous groups according to the amount of the proper motions. Treating separately the groups of what we will call the large, the mean and the small proper motions and dividing the mean Ji\,p obtained from the different groups by the mean value ~jü of all the large,
For the sake of brevity we will in future denote the angle of position, which in Table I has been called x — P iQ accordance with Publ. 9, by p.



resp. mean or small proper motions, we must get theoretically the same results from the three groups. By taking finally for each of the groups a i), a a) . ( . b i) . . . etc. the mean values of the q furnished by the three groups (of large, mean and small proper motions) we have finally obtained a set of values from which the irregularities have disappeared to a great extent. The values of q, determined empirically in this way, have been called q0. They have been given, together with the values from the large, mean and small proper motions separately, in the Notes belonging to this Chapter ])
On the other hand the values of q may also be derived theoretically if we make some assumptions about the distribution of the proper motions. For this purpose the iollowing assumptions have been made:
1. In every part of space that contains a sufficiënt number of stars the peculiar proper motions are distributed equally over all directions and the amount of this proper motion is independent fróm the direction. This comes to adopting the hypothesis of the random-distribution.
2. The amounts of the projections of the peculiar velocities on a line are arranged according to the law of accidental errors.
3. The mean values of the peculiar velocities are the same in different parts of the space.
If we call the velocity of the sun h, the mean value of the projection of the peculiar proper motions on a plane n, it follows from our supposition that
^ • * *
— is constant for every part of space. n
Of course our first supposition is liable to objection. We have to consider, however, that the values of q are derived merely for the purpose of eliminating the effect of the sun's motion on the observed distribution of the proper motions. We thus have only to take into account such disturbances of the radial symmetry of this distribution as can be caused by the sun's motion. For the present purpose, therefore, I think that any error in our first assumption cannot have any serious effect.
As for the rest, if the assumptions made are not quite in accordance with the reality, they will only make the taxation of the distances for the individual stars slightly less exact than they would be if the peculiar proper motions could be taken into account instead of the reduced observed proper motions.
Now let:
Q = the mean linear value of the observed proper motions, corresponding to a determinate value of A and ƒ,
h = the sun's linear velocity (as before):
y. — h sin A cos p;
m = measure of precision2) of the projections of the velocities upon a line, considered as accidental errors and let us take as the unit of velocity the quan-
*) Notes to Chapter II 1).
a) Chauvenet, Spherical and practical astronomy II, page 485.



tity n — the mean value of the projections of the linear peculiar velocities on a plane. We get the following equation:
tn (1 + 2 m*xÈ) + +(1 +2 m%xa) dl
(11) . . Q = 
2 m*x + me~+ 2 e~iXdt
0
This formula may be derived from the formulae (26) and (27) in Publ. 5 of the Astr. Lab. of Gron. by taking F (») in such a way that it is in accordance with the distribution of the projections of the peculiar velocities supposed under 2. A simpler derivation has been given in the Notes1).
As a consequence of the assumptions made, the formula for Q is found to be quite independent of the distances of the stars. It may therefore be considered to be the same for stars at all distances. As further we may for stars at a determinate distance replace the ratio of the linear values corresponding to observed and peculiar proper motions by the angular values, we may conceive Q as the ratio of the mean angular values /JxTjï» as defined above, and the mean angular value of the peculiar proper motions a — which ratio will therefore be equal for groups of stars at all distances. Taking together the stars of all distances, we thus get:
(12) Q = J^hJL,
G
03 ) ?=4rQ.
f*
The values of Q may be derived for every value of X and p by ineans of the formula (11), if we adopt an approximate value of h. In this way the values of Q have been derived for the same values of sin A and p for which the values of have been determined empirically 8). For m we adopted the value:
m = 0.886 a).
In order to obtain the quantities q we have to multiply the quantities Q
by the ratio _ (see formula 13), which we will call C, therefore M-
04 ) ? = CQ.
The value of C cannot well be determined wholly theoretically as it depends partially on the distribution of the stars over the sky. For if all the stars were concentrated in a region near the apex or antapex, C would be nearly equal to unity; if on the other hand they were all distributed over the parallactic equator *) it would be considerably less. For this reason the quantity C has been deter-
l) Notes to Chapter II 2).
*) Notes to Chapter II 3).
3) Notes to Chapter II 2).
*) This name is given by Bravais to the great circle of which the apex is the pole.
4



mined empirically in such a way that the mean value ~jl' of the reduced proper motions is equal to the mean value ~jü of the observed proper motions *).
By means of formula (14) we get values of q which we will denote by qc. If now the adopted value of h is in accordance with the best one, which can be derived from the materials used for the determination of the values of q0f then the variation of the calculated values of qc with the angles p must agree with that of the observed quantities q0. As this was notthe case, the originally adopted value of h has been improved by means ot the empirical quantities q„. After some trials*), I found that the value
(15) k = 0.750
produced a satisfactory accordance. Therefore this value has been finally adopted. By means of this value a set of quantities Q has finally been calculated for intervals of io° for A and p. Adopting further for C the value
C = 0.884
which has again been derived in the way quoted above, the corresponding values of q and the reciprocals
<■«> /= f = é
could be calculated. In this way the Table II at the end of our paper was obtained.
In order to find the distances the observed total proper motions were now reduced to the corresponding quantities by means of the formula
(17) ^ =f^
in which the quantities ƒ have been taken from Table II without interpolation. These quantities fi' may now be considered to be independent of the angle of of position p.
On the other hand a table has been formed for the derivation of the distances by extending the table on page 31 of Publ. 8 which gives the parallaxes of the stars with the arguments m and ft. Instead of the parallaxes however, the table was made to give the distances (unit of distance for n = o".i). From these tables the values of the distances have been obtained by taking /u' as argument instead of /u. The values thus obtained for the distances y have been substituted into the formulae (4).
Table for the coefficients.
The coefficients of £, y and £ in the first and those of ^.15 jua cos S and (}. /us in the second members of the equations (4) have been taken from tables which give these quantities for intervals of iomina and i° in «5. In Table III at
*) Notes to Chapter II 3). 2) Notes to Chapter II 3).



the end of this publication they have been reproduced excepting cosa <5, sin a, cos a and cos 8.
Table giving the equations of Bravais for the individual groups.
In order to be able to derive the position of the apex frotn stars of different galactic latitudes separately, each of the groups mentioned on page 17 provisionally excluding Bradley's stars, has been subdivided into five groups defined by the following limits of galactic latitude:
I Gal. lat. — 90° to — 40°
II „ — 40° to — 200 (K) III „ — 200 to + 200
IV „ + 20° tO + 4O0 V ,, + 40° to + 90°
For the stars of Bradley three declination-groups have first been formed, viz.:
Deel. + 90° to -f 520 (L) „ + 520 to — 20°
„ south of — 20°
By this arrangement it became possible to combine the stars of Bradley between + 90° and + 520 with those of Auwers bet ween —520 and —90° and those south of —20° with the stars of Newcomb and Taylor. The three groups (L) of Bradley have been also subdivided afterwards into the groups (K).
The data necessary for immediately finding the equations of Bravais (4) for the different groups thus obtained have been given in Table IV at the end of this paper. The following notations have been used:
A = 2 (1 — cos1 8 cos2 a).
B = 2 (1 — cos2 8 sin2 a).
C = 2 cos1 8.
D = 2 cos2 8 sin a cos a.
(18) E = 2 sin 8 cos 8 cos «.
F = 2 sin 8 cos 8 sin «.
P = 2 (t (sin « . 15 f.ia cos 8 + sin 8 cos a . //ü).
Q = 2 () (— cos a . 15 /ua cos 8 -f sin 8 sin cc. /l/s).
R = 2 y (— cos 8 . ps).
In calculating P, Q and R, for the quantities 15 //„cos 8 and the centennial proper motions have been taken, expressed in seconds of are.
The quantities A, B, C, D, E, F, P, Q and R have been given for each of the groups, obtained by subdividing the groups (L) of the stars of Bradley



and further the groups 2), 3), 4), 5) and 6) of page 17 into the groups (K). They have also been given further for the groups (L) of the stars of Bradley and the groups 2), 3), 4), 5) and 6) of page 17 as a whole (See Table IV: all stars together). Moreover for the stars of Newcomb in the zone between — 40° and — 5 20 and those of Gill, a separate solution has been made. In this separate solution Newcomb's stars have been given doublé the weight of Gill's stars. The weights of the individual stars were then taken in such a way that, in the final equations, opposite three-hour-groups entered with equal weights. This was done for the purpose of eliminating any constant error in fia or any magnitude-error remaining in the proper motions (see page 19 etc ).



CHAPTER III.
DISCUSSION OF THE RESULTS FROM ZONES OF DIFFERENT DECLINATION.
The components g, rj and £ of the solar motion and the coordinates A and D of the apex have been determined separately for each of the groups (L) of the stars of Bradley (see pag. 27) and further for the groups 2), 3), 4), 5) and 6) of page 17. This course was pursued with the doublé aim:
a. of more easily detecting remaining systematic errors;
b. of detecting any real difïferences that may exist between the apex furnished by the stars of different zones
Before doing so, however. a solution has first been made from all stars of Bradley together. They represent somewhat more than 70 percent of the whole of the materials used. The interest of this solution lies in the fact that it furnishes a comparison of the coordinates of the apex obtained by means of the method of Bravais with those derived by Prof. Kapteyn in A. N. N°. 3722 from the same stars by means of other methods. Our solution led to the values:
A = 2 7g°.o D = + 30°.8
whereas Prof. Kapteyn obtained the followiner results:
o
by the meth. of Argelander: A = 274°.3 ±- i°.3 D = + 27°.2 ± i°.4
n v v » Kapteyn : A = 2Ó7°.3 ±: 2°.2 D = + 29°.4 dz i°.y
„ „ „ „ Airy : A = 2740.7 ± i°.7 D = -f 280.5 — i°-2
mean value : A = 2J2°.2 D = -f 28°4.
The differences between the values obtained by the different methods are of the same order as that between the mean value and the value derived by the aid of Bravais' method.
This fact might seem very surprising, seeing that all these older determinations professedly rest on the assumption of the hypothesis of the random-distribution of the proper motions — a hypothesis which as we said before is not nearly satisfied in nature. Still it is not difficult to show reasons which might have led us to expect that the difference of the result of the application of Bravais' method from that of the older methods would be rather small.



For as we pointed out before, the equations which embody Brayais' theory — in the case that we take the distances of all the stars to be equal — are the same as we get in Airy's theory, under the same very common supposition, if we combine the equations of Airy furnished by the right-ascensions and declinations in a suitable way Therefore, if we had supposed all distances equal, we would have been led to results nearly accordant with those obtained formerly by Airy's method. Now it is true that we have not supposed the distances equal. But as this comes in the main nearly to introducing a different system of weights, very great changes are not to be expected. Furthermore Prof. Kapteyn has shown') that, owing to the circumstance that by the very common usage of „abridged calculation" the methods of Airy, Kapteyn, Argelander will lead to results which can be but little different.
In Table IV the data necessary for the formation of the equations of Bravais (4) for the separate groups have been collected (see page 27 and 28; the meaning of the notation „Combination Newcomb-Gill" has been also explained there).
By solving the equations the following values for the components of the solar velocity g, rj and £ and the coordinates of the apex A and D have been obtained.
Table i.
* s» a ta Number
l I) \ Z A D f
| I j | i °f stars.
Bradley -f-9°0to + 52° —02 I — Ï9-I | +13.6 26g°.4 : -j-35°.5 297
„ 4- 52° t° — 20° —0.1 |—26.6 -f-15 3 269°.8 -f"29°-9 2115
„ south of—20° . -f- 1.7 |—277 +114 273°.5 1 -f- 220.3 139
Newcomb — 20° to — 40° —0.2 j—27.1 + 2I-7 2Ó9°.6 -J- 38°.? 114
Taylor —20° to — 350 —2.0 | — 15.8 -|-20.2 262°.8 —51°.8 198
| |
Newcomb — 40° to—520 —1.6 —27.9 -f~20-8 266°.y -f-3Ó°.6 ! 38
I
Gill —40°t0—520 —0.5 : — 28.0 -b27-9 269° o -f-44°.9 490
Comb. Newc.-Gill —0.3 —27.4 +26.5 2Ö9°.4 -}~440.o
Auwers —520 to — 90° 1 —2.3 —26.7 -(-22.9 265°.! +40°.5 ; 225
The unit in which the components f, rj and £ are expressed is equal to the linear velocity of a star with a parallax of o".i and a centennial motion of 1". We will now discuss the values of the coordinates A and D obtained for the different groups.
') Koninklijke Academie van Wetenschappen te Amsterdam. Proccedings of the section of Sciences , Jan. 1900.



The right-ascensions.
First of all we will contract the values obtained from the different sources in the same zones of declination. In the zone of declination — 20° to — 40° the results yielded by the stars of Bradley, Newcomb and Taylor were combined with the rcspective weights 1, 1 and £ per star. In the zone —40° to —520 the result from the „Combination Newcomb-Gill" will be adopted l). The following abbreviations for the different sources will be used:
Br. = Bradley.
N. = Newcomb.
Tay. = Taylor.
Gi. = Gill.
Auw. = Auwe.rs.
If now we arrange the results according to the declination of the zones we get:
Table 2.
I ! 1 I I
T. . #• * t I „ i Numb. i
Limits of deel. j Source ! A . p R
j of stars. j
| ; j
-h 9°° to + 52° ! Br 2Ó9°.4 297 2.7 -f 0.2
-f- 520 to —20° Br 2Ö9°.8 2115 12.2 +0.6
— 200 to — 40° N, Br. and Tay 268°.9 451 2.4 — 0.3
— 40° to — 520 N and Gi 269°*4 528 4.0 -f- 0.2
— 520 to —90° Auw. 265°.1 225 2.0 —4.1
All stars together 2Ó9°.2 3616 23.3
The weights p have been taken proportional to 2(1 — cos 2rJ cos 2a) by dividing this coëfficiënt by 100; only for Taylor this coëfficiënt was divided by 200. The last line contains the weighted mean.
The reason of the smaller weight attributed to Taylor lies not only in the larger accidental errors, but also in the fact that the average brightness, consequently also the average proper motion is much smaller than in the case of the other authorities and it is evident that the smaller the motions the greater will be the influence of determined errors on the coordinates A and D.
The deviations R of the individual zones from the mean are shown in the last column. They are very small and no regular change with the declination
') In future if Newcomb and Gill have been taken together in this zone, always the „Combination" denoted above will be used.



is shown. By comparing the results obtained for the individual groups separately with the mean value we get the values of R given in Table 3.
Table 3.
Numb.
Limits of deel. Source A ^ g^ars P
-f 90° to -f 520 Br 2Ó9°.4 297 2 7 + 0.2
+ 520 to —20° Br 2Ö9°.8 2115 12.2 +0.6
— 20° to — 310 Br 273°.s 139 0.9 + 4 3
— 20° to —40° N 2Ó9°.6 114 0.8 +0.4
— 20° to — 350 Tay 2Ö20.8 198 0.6 — 6.4
— 40° to — 52° N 266°.7 38 0.3 —2.5
— 40° to — 520 Gi 269°.0 490 3.7 — 0.2
— 520 to —90° Auw. 265°'! 225 2.0 —4.1
It will be remarked that in the zone — 40° to — 520 the residuals both for Newcomb and for Gill are negative, whereas in the preceding table the combination of the two gives a positive value of R. The cause lies of course in the different distribution of the weights over the three-hour-groups. In the present table every star has got a weight i, in the preceding solution opposite three-hour-groups got equal weights in this zone. No importance need be attached therelore to the series of negative values in the second half of the column of R. If we consider the residuals as wholly accidental we may derive a mean error from them. Denoting the mean error ') belonging to the unit of weight by f0, we get:
(19 ) fo = ± 3°-4
and as a preliminary result for A and its mean error, from all groups together
(20 ) A = 2Ó9°.2 ± o°.7.
This value has been derived from 3517 stars if a star of Taylor is counted for Therefore if we denote by f100 the mean error in the result derived from a group of 100 stars distributed over the whole of the sky we get:
(21 ) ^100 — 4
Comparing this value with those for the mean errors in A, determined in A. N. n°. 3722 from different groups of stars and taking into account the numbers of stars from which they have been derived , the result must be considered satisfactory.
') In future we will always work with mtan errors.



The declinations.
As may be seen at once from Table i the agreement of the declinations of the apex is less satisfactory than that of the right-ascensions. We again contract the results obtained from the different groups of stars in the same zone of declination. In the zone — 20° to — 40° the weights of Bradley , Newcomb and Taylor were again taken to be respectively 1, 1 and £ per star. In the zone from — 40° tot — 5 20 the „Combination Nevvcomb-Gill" has again been used. We thus get the following summary:
Table 4.
Limits of deel. Source D Numb.
of stars. 1 ^
+ 90° + 52° Br. -f 350.5 297 0.6 + 2°.2
+ $2° to—20° Br. -f 2g°.g 2115 18.0 — 3°.4
— 200 to —40° N. Br. and Tay + 35°.9 451 2.8 -f 2°.6
— 40° to — 520 N. and Gi. -f- 44°o 528 2.6 -f- io°.y
— 520 to — 90° Auw. -f 4o°.5 225 0.4 + 7° 2 '
All stars together + 33°.3 3616 24.4
The weights p were taken proportional to 2 cos *S (the factor for Taylor having been halved). The last line contains the weighted mean, the last column the deviations from the mean. There seems to be a slightly systematic increase of the declination of the apex derived from stars of decreasing declinations.
For the individual groups we get the following table:
Table 5.
Limits of deel. Source. D Numb. of ; _
stars I
+ 9o° to -f 520 Br. -f 35°*5 297 j o-6 -j- 2°-2
+ 52° to —200 Br. j -|-290,9 2115 i8'o — 30,4
— 200 to — 310 Br. | -f220 3 139 i-i — ii°-o
— 200 to — 40° N. +38°7 114 0 9 -f 5°-4
— 200 to — 350 Tay. + 5i°*8 198 o*8 -f- i80>5
— 40° to — 520 N. +36°-6 38 0-2 + 3°-3
— 40° to — 520 Gi. +44° 9 490 2-4 -fu°*6
— 520 to —90° Auw. + 4°°'5 225 0*4 -f- 7°'2
5



The three groups of Bradley taken separately do not show a change of the declination in the sense of the preceding table, but rather a change in the opposite direction. This seems to show that there must be a systematic difference between the fundamental systems of the three first and those of the remaining groups» In order to get somewhat more certainty about the reality of such a systematic difference, we derived a mean error in the supposition that all residuals are accidental. We get, denoting the mean error belonging to the unit of weight by e0:
(22 ) f0 = U°9-
Therefore as a provisional result for D and its mean error, from all stars together we get:
(23 ) D = + 33°.3 ±> 2°.4-
If fI00 represents a mean error analogous to that introduced in the discussion of the right-ascensions we get:
(24 ) *100 = - I4°*3
The value ±. 2°.4 of the mean error in D is enormously in excess of the corresponding value ±. o°.6 derived by multiplying that of the preliminary value of A (20) by cos D. We are thus led to conclude that it seems inadmissable to attribute the residuals of the several values of D simply to accidental errors. A comparison of the value (24) found from the declinations with the values for the mean errors in the declinations found in A. N. n°. 3722 taking the numbers of stars into account, seems to confirm this conclusion.
If we combine on the one hand the stars of Bradley t on the other hand all the remaining stars and if we call D, and Da the two values of D, we get:
Stars of Bradley: D, = -f 3o°.8 Remaining stars: Da = + 43°-6
Therefore: D2 — D, = + 12°.8
Considering this difference to be real we may derive another value for f0, starting from the supposition of two really different values D, and Da for the two groups. We get:
(25 ) *0 = — 5°-8
(26 ) eiW=z± 7°.o
and denoting by *Dl and fDj the mean error of Di and Da and by the mean error in the difference Da — Di:
fDi = i°.3
fn, = ± 2°.7 fDt-Dl = - 3° °-
The values (25) and (26) of fo and €100 are considerable smaller than the values (22) and (24). Meanwhile the difference D2 — D, is more than 4 times larger than the mean error of this quantity. It may thus be considered probable that the difference between D, and D2 is not accidental. We have to choose therefore between two possibilities:



i°. there still remain systematic errors in the proper motions, large enough to explain the difference;
2°. there is a real difference between the motion of the centre of gravity of the northern and that of the southern stars.
The probability of systematic errors in the proper motions of the southern stars.
In order to get a better insight into the influence of systematic errors let us write our equations (4) in the form:
A| - Dr] — E£ = P
B * — D| — F£ = Q
CS — E| — Ff] = R
The coefificients D, E and F are relatively small for most of the groups. This will generally be the case if the distribution of the stars over the different hours of right-ascension is not too irregular. If therefore we neglect the terms with these coefficients we get:
' r-JL
A 71 B ^ ~ C "
In these expressions we have:
P = S(j (sin « . 15 fia cos 8 -f sin § cos a . /us).
Q = (— cos a . 15 fia cos S + sin S sin « . m ).
R = 2(/ (— cos d. jus)>
We thus see that systematic errors in fia will influence only the components £ and rj and not the component £. The same may be said of periodic errors in ps. On the contrary an error in fis, constant for a whole zone, will get into the quantity R multiplied by — cos 3, that is always with the same sign and (supposing equality of distance) of the same amount, at least if the zone is sufficiently narrow. It will therefore influence the component £, consequently the value of D, which is determined by the equation
tg D = ? 
s + V1)
On the other hand, if we compare the values of r\ and £ of Table 1 obtained from the different groups of stars, we see that the values of § differ only little from each other. The same is generally the case with the values of rj. There is only exception for the value of r\ from Bradley + 5 20 to + 90° and from Taylor. The value of £ on the contrary becomes at once larger if we pass from the stars of Bradley to those of Newcomb in the zone between — 20° and — 40° (see Table 5).
If we denote the values of §, rj and ï, furnished by the stars of Bradley and those obtained from the remaining stars respectively by £,, r/t, £1 and §2, rja, , we have:



£,=0.0 J?i=— 25.3 £, = +15.1
§2 == I .O Tfe = ~™ 26.6 1)] — "f 24.7.
So wc see that the difïferencc between D, and Da depends on the difference in the values of £1 and £a If therefore it must be ascribed to systematic errors, these must be errors of /u$, dependent only on the declination and not on the right-ascension.
For the stars of Bradley large systematic errors of this kind do not seem very probable. For the corrections of the proper motions of Bradley-Auwers were derived by Prof. Kapteyn independently from a system of fundamental stars, starting from the supposition that the stars with larger and those with smaller proper motions must really give the same values for the coordinates of apex. They agree in generally fairly well with those obtained by comparing the system of Bradley-Au wers with that of Newcomb. This may be seen from the data in Publ. 9, page 5. As will be seen afterwards these corrections also differ but little from those necessary to reduce the proper motions of Bradley-Auwers to the system of Auwers given in the „Astronomische Abhandlungen Nr. 7" '). Thus three systems which we may denote as the systems of Kapteyn, Newcomb and Auwers confirm each other in the main for the part of the sky covered by the catalogue of Bradley.
On the other hand the probability of systematic errors in declination is much larger a priori for the southern stars, used for the determination of the apex, because the fundamental proper motions are generally much less exactly determined for these stars. We will consider the different zones separately.
Zone — ro° to — 40°.
In this zone we have made use of BRADLEY-stars (taken from Publ. 9 of Gron.), of fundamental stars of Newcomb and of TAYLOR-stars reduced to Newcomb's fundamental system. By a comparison of the proper motions of Publ. 9 and those of Newcomb's fundamental catalogue, we find for this zone: (27) .... ^/^(N — Br.) = —o".oo22 ± o".ooi8 (51 st.).
If two stars south of —30°, which give relatively large differences are excluded, we get:
J ju$ (N — Br.) = — o".ooi4 ±. o" 0016 (49 st.).
The correction J /us = — o".oo22 applied to the BRADLEY-stars leads to a correction of D of about -f- 3°.5-
Applying the same correction with the opposite sign to the proper
motions of the stars of Newcomb, (of which the adopted distances are somewhat smaller) we get a correction of D of about — 2°.5.
We thus see that the difference J lii found above can at most explain a relatively small part of the difference in question. As the correction (27)
') Tafeln zur Rcduction von Sterncatalogen auf das System des Fundamentalcatalogs des Berliner Jahrbuchs von A. Auwers.



has been derived only from stars in the zone between — 20° and — 310 it might be considered possible that in the zone between —310 and —40° the Newcomb proper motions have a larger systematic error which might explain the difference. If this is the case we must expect to find different values of D from the zone between — 20° and — 30° and that between — 30° and — 40°. In reality we find from the stars of Newcomb between — 20° and — 30°
D = + 38.8 (68 st.)
and from those between — 30° and — 40°
D = + 38°.6 (46 st.).
Though the numbers of stars in the two zones are small, there seems to be no reason for assuming a systematic difference between the proper motions of the two zones.
We can hardly escape the conclusion that the difference of 160 between the results from the Bradley- and Newcomb stars cannot be explained by systematic error and that at least the greater part of it must be due to accidental error.
As for the difference between the values of D obtained from Newcomb and Taylor , it does not seem admissable to attribute it to a systematic difference between the proper motions derived from the two sources, because the proper motions of Taylor have been reduced to the system of Newcomb as rigourously as possible (see page 18). As the stars of Taylor are distributed rather irregularly over the different hours of rightascension an imperfect correction of the error dependent on the magnitude must influence the components in the plane of X-Y and therefore the declination of the apex. For this reason I made another solution in which the Taylor stars were divided in three-hour-groups. Equal weights were given to opposite groups. The result is:
(28) A = 258°. o D = + 510. 4
The declination is not sensibly changed.
Another reason for the difference might be supposed to lie in the fact that, owing to a greater percentage of faint stars, the average proper motion of the TAYLOR-stars must be smaller than that of the Newcomb stars. A common systematic error in the /u$ must therefore differently affect the results obtained from the two sources. We will presently discuss the value of this supposition.
Zone — 40° to —5 20.
In this zone all the proper motions have been reduced to Newcomb's system. As a comparison with Bradley is not possible, we will compare the system of Newcomb with other fundamental systems in order to see to what extent a systematic error may still exist. By a direct comparison of the proper motions we get:
(29) Auw. — N = + o".oo5ó (50 st.)
Boss — N = —o".oo22 (45 st. betw. — 370 and — 550).



The stars of Auwers have been taken from the catalogue in A. N. 343», those of Boss from that in A. J. 448. A small supplementary correction has been applied in deriving the correction (29) in order to take into account the difiference in the precessions used by Auwers and Newcomb The correction would of course have been zero, if the stars were distributed uniformly over the zone.
Now if we apply a correction of -f- o".oo5 to the values of of Newcomb and Gill, we get from the „Combination Newcomb -Gill"
D = + 34°o
instead of
D = -}- 44°.o (see Table 4).
On the other hand the stars of Bradley give (see page 29):
(30 ) D = + 3o°.8.
We thus see that an error of the same order as the correction required to reduce the proper motions from the system of Newcomb to that of Auwers (and therefore of the same order as the uncertainty left by the fundamental-system chosen), is sufficiënt for explaining the difference between the declination of the apex derived from the stars of Bradley and that from the stars of Newcomb and Gill.
Zone — 5 20 to — 90°.
We ought not to attach any serious importance to the deviation of eht declination of the apex yielded by this zone from that obtained fromt he rest of our materials. For first: a little constant error in the values of^a has a relatively large influence upon the component of as may easily be seen from the equations. Secondly the uncertainty left by the fundamental-catalogues in the system of the proper motions in declination is also rather large. By a direct comparison of the systems of proper motions of Newcomb and Auwers, made in the same way as above, we get:
(31 ) N — Auw. = — o".ooio
A comparison of Boss and Auwers is obtained from A. J. 448. If the zones — 55°, — 6o°, — 65°, — 70°, — 750, — 8o° and — 85° are combined with the weights 7, 6, 5, 4, 3, 2, 1 , we get:
Boss—Auw. = — o".oo5o.
These corrections if applied to the proper motions of Auwers would still further increase the declination of the apex. The amount however of the mutual difïferences may give us an idea of the uncertainty left in this zone by the choice of the fundamental system.
Summing up what has been said about the three zones south of — 20°, we find that as yet no conclusive evidence is obtained in regard to any real difference in the apex furnished by the southern and northern stars.
There is however another consideration by which we may try to get a clue to the true significance of the systematic differences shown in table 5. This consideration starts from the evident fact that systematic error must cause a much



smaller change in the position of the apex derived from stars with considerable proper motion than in that found from slowly moving stars.
For this reason we will divide the southern stars in two groups according to the amount ft' of their reduced proper motion (17). We will again treat the different zones separately.
Zone — 40° to — 5 2°.
The number of stars in this zone is particularly large; nearly all of them are stars of Gill. The declination of the apex (see Table 5) obtained from these stars is higher than in any of the other groups. In classing these stars in two divisions according to the amount of their reduced proper motions, we have taken care that the distribution over the different hours of right-ascension has become fairly well the same for both groups. This compelled us to vary to a certain extent the limit of fi' separating the two divisions. Treating both divisions separately we find from the group of larger proper motions:
D = + 39°-2 (190 st) from that of the smaller ones
D = -f- 5o°.4 (294 st).
The value furnished by the larger motions, on which the influence of systematic error is smallest, indeed leads to the more normal declination of the apex.
If we might assume that the stars of greater and those of smaller motion ought to yield the same apex, we might even derive the amount of the systematic error of the proper motions in declination. We find:
(32 ) J /n s = +o".oo57
in that assumption. Adopting this value both groups lead to the value
(33 ) E> = +34° 2
which already agrees fairly well with the value obtained from the bradley-stars. At the same time the correction (32) found in this way agrees nearly exactly with the correction (29) which would be required to reduce the proper motions to the system of Auwers.
If therefore the values of /ui of Gill are reduced to the system of Auwers we get the following results:
i°. the larger and the smaller reduced proper motions lead to the same value of Dj
20. this value of D agrees with the value derived from the bradley-stars much more closely than before.
There thus seems to be a certain a posteriori probability that, for this zone. Auwers' system of declinations is to be preferred to that of Newcomb.
Zone — 200 to — 40°.
In this zone the larger value of D furnished by the rather faint stars of Taylor of which the proper motions are in the mean considerably smaller than those of the brighter stars of Newcomb may be considered as an indication in the same direction. A moment ago we found from the stars of Newcomb (see Table 5)
D = + 38 °-7



from those of Taylor treated in such a way, that opposite three-hour-groups get equal weights (see (28) on page 37)
D = + 5i°.4
The correction A/uz necessary to bring the two determinations to agreement is found to be
(34 ) = + O".oo87
the common value of D being
(35 ) D = + 25°*3-
On the other hand the correction needed by both Newcomb and Taylor in order to reduce them to Auwers' system is
(36 ) = -f o".oo38 (88 st.)
which, though considerably smaller is still in the same sense. In deriving this correction from the values of fig of the stars common to Auwers and Newcomb a small supplementary correction has been applied to eliminate the influence of the difference of precession. The correction (36) leads to
(37 ) D = + 33°-2
for Newcomb's stars and to
(38 ) D = + 42°*i
for those of Taylor. The divergence from Bradley is thus greatly diminished. Lastly, in order to reduce the /ug of Bradley in this zone to Auwers' system, we have to add the value (36) to the difference (27). The value
A /ug — + o".ooi6
thus obtained leads to
(39 ) D = + ï9°-8.
The reduction to Auwers is thus seen to reduce considerably the divergences from the result (30) found from the whole of the Bradley-stars. The mean of the three values (37), (38) and (39), combined with the respective weights 1, £and 1 per star is D = + 30°-5, a value accidentally in nearly perfect agreement with (30) Zone — 520 to — 90°.
For the sake of completeness the stars of Auwers in the region between — 5 20 and — 90° have also been subdivided in two groups. From the larger proper motions we obtained
D = + 37°.o (101 st.)
from the smaller ones
D = -f 44°.6 (124 st.).



Owing to the high declinations of the stars, the determinations are rather weak and no great weight ought to be attached to their difference. Still as far as the evidence goes it points the same way as that obtained from the other zones. The correction needed to bring the two values into agreenient is
(4°) A//<J = + 0".0020
leading to the common value
(40 D = + 34°.9.
On the other hand, reducing the proper motions of Auwers to the system of Newcomb by applying the correction (31), derived above, we get:
(42) D = + 43° o.
The reduction to Newcomb thus increases the disagreement. raking all our results together, we see that corrections for the different groups of proper motions in declination of the southern stars, derived Irom the supposition that the stars of greater and those of smaller proper motions must lead to the same position of the apex, are found to be always positive. At the same time we see that these corrections lead to a better agreement between the values of D obtained from the northern and southern groups These facts may be regarded together as an indication for the existence of negative systematic errors in the used values of {/$ of the southern stars. At the same time these corrections are in the same sense as those necessary to reduce the values of /us from the system of Newcomb to that of Auwers
The probability of a real divergence of the values of the declination of the apex.
If 011 the other hand we assume that the difference found between the values of D from the northern and southern groups of stars has a cosmical cause, it ought to be ascribed to systematic motions, directed in the main toward the south pole, of the southern stars relative to those in the northern hemisphere. As the divergence is considerable only lor the stars of small proper motion we have to assume that practically only the more distant stars show such a drift. We will now examine the effect of such a drift upon the components of the solar motion in the plane of £ rj as compared to that upon the ^-component.
Suppose that in a determined zone there is a drift of the stars between the right-ascensions and «» = «, + tp and let us assume that the stars are uniformly distributed over the zone, a condition fairly well satisfied by the greater part of our materials. Where it is not, the same effect is obtained by attributing equal weights to the opposite three-hour-groups '). Further while we keep the £-axis unchanged let for a moment the £ and tj axes be taken to pass through points
with the right-ascensions and 6h + -L±ü?f and let the components of the
solar motion in this system be j/, £. Finally let A A n\ a £ represent the change of the components caused by the drift. Then if A, B, C represent the
') For the stars of Taylor and those of the zone between —40° and — 52° we have therefore to consider the solutions in which opposite three-hour groups have got equal weights.
6



coëfficiënt of £ in the first, resp. that of »? in the second and that of £ in the third equation of Bravais , we will have '):
(«>••«- TÜn » *
We distinguish two cases:
A W
ist Case: y <n. In this case the quotiënt will lie between the limits:
(44)
2C ^ % ,
= A + B g 8 for (p = ° and
4 C ^ w
a+B 'g for 'f=*•
Now consider in the first place the zone — 40° to — 520 which (see Table 5) gave a value for the declination of the apex differing most widely from that yielded by the bradley-stars. For the whole of the Bradley stars we have
(/).... | = oo. rj = — 25.3. £ = +15.1.
for the „Combination Newcomb Gill" in zone — 40° to —520 (see Table 1)
(?) • • • • £ = — 0.3 n — — 27.4. £ = +265.
We thus have for the proportions of the differences Arj, disregarding the signs:
3f=0°J Tr°-lS-
These dififerences cannot be explained by a stardrift, for according to (44)
A£'
this would require that the value of were contained between the limits 0.64
and 0.40 and probably rather nearer to the first value, because that is the value for small values of q>. For, as has been shown above, the deviations are greatest for the smaller proper motions, consequently for the more distant stars. Now, the greater the distances, the less probable it seems that there will be a stardrift embracing anything approaching twelve hours of right-ascension.
In zone — 20° to — 40° the taylor-stars, reduced to Newcomb's system (equal weights being given to opposite three-hour-groups) yielded the values:
(**) £= 3*3 V ~ '5*5 is= H~ 19*8
Comparing these with the values (p) we find the difference of the y to be such that an explanation of the deviation of the value of D by star-drift is not excluded. But owing to the large accidental errors of Taylor and the only moderate number of stars (198) the result is little trustworthy. Moreover not only is it, as it were, neutralized by the value of D obtained from the bradley-stars (139 st.) in
') For the proof see Note to Chapter III.



this zone, which shows a deviation in the opposite direction, but the Newcombstars (114 st.) give:
_ Ar\
^-°.°3 ^ = 0.24
which values are incompatible with a star-drift which would require to lie
AC
between the limits 0.71 and 0.45.
Finally as to the zone — 5 2° to — 90». No inference of any importance
can be drawn from the deterraination of £ which in this zone is particularly uncertain.
2mi Case: cp > n.
Evidently by a star-drift extending over a region of more than 12' in right-ascension a disturbance of the components f may be caused whilst the components g and r< are hardly influenced '). The existence of such a drift however by which the differences of the D found above might be explained may be considered little probable a friori. For as will be presently shown the corrections derived by Prof. Kapteyn for the proper motions of Bradley-Auwers from the assumption that the stars with small proper motions must give the same position of the apex as those with larger motions, agree in general fairly well with those obtained by a comparison with the systems of Newcomb and of Auwers It must be considered probable therefore that in the northern sky the correct proper motions of the more remote stars will yield a position of the apex which is in accordance with that furnished by «//the northern stars together. In the southern sky we found that principally the stars of small proper motion lead to a divergent value of the declination of the apex. Therefore if we wish to explain this divergence by star-drift, we have to assume that, whereas the whole of the stars of the northern and at least the nearer stars of the sout/urn hemisphere show no relative systematic motion, such a motion exists for a group of remote southern stars extending over more than I2» in right-ascension, that is filling an enormous space, which in part surrounds an unaffected portion of the system. Such an assumption seems very improbable a priori.
Summing up, we find that there is but little evidence of a real difference between the declination of the apex for northern and southern stars.
Between the supposition of star-drift or systematic error, as the cause of the divergences in Table 5, the choice is not difficult. As long as further evidence is wanting, we can hardly do otherwise than make the remaining systematic errors in the adopted proper motions responsible for them,
The proper motions reduced to Auwers system.
The preceding discussions point to the conclusion that, for the proper motions in declination of the southern stars Auwers' fundamental system is pre-
This may be seen from the formulae for A?, A» and derived in Note to Chaptcr III.



ferable to that of Newcomb. For the northern hemispherc we have no such direct evidence, but the difference of the systems north of the equator is small and consequently the choice not very material. For the sake of greater homogeneity we will finally adopt Auwers' system of /ug for the whole of the sky.
For the /ug of Auwers-Bradley the data necessary for such a reduction have been taken froni the tables of Auwers in the Astronomische Abhandlungen no. 7: „Tafeln zur Reduction von Sterncatalogen". The corrections were found from the relation:
(45) 4«(Auw -Br ) = Greenw. 1860 -f- A Greenw. 1864) — A Bradley
108
For the region between 6o° and 90° the correction has been determined by combining the corrections at 60°, 65°, 70°, 750, 8o°, 85° with the respective weights 6, 5, 4, 3, 2, 1. From the corrections found in this way those already applied by Prof. Kapteyn (see Publ. no. 9, page 5) have been subtracted. The remaining corrections are given in the following table under the head Auw. —Kapt. For the sake of comparison I have added the differences Newc.—Kapt. derived from the data on page 5 of Publ. 9.
Table 6.
Decl. Auw.—Kapt. Newc.—Kapt.
South. decl. -f o".ooo4 + o".ooio
o° to -f- 200 — o".oo 17 — o".ooo9
-f- 20° tO + 4O0 — 0".0025 — 0".0040
-f 40° to -f- 6o° — o".ooi2 -f o".oooi
+ 6o° to -f- 90° + o".oo55 + o".ooï4
The difterences Auw.-- Kapt. are mostly small and of the same order as the differences Newc.—Kapt. There is only an exception for the zone 6o° to 90° in which, owing to the very limited number of stars, the reliability of the determination is smallest.
Combining the corrections for the different zones with weights proportional to the numbers of stars in each of them, we find as an average correction of the proper motions in declination in the reduction to Auwers:
(46 ) Afig — — o".ooo7
in the reduction to Newcomb:
(47 ) A = -- o".ooo8.
Now let us compare the values of D obtained from the different groups of stars after ha ving reduced the /us respectively to the systems of Auwers and Newcomb. For each of the three groups of stars of Bradley the average corrections (46) and (47) have been applied in the present discussion. ') For the southern stars which have been reduced originally to Newcomb the corrections
*) Afterwards the proper motions of Bradley have been more exactly reduced to the system of Auwers (see page 50).



(29) and (36) have been used for the reduction of the ug to Auwers. Summing up we get:
Table 7.
Limits of deel. Source
— 20° to — 40° N 4- o".oo38
— 20° to — 350 Tay + o".oo38
— 40° to — 5 20 N + o".oo5ó
— 40° to — 520 Gi -f o".oo5ó.
On the other hand for the reduction of the proper motions of the stars of Auwers between —520 and —90° to Newcomb the correction (31) originally neglected (see page 22), has been applied for the reduction to Newcomb.
The following table shows the resulting values of D, DA and DN denoting the values respectively obtained if we adopt Auwers' or Newcomb's system.
Table 8.
, . , _ ^ _ I Numb. I „ _
Lim. of deel. Source. DA Dn P Ra Rn
| of stars |
i ' 1
-I-900 to +52° Br + 390-1 + 39°-6 297 0.6 + 7°.3 -f- 6°.o
+ 520 to —20° Br -j- 3i°.3 +31 °.6 2115 18.0 — o°.5 — 2°.o
— 20° to — 310 Br + 230-9 -f-24°.i 139 1.1 — f.9 — 9°.5
— 20° to —40° N + 33°.8 -j- 38°.7 114 I 0.9 2°.o -f 5°.i
i
— 20° to —350 Tay + 42°.6 -J- 5l0-8 !98 ° 4 + I0°-8 + l8°-2
— 40° to —520 N -|-28°.9 -f-36°-6 38 0.2 — 2°.9 + 3°-°
— 40° to — 52° Gi +33°-4 + 44°-9 49° 2-4 + i°.ö + "°.3
— 520 to —90° Auw. +40°-5 +43°.o 225 0.4 8°.y -f- 9°«4
A .1 I I
All stars . , ^ !
+ 3i°.8 +33-6 3616 24.0
together j
The mean values of the last line were obtained by combining the separate values with weights obtained by dividing the coëfficiënt 2 cos- d l) by 100. For Taylor l 2 cos2 öa) has been taken instead of this coëfficiënt. The two last colums show the residuals.
As was to be expected the agreement between the values of DA has become much better than before the reduction to Auwers; e0, fi00 and fd,
') See equations (4).
8) As, by the preceding discussions our confidence in Taylor has been rather weakened I resolved to diminish here the weight still more than was done originally.



being the quantities defined above (page 32) and eD the mean error in DA we get from the RA
k8) f0= ± 50.2
(4^) £l00 = ±6°.3
(5o) 
f d = — i .1
Taking into account the numbers of stars, this last value is about of the same order as the values for e in the declinations derived in A. N. 3721 '22.
If for the purpose of a comparison we derive the analogous quantities from the residuals Rn, we get:
(51) = ±. io° . o
«,oo = ±. 12 .2
eD = ziz 20 . o
(52 ) 
(53 ) 
They are very considerably larger.
If now we combine the values from the different groups of stars in the same zone with weights equal to the quantities p given in Table 8 , we <ret!
Table 9.
Limits of deel. Souree Da D„ | p ra rh
+ 90" to + 52" Br. + 39°. 1 + 390.6 297 0.6 + 70.3 + 6°.o + 520 to — 20° j Br. + 3r°-3 + 3i°-6 2115 18.0 — o°.5 — 2°.o 20° to 40° Br.N.Tay. + 30°.7 + 34° 2 451 2.4 - :°.i + o°.6 -40°to-52° N.Gi +33°.i + 44°-3 528 2.6 + l°.3 + io°.7 - 53° to - 90° Auw. + 400.5 + 430.0 225 0.4 + 8°.; + 90.4 . . 
All stars together + 3i°.8 + 33°.6 3616 24.0
^HRS^ WMM■SHHMimhmmm^HHHNBMBBsI ■■■■■■■■**■* naaaHan^H|aannaMa
Excepting for the extreme zones, the uncertainty of which is necessarily
very considerable, the agreement of the values of D for the different zones of
dechnation both in the northern and in the southern hemisphere, obtained after
the reduction to Auwers leaves nothing to be desired. On the contrary the
reduction to Newcomb has hardly improved the results of Table 4. In the absence
of other data for judging the relative reliability of the two fundamental systems,
this fact has turned the balance in favour of that of Auwers. In deriving fïnal
results we have definitively adopted Auwers' system for the proper motions in declination.
From the good agreement of the values of A derived from the different



sources (see lable 3) we may conclude that in the proper motions in rightascension there are probably in general no systematic errors of such a kind or of such an amount as to have a considerable influence on the position of the apex. From this point of view there would not seem to be any reason for the application of corrections to the values of pa There seem however to be traces of a small periodic systematic error in the values of /ua of the stars of Bradley. In Publ. 9 no periodic corrections have been applied to the proper motions except those for precession. Therefore any periodic systematic errors in the original proper motions of Bradley-Auwers are still contained in the proper motions of Bradley as here used. Now from the data of Auwers in „Astron. Abhandl. no. 7" a slight periodic correction to the values of /um of Bradley-Auwers may be derived. A direct comparison of the values of /ua of Publ. 9 for the stars contained in Newcomb's fundamentalcatalogue with the corresponding values obtained from this catalogue gives a correction in the same sense. The sense of the correction agrees also with that derived by Prof. Kapteyn for the proper motions of Bradley-Auwers in A. N. 3859 — '60. It is for these reasons that in deriving our definitive results we have applied corrections as well in right ascension as in declination for the reduction of the proper motions of Bradley to the system of Auwers, derived from the data given in „Astron. Abhandl. no. 7".
A reduction of the whole of our proper motions to the system of Auwers — which might seem desirable for the sake of homogeneity — would require further the derivation of corrections for the greater part of the proper motions in right-ascension of our southern stars. For the proper motions of Auwers between 520 and —90° no corrections are of course required. There thus would remain to be found corrections to the values of fia of Newcomb , Gill and Taylor in the zones of deel. — 40° to — 520 and — 20° to — 40°. In deriving such corrections we meet with a difficulty. The corrections in na which chiefly affect the position of the apex are the periodic corrections. For the determination of such corrections however a sufficiënt number of data is not available. On the other hand a constant correction to the fia can be better determined but is of little importance. For it is evident that equal corrections applied to the fia of stars dififering i2h in right-ascension will neutralize each other in the second members of the equations of Bravais. Therefore a constant correction to the fia will have no effect on the position of the apex if the stars are distributed equally over the different hours of right-ascension. Now this last condition is either well fulfilled for the stars used in the two zones or the same effect has been artificially secured by the choice of the weights with which the stars enter in the equations of Bravais. There is an exception only for the stars of Taylor, which are distributed very irregularly over the different hours; but these influence the position of the apex only to a very small degree, as a consequence of the small weight attributed to them. This would seem to be sufficiënt reason for not applying such a correction to the /ua. — But even if constant corrections of the /ua were not eliminated, there would be objections to their application.
For the stars of Gill the original values of /ua, wich where based on



the system of Newcomb, showed a distinct preference for negative values, a property which seemed to be common to the brighter and the fainter stars. We have discussed this anomaly in Chapter II and we came to the conclusion that it is probably attributable to systematic error. For that reason we have applied to the .values of /ua of these stars a positive correction of such an amount that the anomaly disappears. At the same time we have seen that it would be still increased by the application of a correction necessary for the reduction to Auwers. It must thus be considered preferable not to destroy the effect of the correction already applied by a reduction of the values of f./a to Auwers.
A similar irregularity was shown by the proper motions of the faint stars of Taylor, derived originally by Prof. Kapteyn from the positions of Taylor and Tucker after reduction to Newcomb. In the same region the values of /ua of the stars of Newcomb, which are much brighter in the mean, do not show a preference for negative values. The anomaly of the proper motions thus seems to be attributable to an error of magnitude for which Prof. Kapteyn has applied a positive correction of such an amount that the mean value of fia obtained by combining the different hour-groups with equal weights, became zero (See page 18 etc).
The process is equivalent to the supposition that the peculiar proper motions in right-ascension of Taylor-Tucker as well as those of the newcomb-stars in the same region do not show a preference for positive or negative values. This correction too would be destroyed if to the whole of the taylor-stars we were to apply corrections obtained from a comparison with the proper motions of the stars of Auwers in the same region, which as a rule are relatively bright stars.
To sum up: there are objections to the application of any further constant correction to the n* of the stars of Newcomb, Taylor and Gill. Happily such a constant correction is practically without any influence on the position of the apex. More important would be the derivation of periodic corrections for the na. The number of our stars in however hardly sufficiënt for the derivation of trustworthy corrections of this kind.
In order to avoid any misconception, I will remark that my statement, that the proper motions have been reduced to the system of Auwers, must not be taken to the letter. It has been my aim to reduce the centennial variations to Auwers as sharply as possible. After that the best results for the proper motions would have been obtained, if from these centennial variations a new constant of precession had been derived by means of which the proper motions themselves would then have been found. The difference however of this constant with that of Newcomb must be very small. This may be concluded from the data of Table V (see the values of » depending on the declination)*). Add to this the fact
') As will be seen from the explanation of Table V in the beginning of Chapter IV these values represent the corrections for the equinox required for the reduction of the proper motions of Publ. 9 to Auwers. These proper motions have been reduced to the equinox of Newcomb by Prof. Kapteyn. As a rule the corrections are small.



that the precession is of no influence at all in a determination of the solar
motion, if the stars are distributed uniformly over the whole of the sky — a condition,
that is fairly well satisfied for the stars, used for the present determination of
the apex — and it will be seen that the influence of such a small correction to
the constant of precession upon the position of the apex must be wholly
van is hing in our case. I have feit justified in retaining Newcomb's precession for these reasons.
ï



CHAPTER IV.
DEFINITIVE RESULTS.
Corrections of the second members of the equations for the reduction of the
proper motions to the system of Auwers.
For the derivation of the definitive results the corrections a p, a Q and a R required on account of the reduction of the proper motions to the system of Auwers have been applied to the second members P, Q and R of the equations. For that purpose our groups (K) of page 27 according to the galactic latitude have been subdivided into groups of such an extent in right-ascencion and declination that for each of the subdivisions the values of a and ö and that of the correction to be applied to the proper motions may be considered to be constant.
For the stars of Bradley the divisions of Table 6 (see page 44) according to the declination have been each subdivided into groups of one hour in rightascension. For each of the groups obtained in this way corrections a /ua and a /u$ for the reduction to Auwers have been calculated by means of the tables of Auwers published in the „Astron. Abhandl. n°. 7". In Chapter III we derived already the corrections a ps (Auw.—Kapt.) depending on the declination; these corrections which have been given in Table 6 (page 44) have been used. Moreover corrections for the jug, depending on the right-ascension as well as corrections for the /na depending on the declination and such depending on the rightascension have been calculated by means of the formula (45). From the corrections a ju„ depending on the declination the constant correction -fo8.ooioo, applied already by Prof. Kapteyn (see Gron. Publ. n°. 9, page 4) has been subtracted. In this way the corrections given in Table V have been found. I found the total corrections a and a fts by adding, for every area, obtained by means of the doublé subdivision, the corrections a jia and a pt depending on the declination to those depending on the right-ascension.
For the stars of Newcomb , Taylor and Gill the constant corrections given in Table 7 (page 45) have been applied for the j.i$. For the no corrections have been applied for the reasons explained in the last part of Chapter III. For the southern stars of Auwers no corrections are needed (see Chapter II, page 21 and 22).



For the calculation of the corrections AP, AQ and AR it was not necessary to apply corrections to the individual proper motions. For, according to what has been said already, our areas are so small that we may assume the corrections to be constant for the whole of their extent. For the stars of Bradley the subdivisions made have already been indicated above. For the southern groups. except that of Auwers, for which no corrections need to be applied, the limits of declination are so narrow that they have been only further subdivided into groups of one hour of right-ascension. According to the equations (4) the computation of the corrections in question has to be made by means of the formulae:
AP = (sin a . 15 Afia cos 8 + sin 8 cos a kfi$) (54) AQ = (— cos a . 15 Ajfo cos 8 + sin 8 sin a Afi$) JSq
AR = (— cos 8 Au$) 2(j.
From the corrections ap, aQ and ar thus obtained for our subdivisions we easil get the analogous corrections for the larger groups.
Summing up: the groups of different galactic latitude have been kept separate for the calculation of the quantities aP, aQ and AR. For the stars of Bradley the corrections Afia and A//$ necessary to reduce the proper motions to the system of Auwers given in the „Astron. Abhandl. Nr. 7" have been applied. For the NEwcoMB-stars and those of Taylor and Gill only the constant corrections Afi$ given in Table 7 (page 45) have been applied. For the southern stars of Auwers no corrections have been applied.
The corrections AP, and ^R obtained tor our different groups have been given in Tabie VI.
Results from the groups of different galactic latitude.
After the application of the corrections JP, AQ and ^R the values of g, r\ and £ and those of A and D have been determined separately from the groups of different galactic latitude.
For the weight of a single proper motion I adopted the following values
Bradley i Newcomb i Taylor £
Gill £
Auwers £
which in my opinion must be roughly in accordance with their accidental and remaining systematic errors. The coefficients and second members of the equations finally obtained have been given in Table VII. The notations used have the same signification as those of Table IV (see page 27).
By solving the equations the following values for the components of the solar motion have been obtained:



Table io.
Gal. lat. § t) £
— 90°to-4oc — 2.4 —238 +148
— 40° to — 200 — 1.8 - 27.3 + 18.3
— 20° to + 200 — 0.4 — 28.6 + 15 6 + 20° to + 40° _ 1.5 _ 26.2 + ,7.4 + 40° to + 90° — 1.0 — 27 9 4- 16.6
All stars together — m —26.8 -f- 16.2
From these we derive the coordinates of the apexgiven in the following table.
Table ii.
Gal" lat" A D RA RD pk
— 90° to - 40° 264°.3 + 3<°-7 —3° 3 +o°.s 1.9 4.4
— 40° to — jo° 266°.2 + 33°.8 — ,».4 + 2».6 ,.9 3.3
— 20° tO + 20° 2Ó9°.2 +28°.6 -f i°.6 — 2°.6 98 7.5 + 20°t0+40° 266°.7 +33°.5 — o°.9 + 2*3 3.3 3.2 + 4Q°to +90° 2ó7°.9 +3°°.7 -f 0°.3 — o°.5 2.1 4.2
All stars together 2670.7 +3i°.2 2oo 22.6
The values of A and D from all stars together have been obtained by adding the equations for the individual groups and by solving the resulting system of equations
By subtracting the values of A and D obtained from all stars together from those given by the individual groups the residuals denoted respectively by Ra and Rd have been found. A decided trend cannot well be recognised in them. Supposing the difïferences to be purely accidental we may derive the rnean errors from the residuals. For that purpose weights have been given to the individual values of A and D, which are respectively equal to a hundredth part of the coefficients A and C (defined on page 27) in the equations of Bravais. Denoting the mean errors of the values of A and D from all stars together by fA and fD, we get:
(55) eA= — o° 8 fD= — i° 0.
These values are in accordance with those of the means errors derived in Chapter III by means of a comparison of the values of A and D obtained from the zones of different declination; those of D after the reduction of the values of taS to the system of Auwers (see (20) on page 32 and (50) on page 46). There thus seems to be no reason to ascribe any reality to the differences found between the results from zones of different galactic latitude.
Results from groups of different type of spectrum.
In order to see whether a difference between the coordinates of the apex from stars of different type of spectrum can be ascertained, the stars ofBRADLEY of Type I and Type II have been treated separately. The data for the formation



of the equations have been given in Table VIII, the second members P, Q and R reduced of course to the system of Auwers. By solving the equations the following values of §, rj and £ have been obtained;
Table 12.
Spectr. £ tj £
Bradl. Type I —1.0 —27.6 +144
Bradl. Type II —2.1 —27.1 +17 3
which we get:
Table 13.
Spectr. AD Pa Pd *a <=d
Bradl. Type I 268°.o+27°5 7-4 8 6 + i°.3 ± i°.7
Bradl. Type II 265°. 5 + 3*°4 6.3 8.1 + i° 4 + i°.8.
1 he difference of the values of A and D obtained from the two groups is
stnall. The weights pA and Pb are obtained in the same way as before. As the
scales of the weights are practically in accordance with those of Chapter III, we
may use the rnean errors of the unit of weight there found (see (19) on page 32
for the A and (48) 011 page 46 for the D). We thus obtain the values of fA
and «d given in Table 13- It thus appears that the differences between the values
of A and D, particulary the latter are slightly larger than might be expected
from the values of eA and fD. Still the reality of the difference is of course more than doubtful.
Taking all the stars of Bradley (the „Remaining Stars" of Publ. 9 included) together we get, the proper motions being reduced to Auwers , the following results:
(56) £ = — 1.3 r\ = — 26.9 £ = + 16.1
(57) A = 2670.3 D = + 3o0.9
These results too differ only very little from those obtained on page 52 from all the stars together (see Tables 10 arid 11).
The definitive results J'rom all the stars together.
As may be seen from the discussion of the difficulty afforded by the unknown radial velocities, it will be best, theoretically, to arrange the choice of the weights in such a way, that zones lying symmetrically relatively to the equator get into the equations with equal weights (see page 7 etc> The condition however loses much of its importance now that we find that, after the reduction to Auwers no marked differences remain between the values of the coordinates of the apex furnished by the different zones of declination. I will take advantage of this circumstance in order to adjudge weights somewhat



more in accordance with the real reliability of the sources of our proper tnotions
than would be those strictly required by our theoretical condition. I have finally adopted:
weight 2 for a proper motion of Newcomb » i v d v » n Taylor-Tucker » 1 n 7> » » „ any other source.
The equations furnished by the several groups have therefore been multiplied by these numbers They have then been added and by solving the resulting equations the coordinates of the apex have been determined.
If we count a star of newcomb for 2, one of taylor for | star, we get the following numbers of stars in the different zones:
table 14.
Deel- Source Nutnb. of stars
+ 520 to + 90° Br. 297
4°° » + 52° Br. 219
+ 200 „ + 40° Br. 626
°° n ~r 20° Br. 677
o° „ — 20° Br. 593
20° „ 40° N., Br , Tay, 417
4°° n — 52° N , Gi. 566
— 52° » — 9°° Auw. 225
The symmetry with respect to the equator is defective. The regions from 20 to 40° and from — 520 to — 90° have a considerably smaller number of stars thau the corresponding northern ones. There is however a sort of compensation in the zone from —40° to —520, which contains a much greater number of stars than the corresponding northern zone. Alltogether we get 18 f9 stars on the northern, 1801 on the southern hemisphere, a remarkable close agreement.
In the zone from 40° to —520 I have used the „Combination Newcomb -Gill" (see page 30) after having applied a correction
(58) AR = — 2503-
for the reduction of the {tg to auwers. to the quantities P and Q no correction need to be applied as opposite three-hour-groups have got equal weights in this combination. For the other groups of stars the corrections AP, AQ and AR, obtained by adding those derived for the partial groups of different galactic latitude, have been applied. They have been given in Table VI (see: All stars together).



The coefficients and second members of the definitive equations have been given in Table IX.
By solving the equations we find:
(59) £ = — 1.1 £ = — 26.8 £=+16.4.
(60) A = 267°. 7 D = + 3i°.4.
These results agree almost absolutely with those found in Table 10 and Table 11 from all the stars together using weights based exclusively on the estimated reliability of the different groups of proper motions. They also agree with the results (56) and (57) obtained from the stars of Bradley separately. We thus see that the values of the coordinates are practically independent of the choice of the weights of the southern stars.
For the mean errors of the results (60) we will adopt the values
(61) «a= ± o°.8 sD= ± 1°.I
in accordance with those obtained formerly from zones of different declination and those from zones of different galactic latitude (see (20) on patre 12, (nó) on page 46 and (55) on page 52).
If h represents the velocity of the sun, then the values (59) substituted in the formula:
. . & = V(?+ *>* + £')
Iead to the value
(Ó2) h = 31.5 — 0 9 e.
The value of the mean error adopted here has been derived by comparing the values of h obtained from the zones of different galactic latitude. As our unit of velocity is the linear velocity at right angles to the line of sight of a star with a parallax of o". 1 and a centennial proper motion of 1", we get, expressed in kilometers per second for the value of the solar velocity and its mean error:
(63) h = 14.9 . KM ±_ 0.5 KM
The value ot h found in this way is dependent on the values, adopted for the distances. These distances in their turn are determined by the parallaxes of the table in Gron. Publ. 8. The parallaxes of this table are based for a large part on the mean parallaxes of stars of different magnitude found in Astr. Nachr. 3487 (see page 5 of Publ. 8), which have been determined from the parallactic motions, adopting for the solar velocity the value:
(64) k= 16.7 KM+1.1 KM
which has been derived by Prof. Kapteyn from the radial velocities of 51 stars determined in Potsdam. The difiference between the results (63) and (64) must be explained by the fact that we used a great number of stars in addition to those used by Prof. Kapteyn. As was to be expected however, the difference is not very considerable.
Afterwards Campbell has derived the value:
(65) h = 19.9 KM + 1.5 KM
from a number of 280 radial velocities. This value must be preferred at all events



to the valtie (63) '). This value together with the definitively adopted position of the apex (60) would lead to the improved values:
(66) £ = — 07 KM n = — 16.9KM £ = -f 10.3 KM.
For the determination of the coordinates of the apex we have used the formulae (4), which have been derived from the rigorous equations by neglecting the radial velocities. As has been explained in Chapter I this comes to the introduction of the hypothesis that the radial peculiar velocities of all the stars, transferred to the geometrical centre of gravity neutralize each other (see page 7). The position of the apex (60) found above rests therefore upon this hypothesis.
As already pointed out (page 7 etc?) there is a certain a priori probability that for stars which, like our stars are fairly uniformly distributed over the sky, the hypothesis will be at least approximately satisfied.
We may consider the hypothesis to be confirmed a posteriori by the good agreement of the positions of the apex obtained from stars in different parts of the sky. The hypothesis might be verified more positively by the agreement of the coordinates of the apex found from the astronomical and those from the spectroscopie velocities, if a suitable number of the latter quantities were available. In the case that there would appear to be a difïference we might get the position of the apex resp. the components of the solar motion free from the hypothesis by combining the values of |, i? and £ found from both groups of proper motions in the manner indicated in the last part of Chapter I.
From his group of 280 spectroscopie velocities Campbell finds the following values for the coordinates of the apex8):
(67) . . . A = 2 77°.5 ± 4°.8. D = ± 2o°.o zt 5°.9.
Combining these with his value (65) for the solar velocity found from the same stars, the following values are found for the components of the solar velocity:
(68) . . | = + 2.4 K.M. n = — 18.5 KM. £ = +6.8 K.M.
Campbell's values (67) for the coordinates of the apex differ rather considerably from the values (60) found in the present paper. As however Campbell's results were derived from a small number of exclusively very bright stars, whereas our results depend on a considerable number of stars which are much fainter in the mean the two results cannot be considered as quite comparable. For the same reasons it does not seem advisable to combine the values (68) for the components of the solar motion, derived by Campbell with the values (66) found above. Moreover a combination of the two sets of values is liable to the objection that in deriving the values (66) Campbell's value (65) for h has been used and therefore the values (66) may not be considered to be determined
') That the mean error of (64) ls less than that of (65) depends on the fact that in deriving (64) another principle has been used.
8) Astrophys. Journal, vol. XIII, page 80 etc.



purely astronomically. It will therefore be better to defer a combination of the results from astronomical and spectroscopie data to the time that a suitable number of spectroscopie velocities of fainter stars will be available and that a value of h will have been obtained froin purely astronomical data.
Happily the position of the apex is not in the least influenced by the uncertainty in the absolute values of tj and £, as it depends only on the proportions of these quantities and not of the value of h. Finally I will not adopt the values (66) for the components of the solar velocity but only the values (60) for the coordinates of the apex and together with these the value (15) derived for k
-=-1) from the BRADLEY-stars by a comparison of the values q0 and qc (see page
h
26). It is true, that this value for -==- is derived in the supposition of a random-
distribution of the proper motions. But as it has been obtained by comparing the quantities gQ and ^Cj the former of wliich is independent of that hypothesis, and as the differences of the two for the several zones show no systematic divergences we conclude that the influence of the systematic deviations from the random-distribution must be very small.
Summary of the results.
The results of this Chapter may be summed up as foliows:
d) There seems to be no reason to admit the existence of real differences between the values of the coordinates of the apex from groups of stars of different galactic latitude.
b) For stars of different type of spectrum the results are somewhat more divergent. Still there seems to be no ground for assuming that there is a real difference.
c) All the stars together lead to he following values for the coordinates of the apex and their mean errors. Thcy will be considered as the definitive result of our investigation.
A = 267°.7 =t 0°.8. D = + 31°.4 - 1°.1.
d) Between the h and n we have the following relation:
h — 0.750 n.
This relation was derived exclusively from the BRADLEY-stars.
') As on page 26 the mean value n of the projections of the peculiar velocities on a plane is taken as unit of velocity, the quantity 4- has been denoted there by h.
8



NOTES TO CHAPTER I.
1) Let the rectangular coordinates of an arbitrary star relatively to an arbitrarily chosen system of coordinates be x, y and z, the number of stars of group the N. We will call geometrical centre of gravity the point of which the coordinates ~x, ~y and F are defined by the following equations:
N* = £x Ny = Sy Ni = Sz.
Denoting the components of the velocity of the geometrical centre of gravity by \x, by and Az, those of an arbitrary star by Ax, Ay and Az, we have therefore:
Na* = SAx NAy = SAy N&F — SAz.
If now we take as origin of coordinates the geometrical centre of gravity or a point rigidly connected with it, the quantities A~x, Ay and Az will be identically zero. Therefore we get the equations:
2Ax = o SAy = o SAz = o. denoted by (3) on page 5.
2) To find formulae for the derivation of the components £, q and £ from the spectroscopie proper motions, quite analogous to the formulae (4) which determine them from the astronomical ones, we will again start from the fundamental equations (3) of page 5.
If we denote the components of the total velocities of the stars, relative to the ntoving sun by Sx, Sy and Bz, these equations may be written:
2(èV + l) = o 2(Sy -f- ,)) = o £($z + £) = o.
In working out the values for Sx, Sy and Sz, we have now to neglect the tangential peculiar proper motions. We will take the observed radial velocity v positive in a direction from the sun. The projection of the parallactic motion on a plane perpendicular to the line of sight, will be decomposed in the direction of the rightascension and that of the declination. The corresponding components will be called p and q. We get the equations:
2 (vx -f- px -}- qx -J- £) = o
2 (vv + A + 9y + 1) = 0
2 (vt -f- Pz +?»+?) = O
in which vx, pX} qx denote the projections of the quantities v, p, q on the axis of x, etc. We have further:
P — K sin a — q cos a q — $ sin S cos a -f- 1/ sin 8 sin a — £ cos S.



Taking into account that the cosines of the angles between the axes of coordinates and the positive directions of p and q are represented by the expressions
— sina, + cos a, o for/
— sin 8 cos a, — sin 8 sin a, cos 8 for q
we easily get the equations:
£2 cos* 8 cos9a -f •»£ cos*8 sin a cos a -f- £2 sin ê cos 8 cos a -f Sv cos 8 cos a = o cos* 8 sin a cos a + cos'S sinaa + £2 sin 8 cos 8 sin a + cos 8 sin a = o sin S cos S cos a + i)£ sin 8 cos 8 sin a + ££ sin'd + Zv sin 8 = o.
which are identical with the equations (5) of page 12.
These equations have the form of the normal-equations, obtained from a set of equations of condition of the form:
^ cos d cos a + ii cos 8 sin a + K sin è -f v — O
which are identical with those used by Campbell 1). Although these equations of condition are the expression of the assumption that in deriving the sun's motion we may treat the peculiar radial velocities as accidental errors, we thus see that the normal-equations derived from them are independent of this supposition.
<) Astrophys. Journal, vol. XIII, page 83 (eq. 4).



NOTES TO CHAPTER II.
1) Denoting by q{, q.t and q$ the values of q obtained from the large, ntean and small proper motions, and by q0 the mean of these three quantities, the following values were empirically found for the different parallactic zones and angles of position (the latter representing the mean of the two limits of p).
Table 15.
1.00 > sin A > 0.80 (mean value = 0.94).
P 9\ q* q» n
i i j 
o 1
7 1.11 j 1.17 1.28 ; 1.19 364
30 1.24 : 1.21 1.15 | 1.20 539
| i
60 0.96 0.98 0.87 0.94 220
90 | 0.80 0.81 0.80 0.80 158
120 j 0.76 0.76 0.85 0.79 164
150 : 0.49 0.57 0.62 0.56 95
l73 | 0.94 0.56 o 50 0.67 ! 48
——i—i—1—■—mm_____
0.80 " • sin A > 0.60 (mean value = 0.72).
~ i
P q\ ?2 q$ | q» n 1 
o I
7 | 0.88 0.95 1.06 0.96 83
30 0.95 1.05 1.06 1.02 160
60 0.99 0.83 0.84 0.89 102
90 0.97 0.91 o 82 0.90 57
120 0.94 0.83 0.75 0.84 37
150 0.65 0.78 0.58 0.67 39
173 0.63 0.51 0.72 0.62 14



o 60 > sin A > 0.30 (mean value = 0.48).
P 9% ia 9o n
O
7 0.73 1.04 1.16 098 60
30 1.06 1.05 1.03 1.05 in
60 1.10 1.08 0.92 1.03 85
90 1.59 1.32 0.95 1.29 63
120 0.94 0.86 1.09 0.96 49
150 0.46 0.56 0.87 0.63 42
173 0.57 0.97 1.52 1.02 15
The numbers of stars used for the derivation of q0 has been denoted by n. As a matter of fact the values of qx, q%, q9 and q0 have not been obtained immediately by
taking the quotients , but by computing first the quotients — -— and afterwards the
_ <"
quotients ——, the latter quotients being calcuted by taking the large, mean and small
proper motions together, without excluding any proper motion.
For the zone 0.30 > sin A > 0.00 it was of no use to derive values for q0. The influence of the small value of h sin A for the stars in this region must be masked by the irregularities in the distribution of the proper motions.
2) To derive the formula for Q we imagine a group of stars, for which the \ 1:- 1-4....-— *■— '-'mits, which are so narrow that sin A may be considered
as a constant. For all the proper motions we consider the linear values. Let v be the linear value corresponding to the observed proper motion, represented by the line O P in the figure. Let the peculiar proper motion Q P be decomposed in the direction of the antapex and at right angles to it and let these components be represented by the lines Q S — x and P S = y in the figure.
As a consequence of the supposition made under
2 on page 24, we may represent the probabihty that the projection of the peculiar proper motion on the axis of x will lie between x and x -f dx by the expression
m
Vn
^ — m'x* dx.
In the same way the corresponding probability for the y will be
m'
e-"*v%dy.
Therefore the probability that the projection on the axis of x will lie between x



and x + dx and at the same time the projection on the axis of y between y and y + dy will be
tn%
e-«*V+*idxdy.
Now let us replace y by the angle of position p of the total proper motion as independent variable, using for that purpose the equation
y = (* + h sin A) tg p.
By differentiating this, considering x as a constant and by then substituting the value thus obtained for dy in the expression found above, we get for the probability, that the *-projection will lie between and * + dx and at the same time the angle of position between p and p + dp the expression :
(a) ^SÏlL*I g— m» [** + (* + A sin *)• tg»p) dxdp
v cos p r
Now consider all the proper motions for which the angle of position lies between p and p -f dp. The amount of the proper motion v will only depend on x, which we will suppose to vary between xx and x2. Therefore as
v = (x -f- h sin A) sec p
we will have as a consequence of (a) for the mean value Q of all proper motions, belonging to a determinate value of p the expression:
f — — — s*n ^ e~m* I*' + (« + sin x)« tg'p] dxdp
q = J *. cos P 
r** x -f ^sin A ^_m,[x« + (K + A8in\?tg«p] dxdp J >, cos p
or after some reductions:
Qƒ*t
{x + h sin A)**-1"»,(*secp + *sinXtgpsinp)*<£r
x,
~rX% •
cosp (x + h sin A) e~m*l*866* + fe8ln a Utp*foprdx
J
If now we put:
x secp -f h sin A tgp sin/ = z we get, denoting the limits of z by zt and z2:
fz*(z + h sin A cos p)*e~ m,«' zd Q — 1-h .
f**(z + h sin A cos p)e~m* * dz
To find the values of zi and z2, we have to consider that we have:
for 90° >p > — go0 *,= —AsinA x2= + oo
therefore: zx — — h sin A cosp z2 — + oo
for 2;o° >/> —po0 *,= — hsm\ x2 = — oo
therefore: zx — — ft sin A cos p z2 = -f* °o •
The limits of z are therefore independent of p. Again putting in accordance with what was done in Chapter II
h sin A cos p — *



we get:
f(* + ic)® € wi**" dg
(b) Q =
+ k) e~m'* dz
It is well known, that the integrals entering in this expression are easily reduced by partial integration to the integral fe~*dt. We get:
—8 + -s r+ —V + — C*e~*dt +
/r\ q _ 4** 2m Jo 2tn% tn J 0 2tn
1 * rm' kV*
—L^e-tnw + JLf e-*di+wJL
2 nr J 0 2tn
Thejralue of tn is obtained as follows:
Let t represent the average value of the linear velocities projected on a line, then the quantities t and m are evidently the same quantities which, in the theory of errors, are called:
i) = mean of the errors all taken positively; h — measure of precision.
Therefore the well known formula
h = —17— i) V*
proves that we must have
1
m = .
tVn
But as we took see page 24 etc. n as our unit, we have according to Gron. Publ. N°. 5, form. (8)
7=—.
ÏT
Therefore
m = 2 \/ ir — 0.886.
By the aid of this value we may write the formula (c) in the form:
m (I -f- 2 m*K*) -|- m iee~mtKl -j- (I -f- 2 m* k*) ["" e~* d t
Q = 0 .
2m* ie me-mtKt -f- 2m*Kje~*dt
0
which served for the calculation of the quantities Q.
3) In order to derive the values of Q by means of the formula (11) we have provisionally adopted
h — 0.685
• • ft
in accordance with the value for ^ derived by Prof. Kapteyn for the stars of Bradley in A. N. 3487 1). With the aid of this value of h the values of k have been calculated
*) As n has been taken as unit of velocity, the adopted value of k corresponds to the quantity — of A. n. 3487.
fi



for all the values of sin X and p, for which the quantities qo have been calculated empirically. As we have tn = 0.886 (see Note 2) all the quantities wanted for the calculation of the values of h are now known. For the calculation of the integrals, Table IX of Chauvenet x) has been used. We thus obtained the following values of Q.
Table 16.
Table of Q (h — 0.685).
\ sin A
\ 0.94 0.72 0.48
P \ 
O
7 1.32 1.24 1.15
30 1.27 1.20 1.13
60 1.15 1.12 1.07
90 1.00 I.OO I.OO
120 O.87 O.9O O.93
150 O.79 O.84 O.88
173 °-77 0,81 a87
In order to get the corresponding values of q we must now determine the quantity C (see formula (14) of page 25)* As we have C = the factor C might be calculated
by means of the mean value a of all the peculiar proper motions, which in thits turn might be obtained by multiplying the mean value of all the quantities r, given in Gron. Publ. 9,
by —— (see the formula 8 on page 14 of Gron. Publ. 5)- For our purpose however the factor C
is better determined in another way. For the factors/, if they have been well determined, will be such, that for the different values of A and p the mean values of the reduced proper motions H* agree as closely as possible with the mean value of all proper motions fi. If therefore we call the mean value of all the reduced proper motions fi', of all observed proper motions fi, we have the condition
(d) fi — fi-
From this condition the value of C may be determined. If we call n the number of proper motions belonging to a determinate value of A and p, the total number of all the proper motions N, then we have as a consequence of the definition of fi':
>) Chauvenet, spherical and practical astronomy, vol. II.



Therefore the condition {d) becomes:
In this expression we introducé for the nx, p and the n their values as they were empirically determined, for Q the values from Table 16; we then get
C — 0.892.
With this value formula (14) of page 25 and Table 16 lead at once to the following table for the qc.
Table 17.
Table of qc = CQ . {h — 0.685).
\ sin A 1 ! >
\ ! 0.94 ! 0.72 ; 0.48
t \l i I 
o !
7 1 1.18 I.II 1.03
!
30 ' 1.13 1.07 I.OI
! I
60 1.03 | 1.00 0.95
I
90 0.89 ! 0.89 0.89
120 0.78 0.80 0.83
150 j 0.70 0.75 0.79
173 J 0.69 j 0.72 0.78
I i
I I
In the following table these values are compared with those empirically determined.
9



Table 18. i.oo > sin A > 0.80 (mean 0.94».
* mean ' „ ■ ~ n
P . \ 9o \ qt O —C n
\ P
■ 1 1
OO O
O to 15 7 1.19 1.18 -f O.O I 364
'5 to 45 30 1.20 1.13 -f 0.07 539
45 to 75 60 0.94 1.03 — 0.09 220
75 to 105 90 j 0.80 0.89 - 0.09 158
105 to 135 120 | 0.79 0.78 + 0.01 164
135 to 165 150 0.56 0.70 — 0.14 95
165 to 180 173 | 0.67 0.69 - 0.02 48
I I
0.80 > sin \ > 0.60 (mean 0.72).
i I i
j. mean _ „ r\ r°
P q0 qc O — C n
j I 
O O O !
o to 15 7 | 096 1.11 — 0.15 83
15 t° 4.5 30 I 1.02 1.07 — 0.05 160
45 to 75 60 0.89 1.00 — 0.11 102
75 to 105 ; 90 0.90 0.89 -j- °*01 57
105 to 135 | 120 0.84 0.80 +004 37
135 to 165 | 150 0.67 0.75 - 0.08 39
165 to 180 173 0.62 0.72 — 0.10 14
0.60 > sin X > 0.30 (mean 0.48).
j, mean „ „ r\ r
P . qo qc O —C n P
00 O
o to 15 7 0.98 1.03 - 0.05 60
J5 to 45 3° I-°5 i-oi -f" °-°4 111
45 to 75 60 1.03 0.95 -f- 0.08 85
75 to 105 90 1.29 0.89 -f- 0.40 63
105 to 135 120 0.96 0.83 -f 0.13 49
135 to 165 i 150 0.63 0.79 - 0.16 42
165 to 180 173 1.02 0.78 + 0.24 15
1



In the first place we will consider the variation of q0 and qc with the value of sin X. As may be seen from Table 18 the difference O—C is mostly negative in the second, positive in the third zone.
The cause must be sought in the mtan value o'f in the different zones of sin X.
For we have:
ju\
~~ Number of stars.
f*
1.00 > sin X > 0.80 1.02 1588
0.80 > sin X > 0.60 0.92 498
0.60 > sin X > 0.30 1.02 427
The consequence is that the empirically determined values of q0 must become relatively small in the second, relatively large in the third zone:
In deriving the values of q0, firstly the quotients fiXL'p have been calculated for
f*\
the individual zones, excluding a small number of stars with exceedingly large proper motions. In this way some of the larger irregularities in the values of j"v,° are removed.
i«A
In order to reduce the quantities thus obtained to the mean value of all the proper motions which we have taken as unity, the values found for the different zones have been multiplied
by the quantities _ . These last quantities have been derived from all stars of Publ. 0 f*
without excluding any proper motion.
If now we exclude the three stars having largest proper motions and distributed in the following way:
P H
1.00 > sin X >0.80 o° to ± 150 3".76
0.60 > sin X > 0.30 ± 150 to ± 450 5".2i
0.60 > sin X > 0.30 + 750 to ± 105° 4^.05
we get:
1.00 > sin X > 0.80 1.05
0.80 > sin X > 0.60 0.97
0.60 > sin X > 0.30 0.85
We thus see that the way in which the values of vary with sin X has been
fi
considerably altered by the exclusion.
Multiplying the values of , obtained for the individual zones, by the new
iit
values of we find the values of q0 given in the following table together with
those of qc.



Table 19. i 00 > sin X > 0.80 (mean 0.94)
f m^an ?. 4. O-C n
oo o
o to 15 7 1.22 1.18 + 0.04 364
15 to 45 30 1.23 1.13 -f- 0.10 539
45 to 75 60 0.97 1.03 - 0.06 220
75 to 105 90 0.82 0.89 — 0.07 158
105 to 135 120 0.81 0.78 -f 0.03 164
135 to 165 150 0.58 0.70 — 0.12 95
165 to 180 173 0.68 0.69 — 0.01 48
0.80 > sin A > 0.60 (mean 0.72).
p | mean ^ O-C n
o go /
o to 15 7 1.02 1.11 — 0.09 83
15 to 45 30 1.08 1.07 -f" O.OI 160
45 to 75 60 0.94 1.00 — 0.06 102
75 to 105 90 0.95 0.89 -}~ 0.06 57
105 to 135 120 0.89 0.80 -j- 0.09 37
135 to 165 150 0.71 0.75 — 0.04 39
165 to 180 173 0.66 0.72 — 0.06 14
I
0.60 > sin A > 0.30 (mean 0.48).
1 p 
P ! mfn qo <lc O-C * ! P
i i
o o o
o to 15 7 0.82 1.03 ! — 0.21 60
15 to 45 30 0.88 1.01 - 0.13 III
45 to 75 60 0.86 0.95 — 0.09 85
75 to 105 90 1.07 0.89 -f- O.Ï8 63
105 to 135 120 0.80 0.83 — 0.03 49
135 to 165 150 0.53 0.79 — 0.26 42
165 to 180 173 0.85 0.78 °°7 !5



The differences O—C are now no longer systematically positive or negative in the first and second zone; in the third they have become negative, instead of positive. We thus find that the anomaly is wholly explained by the irregularities introduced by a few extremely large proper motions.
For this reason it seems preferable to adopt a system of values for q which vary with sin X in the way postulated by theory. The procedure has the advantage of accomodating itself closely to the real variations in the average proper motion in the different parts of the sky, whereas, if we use the etnpirical values of q the average proper motion is artificially brought to equality over the whole of the sphere.
We will therefore adopt a system of values of q for which the variation with sin X is determined by the theoretically calculated values. For that purpose we multiply the
values of q0 for every zone by the quotients -- . The values thus obtained will be
ZêtMJo
called q'0'
Having thus fixed the variation of the values of q with sin X, let us now inquire into the variation of these quantities with the value of p. The following tables embody the whole of the data at our disposal for that purpose.
Table 20.
1.00 > sin X > 0.80 (mean 0.94).
. mean / _ r\ c „
p p qo qc O — n
i i
O 0 O
o to 15 7 1.20 1.18 +0.02 364
15 to 45 30 1.21 1.13 | +008 539
45 to 75 60 0.95 1.03 | — 0.08 220
75 to 105 90 081 0.89 —0.08 158
105 to 135 120 0.80 0.78 -f 0.02 164
135 to 165 150 0.57 0.70 —0.13 95
165 to 180 173 0.68 0.69 — 0.01 48
0.80 > sin X > o 60 (mean 0.72^.
mean > r\ C
p p q 0 qc U — ^ n
|
000
o to 15 7 1.04 i.ii —0.07 | 83
15 to 45 30 | 1.10 1.07 +0.03 j 160
45 to 75 60 0.96 1.00 i —0.04 102
75 to 105 90 0.97 0.89 + o 08 57
105 to 135 120 0.91 0.80 +0.11 37
135 to 165 150 0.72 0.75 —0.03 39
165 to 180 173 0.67 0.72 — 0.05 14



0.60 > sin A > 0.30 (mean 0.48).
P P \ 9o 9c O — C n 1 i 
0 0 O
0 to 15 7 0.90 I.03 —0.13 60
15 to 45 3° 0.96 1.01 —0.05 iii
45 to 75 60 j 0.94 0.95 — 0.01 85
75 to 105 90 I 1.18 0.89 -f" 0.29 63
105 to 135 120 0.88 083 -{- 0.05 49
135 to 165 i 150 0.58 0.79 —0.21 42
165 to 180 173 0.94 0.78 +0.16 15
In the first group there seems to be a little systematic deviation in this sense that the positive residuals are somewhat in excess at the beginning, the negative ones somewhat in excess at the end In the third group just the contrary seems to be the case. If now we take all three groups together and if we put:
— X# (O — C) , .
Rt = ^ for the values 70, 30° and 6o°
R2= ——- for the values 120°, 150° and 1730
we find:
R| = + 0.007 Ra == — 0.024
therefore:
Ri Ra = "f" 0.031.
We thus see by taking all three zones together, that the residuals show a little preference for positive valuès at the beginning for negative ones at the end.
We may now choose the value of h in such a way that we get:
R, — R2 = o.
After some trials it was found that the value (&) h = 0.750
satisfies this condition. Therefore the values of Q have been calculated afresh, taking this value of h as a basis. The value of C has also been calculated anew. The value now found is:
C = 0.884.
By multiplying the new values of Q with the new values of C, a new set of values qc has been calculated. At the same time a new set of valuès öf q0 has been formed by
multiplying the values of q in every zone by the quotiënt ——, usingnow for ö'cthe new values.
The comparison of the values of qc and q'0 is shown in the following table.



Table 21 1.00 > sin I > 0.80 (mean 0.94)
1 r-—r-n
. mean . ^ ^
P pi* 1c O-C n
i '
oo o
Otö IJ 7 I.2I I.20 -f 6.61 364
'5 to 45 30 1.22 1.16 -f006 539
45 to 75 6 0.96 1.63 — 0.07 220
75 tö 105 90 0.81 0.88 - 0.07 158
105 tö 135 120 0.80 0.76 -(-6.04 164
135 tö 165 150 0.57 0.68 — 0.11 95
165 to 180 173 0.68 0.67 -f-o.oi 48
0.80 > sin A > 0.60 (mean 0.72).
. mean , _ _
P p q 0 qe O-C n
oo o
6 tö 15 7 I.04 I.I2 —0.08 83
!5 to 45 30 1.10 1.09 -f-0.01 160
45 t° 75 60 0.96 1.00 — 0.04 102
75 to 105 90 0.97 0.88 +0.09 57
105 to 135 120 0.91 0.78 +0.13 37
135 to 165 150 0.72 0.73 — 0.01 39
165 to 180 173 0.67 0.70 — 0.03 14
0.60 > sin X > 0.30 (mean 0.48).
. mean , ^ n
P p q 0 qc O—C ti
t
o o o
o to 15 7 0.89 1.03 —0.14 60
15 to 45 30 0.96 1.02 —0.06 III
45 to 75 60 0.94 0.95 —0.01 85
75 to 105 90 1.17 0.88 + 0.29 63
105 to 135 120 0.87 0.82 + 0.05 49
135 to 165 150 0.58 0.77 —0.19 42
165 to 180 173 0.93 0.76 -f 0.17 15



The agreement has become much better. If we calculate again the values of R, and Ra for all zones together we get:
R, = — 0.002 R, = — 0.002
therefore
R, — R2 = o.ooo
we may thus conclude that the agreement between the values of qe and q'0 is satisfactory if we take for h the value (g).
Therefore this value of h, denoted by (15) in Chapter II, has been adopted for the calculation of the values of ƒ in Tftble II (see page 26).



NOTE TO CHAPTER 111.
To prove the formula for the proportions of the effects of a stardrift on the computed components *?' and Z of the solar velocity, defined in Chapter III, we will call a the angular value of the common velocity of the stars of the drift, directed towards the south pole, expressed in the unit of are, the mean distance of the stars of the drift p. If the distances are very different we can divide the stars of the drift into groups for each of which the distance may be considered constant; the partial groups thus obtained must then be treated separately. We may however also treat all stars of the drift together, taking for p the mean distance of all stars of the group and for a a value which will be chosen in such a way that, whether we consider the real distances and angular drift motions, or imagine all the stars to be at distance p and to have the drift motion a, the effect on the components £, q, £ (resp. q', Z) of the sun's motion will be the same.
Now imagine the equations of Bravais transformed in such a way that they are relative to the new system of coordinates defined on page 41 in which the components of the sun's motion are g', q', £.
A', B' and C be the coefficients of £', q' and g in the first, second and third equation respectively (the coëfficiënt C remaining unchanged),
P', Q' and R the second members of the equations;
A P', AQ' and A R the effects of the star drift on the quantities P', Q' and R, a' the right-ascension of a star counted from a point, which relatively to the original
system of coordinates, has a right-ascension 0| — ,
$ the mean of the declinations, which must not vary over too wide a range,
N the number of stars of the drift,
then, as a consequence of the supposition of a uniform distribution of the stars over the zone, made in Chapter III, we will have:
Let:



Therefore:
a ti N . ? 2 a sin $ *
A 11' = O.
a y N . a $
A X. = —- (» cos S. - ~
2 ir C
A _ 2 sin ^ C
"aT 1— T*5'
As a further consequence of the supposition of a uniform distribution we have
A' = A = B, therefore A' = i (A + B)
consequently
A l' _ 4 si« i <p C , A £ * A-f B * è
A ij' = o
which are the equations ^43) used on page 42.



TABLES.



EXPLANATION OF THE TABLES.
Table I. Catalogue containing the data for the individual stars (see page 22).
Table II. Table of the factor ƒ for the reduction of the total proper motions fi to the quantities fi' (see page 26).
Table III. Table for the derivation of the coefficients of the equations of Bravais (see page 26 etc.)
Table IV. The coefficients and second members of the equations of Bravais, derived from the individual groups of stars (before the reduction of the proper motions to the system of Auwers; see page 27).
Table V. The corrections required for the reduction of the proper motions of the stars of Bradley (from Gron. Publ. 9) to the system of Auwers (page 50).
Table VI. Te corrections to be applied to the second members of the equations of Bravais on account of the reduction of the proper motions to the system of auwers (page 50 etc.)
Table VII. The coefficients and second members of the equations of Bravais, derived from the groups of different galactic latitude (page 51).
Table VIII. The coefficients and second members of the equations derived from groups of different type of spectrum (only the stars of Bradley have been used; see page 52 etc.).
Table IX. The coefficients and second members of the definitive equations from all the stars together (page 55).



TABLE I.
Newcomb —20° to —40°.
No' .875 >875 Pmir • 8» M " V 1 *
Jf fff O / OU HU O O O O
9 o 5*4 — 35 50 5*3 — 73 + 0117 +0129 0180 43 106 115 -f 72
34 30-9 — 25 27 5*8 — 87 + 1*367 — 2 1400 90 106 116 +26
58 52-6 — 30 2 45 — 86 — 23 — 13 0*026 240 in 112 — 128
109 1 39*8 — 25 41 5*6 — 77 4- 70 — 51 0*087 I26 121 110 — 16
127 54*1 — 21 41 4*4 — 73 f M4 — 8 120 95 122 112 + l7
139 2 7*4 — 31 19 5*4 — 7* — 48 — 22 53 245 127 105 — 140
146 i6*8 — 24 23 5*6 — 68 + 188 — 76 200 112 128 110 — 2
179 43*8 — 32 56 4*4 — 63 -f 101 + 156 190 32 136 100 + 68
181 45-4 — 21 31 5*0 — 61 — 61 — 17 63 254 134 iii — 143
191 569 — 24 7 4*3 — 60 — 141 — 44 150 252 *36 109 — 143
202 3 6*7 — 29 29 4*0 — 58 -f 314 + 637 710 26 140 102 + 76
222 28*2 — 22 3 4'5 — 52 + 32 — 39 51 H» '43 111 — 30
239 41*5 — 23 37 4*5 — 49 — 154 — 482 5oo 197 M6 108 — 89
242 42*3 — 24 16 5*2 — 49 -f" 5° 4" 4i 65 51 146 108 -|- 57
243 44*8 — 36 35 4*3 — 50 — 43 — 28 51 237 I48 87 — 150
247 48*9 — 35 6 5*3 — 50 + 9—17 19 I52 149 90—62
275 4 13*1 — 34 6 4*0 — 44 4" 31 o 3' 90 154 88 — 2
279 19*3 — 34 i8 4*i — 43 + 64 + 43 77 56 155 87 + 3»
290 307 — 30 49 40 — 40 — 55 — 24 60 246 158 92 — 154
320 5 0*2 — 22 32 3*6 — 32+17 — 64 66 165 163 116 — 49
335 i3*o — 35 1 5*2 — 32 + 34 — 35i 35i *74 166 70 — 104
347 22*9 — 20 52 3*2 — 26 O — 89 89 l80 l66 I30 — 50
368 35*1 — 34 9 29 — 28 + 7 — 38 39 170 171 62 — 108
370 39*2 — 22 29 40 — 23 — 295 — 354 460 220 169 137 — 83
378 45'9 — 20 53 4*1 — 21 + 228 — 648 690 161 168 147 — 14
379 46-6 — 35 49 3'3 — 26 + 31 + 389 390 4 171 41 + 37 389 / 53*1 — 35 I8 4*5 — 24 — 6+6 8 315 173 37 + 82 408 0 12*1 — 35 6 4*7 — 20 — 12+65 66 350 173 o + 10 411 15*5 — 30 1 3*4 — 19 — 8 — 23 24 199 176 343 + 144 425 29*8 — 22 52 4*7 — 13 + 30 +35 46 41 17° 211 + 17°
451 537 — 28 48 1*8 — 10 — 1 + 3 3 342 170 262 — 80
453 56*7 — 27 45 37 — 9 — 8+2 8 284 171 257 — 27
455 57'8 — 23 39 3*2 — 7 — 8 + 5 10 302 169 238 — 64
460 f 3-3 — 26 12 2*2 — 7 — 20 + 3 20 279 168 250 — 29
470 ' 12*7 — 36 52 2*9 — 10 — 10 — 10 14 225 165 295 + 70
477 19*1 — 29 4 2-6 — 6 + 4+7 8 30 166 265 — 125
502 44*0 — 24 33 3*6 +2 — 5 o 5 270 159 250 — 20
519 59*2 — 39 39 2*5 — 4 — 51 — 6 51 263 156 286 + 23
523 8 2*2 — 23 57 31 + 5 — 88 + 52 102 301 155 251 — 50
557 38*6 — 32 44 3*9 + 6 — 4 + 11 12 340 149 267 — 73
596 9 160 — 25 26 5*2 + 18 — 65 — 32 73 244 139 253 + 9
606 25*8 — 39 55 3*7 + 9 — 207 + 38 210 281 140 270 — 11
622 38*6 — 27 12 5*3 + 20 — 48 +29 56 301 135 254 — 47
664 10 21*4 — 30 26 4*6 +24 — 78 — 23 81 254 127 254 o
696 50*9 — 36 28 4*8 +22 + 136 — 138 200 135 123 255 + 120
710 11 5*5 — 22 9 4*7 +35 0 — i°6 no 180 114 246 + 66
731 26*8 — 31 10 3*9 -- 29 — 204 — 55 210 255 114 249 — 6
762 12 3*7 — 21 55 3*4 + 40 — 71 + 3 71 272 103 243 — 29
792 27*8 — 22 42 3*2 +39 — 10 — 61 62 189 98 241 + 52
8I3 46*5 — 39 3° 4*5 + 24 + 7o — 35 78 "7 102 241 + 124



TABLE I.
Newcomb — 20° to —40°.
vr« a & Photom. b , ,
1875 1875 mag. 1875 j f* M f V l Z Z-V
hm 01 oj# n tt 000 o
833 13 9*9 — 30 51 5*4 + 31 | +0017 —0-071 0*073 167 95 238 -|- 71
838 I2-I — 22 31 3*5 +39+64 — 53 83 130 89 237 + 107
839 136 — 36 3 3-2 +26 — 355 — 96 360 255 96 237 — 18 877 53*o — 24 24 6*0 +36 — 215 — 103 240 244 82 233 — 11
882 592 — 26 5 3-7 +34 +42 — 146 160 165 82 232 + 67
883 59'3 — 35 45 2-3 +24 — 529 — 523 740 225 88 231 + 6 947 14 50 2 — 20 51 6-1 + 32 +1030 — 1*795 2*100 151 71 226 + 75 953 56*8 — 24 47 3-6 +28 — 76 — 47 89 238 72 224 — 14 970 15 15 2 — 36 25 49 + 17 j — 51 — 55 75 223 78 219 — 4
1010 51-3 — 25 45 3-3 -+ 19 | — 13 — 48 50 195 66 214 + 19
1012 529 — 22 16 27 + 22 | — 15 — 35 38 203 61 214 + 11
1035 16 136 — 25 17 3-3 + 17 | — 15 — 39 42 201 62 209 + 8
1044 18*1 — 23 9 4*9 +17 — 21 — 7 32 251 60 209 — 42
1051 217 — 26 9 1*5 +15 - 8—28 29 196 62 209 + 13
1053 23-2 — 34 26 47 + 9 — 9 — 28 29 198 68 205 4" 7
1061 281 — 27 57 3-1 +12 — 17 — 34 38 207 63 205 — 2
1073 42-1 - 34 4 2*5 +6 — 627 — 261 680 247 67 201 — 46
*°75 43'4 — 37 50 3*5 + 3 — 6 — 23 24 195 71 200 + 5
1095 17 7-6 — 26 25 4-8 +7 — 502 —1-167 1*200 204 58 197 — 7
1105 143 — 24 52 36 -f 6 — 8 — 36 37 193 57 196 + 3
1109 187 — 24 3 4-5 _j_ 6 — 14 — 137 140 186 55 195 -}- 9
1113 223 — 37 12 3-0 — 2 — 29 — 35 46 220 68 191 — 29
1118 251 — 37 1 20 —2—5—2 7 27 191 68 191 o
1127 33'8 — 38 58 2*8 — 5 -f- 5 — 15 16 162 69 188 + 26
1158 57 8 — 30 25 3-2 — 5 — 73 — 198 210 199 60 184 — 15
1166 18 6*3 — 21 5 4*2 — 2 — 6 — 2 6 252 51 182 — 70
1169 9 2 — 36 48 1 3 3 — 10 — 131 — 152 200 221 67 181 — 40
"73 13*0 — 29 53 30 — 8 + 30 — 34 46 139 60 180 + 41
1175 15*9 — 34 26 2*1 — 10 — 51 — 122 130 203 64 180 — 23
1182 20*2 — 25 29 31 — 7 — 46 — 199 210 192 55 179 — 13
"99 37'8 — 27 7 3-5 -H+45-6 45 98 5 7 174 + 76
1208 43-3 — 22 18 6-3 —10 — 57—23 62 248 52 172 — 76
1211 47-5 - 26 27 2 3 — 13 — 4 — 75 75 183 56 170 — 13
1216 503 — 21 16 37 — 11 +31 — 23 39 127 51 170 + 43
1222 546 — 30 3 2*9 — 16 — 31 — 19 36 238 60 169—69
1225 591 — 27 51 37 — 16 — 62 — 254 260 193 59 168 — 25
1228 19 i-o — 38 6 4*4 — 20 + 60 — 118 130 153 69 169 -|- *6
1231 23 — 21 13 32 | — 14 — 7 — 36 37 191 52 167 — 24
1237 7 9 — 25 28 5*1 — 17 + 34 — 35 49 136 56 166 + 30
1265 29*1 — 25 9 48 - 21 -f- 60 — 27 66 114 58 161 + 47
1280 391 — 20 4 5*3 — 21 — 140 — 88 170 237 54 156 — 81
1299 55*o — 28 3 48 — 28 +30 + 13 33 67 62 155 4- 88
1317 20 107 — 22 12 6*2 — 29 + 17 — 32 36 152 59 150 — 2
*354 387 — 25 43 4*4 — 36 — 55 — 148 160 200 65 146 — 54
1363 44*3 — 27 23 4 6 —37 — 11—6 13 241 67 145 — 96
1374 53*6 — 32 45 5*o — 41 — 5 — 4 6 231 73 144 — 87
1376 55*o — 39 7 57 — 42 — 47 — 125 130 202 78 145 — 57
1377 57*3 — 20 21 5 2 — 39 — 35 — 47 59 217 63 141 — 76 1386 21 5 9 — 28 8 5 8 _ 43 4. 99 _ I06 150 138 71 141 4- 3 1393 10*3 — 32 42 5'° — 44 + 33 — 10 34 107 72 140 + 33



TABLE I.
Newcomb —20° to —40°.
N°- >875 «875 Ph«4m' 1875 M V 1 * "~V
fH ° ' ° " HM O O O O
1403 21 19*5 — 22 57 4*o — 44 + 0-006 + 0*020 0021 !7 69 *37 4" 120
1405 21*6 — 22 21 4-8 — 45 -j- 126 — 18 130 99 68 137 4" 38
1423 37*5 — 33 36 46 — 50 + 2 — 74 74 »78 87 137 — 41
1434 46*3 — 37 57 3*4 — 52 4- 91 — 21 93 103 84 135 4- 32
I44i 537 — 29 3 56 — 53 4 21 + 19 28 48 79 133 4- 85
1489 22 27*8 — 21 21 5 5 — 59 + 206 — 155 260 126 80 127 + 1
1497 33*7 — 27 42 4*4 — 62 + 11 — 11 16 135 85 127 — 8
1516 507 — 30 17 1*5 — 66 -f- 328 — 172 370 117 89 126 + 9
1531 23 2*8 — 21 51 40 — 67+44+41 60 47 86 124 + 77
1542 I2*i - 33 13 4'5 ~ 70 4 1—66 66 179 94 122 — 57
1548 16*4 — 20 47 4*4 — 70 — 138 — 89 170 237 89 122 — 115
1558 262 — 38 31 48 — 71+83+6 83 86 100 121 -f 35
1560 267 — 21 36 4*9 — 73 — 22 4 18 28 310 91 122 4 !72
1581 42*4 — 28 49 4 8 — 77 + 77 — 133 150 150 97 120 — 30
Taylor — 20° to — 30°.
I I 1
69 o 15*6 — 23 42 7*57 — 84 +0-078 —0*098 0*125 !4* 102 117 — 24
194 36*4 — 20 53 7*04 — 83 — 12 + 10 16 310 105 116 + 166
492 1 26*2 — 24 18 7*39 — 79 — 46 — 70 84 213 117 112 — 101
527 31-2 — 25 39 8*92 — 78 — 94 + 3 94 272 118 111 - 161
539 32*9 — 25 40 6.59 — 78 — 8 — 6 10 233 118 iii — 122
556 35*2 — 22 21 8*29 — 77 — 17 — 7 18 248 117 113 — 135
590 42*8 — 26 53 7*49 — 76 — 29 + 19 35 303 121 110 + 167
1076 3 6*6 — 29 38 7*09 —58+44 — 86 97 153 140 101 — 52
1306 42*3 — 29 51 7*35 —50+44—88 98 153 148 98 — 55
1390 57*3 — 28 52 772 — 47 -^71 ~ 47 85 236 151 100 — 136
1430 4 37 — 21 2 9*90 — 44 — 29 — 23 37 231 150 113 — 118
1605 29*0 — 28 43 7*05 — 40 + 34 — 44 56 142 157 98 — 44
1667 39*5 — 28 11 7*53 — 38 — 66 — 7 66 264 159 100 — 164
1838 5 2*6 — 20 17 7*30 — 30 + 35 — 64 73 151 161 125 — 26
2086 33*7 — 28 55 8*09 — 27 — 24 + 58 63 338 172 96 +118
2310 6 1*6 — 23 5 674 — 18 | — 17 + 23 29 323 173 161 — 162
2360 6 5 — 27 2 7 82 — 19 | + 1 — 13 13 176 175 156 — 20
2435 15*4 — 29 58 7*96 — 18 0 + 17 17 o 175 342 — 18
2658 407 — 20 29 8 39 — 9 — 13 — 11 17 230 167 214 — 16
2670 417 — 20 58 8*13 — 9 — 15 — 12 19 231 168 217 — 14
2733 48*6 — 24 5 7*48 — 9 + 49 + 32 59 57 169 234 + 177
2780 54*2 — 28 48 8*40 — 10 — 17 — 4 17 257 170 268 + 11
2862 7 4*6 — 25 o 576 — 6 + 50 + 6 | 50 82 167 246 + 164
3093 28*8 — 28 18 678 — 3 — 58 + 54 ! 79 313 162 259 — 54
3238 43*6 — 24 39 8*93 +2 +248 — 244 350 134 159 251 + "7
3342 54*6 — 23 1 833 +4 — 29 + 12 31 293 156 249 — 44
3574 8 197 — 23 38 5'61 +9—71+32 78 294 151 252 — 42
3986 9 4*2 — 25 18 7*30 +16 — 56 — 20 60 250 141 253 + 3
4288 39*2 — 27 3 7*19 +20 — 33 — 36 49 222 134 254 + 32
4582 10 13*3 — 28 20 9*23 +24 — 15 + 10 I 18 304 128 253 — 51



TABLE I.
Taylor — 20° to — 30°.
Nr' 1875 1875 PmT 1875 ^ M M V> * t X-V
hm0' O II H H O O O O
4618 10 166 — 28 56 8'Oi -|- 24 ' —o*oio + 0*058 0*059 350 127 253 — 97
4708 26 5 — 22 58 8*30 -f- 30 — 61 — 31 69 243 123 249 + 6
4827 39-1 — 29 2 7 97 -f 26 — 59 + 26 64 294 122 251 — 43
5170 11 167 — 19 56 7-68 + 38 — 66 — 26 7l 248 in 245 — 3
535o 35*5 — 21 57 8-89 +38 — 17 + 23 29 323 108 244 — 79
5506 566 — 21 27 8*88 +40 + 74 -f- 23 78 73 104 244 + l7l
55'9 57'9 — 20 20 8*88 -f- 4.1 --42 — 28 50 124 102 243 -- 119
5585 12 7'2 — 20 56 8-85 + 4i 1 — 11 11 175 101 242 -- 67
5754 27 2 — 22 49 8 07 +39 +65 — 150 170 157 97 241 4- 84
6189 13 216 — 24 34 7*5' +37 — 65 — 16 67 256 89 237 — 19
6227 250 — 25 28 8*34 +37 — "7 — " 120 265 88 235 — 30
6292 314 — 29 12 716 +32 + 16 + 53 55 17 89 235 — 142
6412 44*1 — 20 22 7-82 +40 — 72 — 37 81 243 82 234 — 9
6541 59'2 — 25 59 8*60 + 34 ! + 32 — 53 62 149 82 232 + 83
6561 14 1*4 — 26 4 9*03 + 33 ! + 140 — 46 150 108 82 232 + 124
1
6684 16*2 — 27 16 8*6o +31 — 245 — 278 370 221 80 228 + 7
6691 16*8 — 27 11 903 +31 + 15 +. 19 24 38 80 228 — 170
6744 23*3 — 28 45 8 03 + 28 + 7 — 9 11 142 80 228 + 86
6812 30 9 — 22 37 776 -f 33 + 10 o 10 90 75 227 + 137
6820 32-2 — 24 29 8 26 +32+72—44 84 122 76 228 + 106
6853 35 9 — 24 35 8 46 +31—67 — 31 74 245 75 226 — 19
6935 48*2 — 25 7 860 + 30 + 5 — 11 12 156 73 225 + 69
7060 15 3-9 — 21 36 866 +30 — 51 — 42 66 231 68 223 — 8
7074 65 — 23 54 818 +28 + 39 — 22 45 119 70 222 + 103
7189 21*1 — 20 46 7'84 + 28 I + 47 — 32 57 124 65 221 + 97
7216 24 6 — 27 45 7*99 +22 — 12 — 2 12 260 70 218 — 42
7297 | 35*7 — 25 1 7 29 + 23 + 5—20 21 166 66 216 + 50
7433 57*6 — 20 34 8-35 + 22 I — 76—41 86 242 60 214 — 28
7452 59*3 — 27 23 8*37 + 18 + 29 — 46 54 148 65 211 + 63
7499 16 5*1 — 27 48 8 93 +16 — 20 +48 52 337 65 210 — 127
7522 7*5 — 22 4 7*52 +20 + 10 — 13 16 142 60 212 + 70
7585 16*8 — 26 52 7*51 +15 — 89 — 62 108 235 63 208 — 27
7593 17*8 — 29 6 773 +14 + 26 — 28 38 137 65 208 + 71
7599 18*2 — 26 16 8*37 +16 — 1 — 29 29 182 62 209 + 27
7717 36-3 — 22 53 776 +14 +40 — 68 79 150 59 204 + 54
7930 17 3'9 — 26 33 8*o8 +7 — 51 — 74 90 215 59 197 — 18
7935 4*8 — 26 52 8*41 + 6 + 1 — 17 17 177 59 197 + 20
7951 7*5 — 27 49 8-95 + 6 — 7—63 63 186 60 197 + 11
7999 14 5 — 23 27 797 + 7 — 4 + 9 10 336 55 196 — 140
8009 15*5 — 24 59 744 -4-6 — 58 — 38 69 237 57 196 — 41
i
8028 18*3 — 27 29 7-59 +4—40 — 54 67 217 58 197 — 20
8037 19-2 — 21 18 899 +7—47 — 3o 56 237 52 195 — 42
8066 23*2 — 23 45 7-53 +5 + 14—65 66 168 55 193 + 25
8090 261 — 22 5 8*53 +5—4 — 18 18 193 53 193 o
8137 33*2 — 23 46 7 86 +3—38—23 44 239 55 190 — 49
8171 37-2 — 21 58 922 +3 — 17—64 66 195 53 189 — 6
8181 38 2 — 26 55 7*56 +0 — 9 — 24 26 200 58 189 — 11
8249 47*4 — 22 57 8*41 + 1 +51 — 19 55 m 53 186 + 75
8355 18 o*2 — 21 52 8-99 — 1 — 4 — 22 22 190 52 183 — 7
8364 1-5 — 26 7 7*64 — 4 — 57 — 30 64 242 56 183 — 59



TABLE I.
Taylor — 20° to — 30°.
Nr' ,8°75 1875 P™T' >875 M'' M * V * * *~V'
k fft ° f ° ° 0 0 O O O O
8376 18 2*5 — 23 47 7 81 — 3 —0029 —0052 0060 209 54 183 — 26
8403 7 5 — 24 2 8*56 — 4 — 7 + 2 7 286 54 182 — *04
8436 14 6 — 26 29 878 — 6 — 36 -j- 4 36 276 56 180 ■— 96
8475 2i*2 ~ 25 7 8*24 — 7 4* 58 — 43 72 *27 55 *78 + 51
8492 22-8 — 24 9 8*35 — 7 — «3 — 8 15 238 54 177 — 61
8537 29 2 — 29 20 8*46 — 11 — 58 + 6 58 276 59 176 — 100
8539 29'3 — 29 34 8'11 — 10 — 25 — 25 35 225 60 176 — 49
8613 41*4 — 20 17 8-13 --9—48—31 57 237 50 171 — 66
8628 43*1 — 22 24 874 — 10 — 22 — 25 33 221 52 172 — 49
8665 49*0 — 23 18 8'II — 12 — 3 — 86 86 182 53 170 — 12
8689 52'i — 28 13 7-88 — 15 — 3 — 10 10 197 58 169 — 28
8698 53 8 — 23 24 8-35 — 13 4- 10 — 11 15 138 54 169 + 31
8727 57*i — 25 o 8*56 — 14 + 41 — 7 42 100 56 169 4" 69
8738 58*5 — 27 28 T34 —16—7+5 9 305 58 168 — 137
8783 19 3'9 — 20 33 T93 — 14 + 29 — 20 35 125 52 165 + 40
8794 57 — 20 38 804 — 14 + 51 — 17 54 109 52 165 4- 56
8796 61 — 22 47 8 38 — 16 — 79 4* !4 80 280 54 166 — 114
8926 223 — 21 36 8*38 — 18 + 21 — 23 31 138 54 161 4- 23
9006 32 8 — 23 37 8*85 — 21 -f" 10 — 22 24 156 57 160 -f- 4
9158 53*1 — 21 12 8*15 — 25 — 11 — 4 12 250 56 153 — 97
9160 53*3 — 22 59 8-38 -26 4- 14 -f 5 15 70 58 154 4- 84
9213 59*2 — 22 2 7*66 — 26 — 234 — 44 240 259 58 152 — 107
9230 20 2 3 — 20 57 7*22 — 27 — 24 — 81 84 196 57 152 — 44
9343 14*8 — 22 21 7*33 — 30 + 6 — 23 24 165 59 150 — 15
9359 16*9 — 23 52 8 32 — 31 — 12 4-25 28 334 62 149 4- 175
9422 24-8 — 25 18 7*37 — 33 4* 50 — 1 50 91 63 148 -f 57
9424 24*9 — 22 35 8-64 — 32 4- 3 + 34 34 5 62 148 4- 143
9425 25 0 — 22 35 8*97 — 32 — 15 -h 37 40 338 62 148 4- 170 9478 31*2 — 21 26 679 — 33 4" 101 — 25 100 104 61 146 4* 42 9534 36-4 — 26 17 801 — 36 4- !03 4* 1 100 90 66 146 4" 56
9567 41*0 — 23 18 8-21 — 36 4- 36 4- 33 49 47 64 144 4- 97
9586 42*6 — 27 50 716 — 38 4-42 — 17 45 112 68 146 4" 34
9629 470 — 26 3 7*69 — 38 0 — 70 70 180 67 143 — 37
9634 47 9 — 26 35 9.14 —38+31—2 31 94 68 144 4" 5°
9673 52*8 — 27 50 8 09 — 40 4-69 — 49 85 125 69 143 4" 18
9703 56*0 — 25 34 773 — 39 + 48 — 21 52 114 68 142 4- 28
9771 21 30 — 29 o 803 — 42 +81 -f- 18 83 77 71 142 -f- 65
9788 49 — 20 50 76o — 40 4- 19 — 54 57 161 66 139 — 22
9810 7-9 — 21 18 7-80 —41 — 107 — 110 160 225 66 139 — 86
9887 17-0 — 26 5 8-17 — 45 + 27 — 36 45 H3 71 138 — 5
9905 18*9 — 25 1 7*36 — 45 — 69 — 40 80 240 71 138 — 102
9908 19*3 — 21 32 78 o —44+78 + 14 79 80 68 137 + 57
9922 21'1 — 22 15 8*51 — 45 + 135 — 283 310 154 68 137 — 17
6944 23*2 — 24 58 8*67 — 46 +20 — 12 23 121 72 137 + 16
9965 26*2 — 21 14 8*82 — 45 + H + i2 18 49 69 136 + 87
9964 26*2 — 28 26 7-63 — 47 + 215 — 51 220 104 74 138 + 34
9968 26*9 — 28 27 8*67 —47+91 — 81 122 132 74 138 + 6
9979 27-8 — 21 o 8-51 — 46 — 51 — 14 53 255 70 136 — 119
iooii 31-2 — 28 27 8*17 — 48 — 8 — 23 24 199 75 137 — 62
10036 34*4 — 22 29 8'i 1 — 47 +120 + 4 120 88 71 135 + 47



TABLE I.
Taylor — 20° to — 30'.
i
xt a d Photom. b , ,
Nr* 1875 1875 | mag. 1875 /4« M P V *■ X X-r
1 ^______ ______„^
kin O / O U HM O O O O
10038 21 34*5 — 22 14 8 31 — 47 4- °-022 - 0034 0 041 147 71 135 - 12
10106 421 - 23 24 8*30 - 49 - 7 O 7 270 73 134 - 136
10137 46 9 - 20 36 8 41 - 50 + 18 + 127 130 9 73 133 -I- 124
10173 52 6 - 29 13 745 - 53 -f 21 + 20 29 46 79 134 4" 88
10181 54 2 - 25 36 807 - 52 - 32 - 64 72 206 77 133 - 73
10196 560 - 27 39 8 04 - 53 - 17 - 13 21 233 78 133 - 100
10205 57 2 - 22 23 8 31 - 52 - 54 -f 14 56 285 74 132 - 153
10216 59 0 — 29 40 8-32 — 54 j -}- *9 — 24 31 M2 81 l32 - 10
10293 22 8 2 ~ 26 35 8-54 - 56 ( - 59 + 3 59 273 79 131 - 142
10395 24*o - 24 48 8.11 — 59 I - 4 - 37 37 186 81 129 - 57
10440 300 - 21 44 8*i8 — 60 — 28 -f- 24 37 311 80 127 -}- 176
104451 30'7 - 21 2 7*30 — 60 -|- 82 — 44 93 118 80 127 -f 9
10471 34*6 - 27 55 8 54 - 62 j - 30 + 5 30 280 86 127 - 153
10518 41*6 — 20 22 8 95 — 62 — 102 — 159 190 212 82 126 — 86
io577 53'6 - 26 48 9-08 — 66 — 8 4~ *4 16 330 88 125 -f- 155
10655 23 78 — 29 8 870 — 69 — 52 o 52 270 91 123 — 147
10678 ii*8 — 29 10 816 — 70 -|- 31 — 42 52 144 92 122 — 22
10729 19 3 - 21 18 863 — 70 — 60 — 192 200 197 89 122 — 75
10735 I9'9 - 21 53 9'20 - 71 -f- 42 + 34 54 5i 9© 122 + 71
10796 3°'i - 22 56 7 89 - 74 4. 36 + 27 45 53 93 121 4- 68
10809 32*2 - 21 34 817 - 74 ! - 35 + 39 ! 53 318 92 121 4- 163
10838 38-0 — 26 57 643 —76 — 77 — 3 77 268 96 120 — 148
10857 j 40-9 - 22 58 7 82 - 76 — 8 - 95 95 185 95 120 - 65
. I
Taylor —30° to — 35°.
I I !
951 i 2 44-0 — 32 54 9*07 | — 63 4-°'o87 -f 0-003 0087 i 88 135 100 -}- 12
952 441 - 31 20 774 i — 63 -j- 18 o 18 j 90 135 102 -j- 12 1632 4 32*9 - 31 40 8*oo — 40 — 22 o 22 270 158 90 -- 180 2460 6 18 0 - 33 48 8 84 - 19 - 56 4- 1 56 271 173 344 4- 73 2585 32-4 - 32 7 796 - 16 4- 323 - 62 330 101 173 300 - 161
2708 457 - 31 34 913 _ 13 _ 5- 20 21 194 171 287 4- 93
3047 7 22-6 — 33 38 7 42 — 7 4" 42 - 9 43 102 164 281 4- 179
3471 8 8*3 - 31 47 824 4- 2 4- 13 - 49 51 165 155 268 4- 103
4089 9 15-4 - 31 14 6-95 -j" 14 — 15 — 38 41 202 142 260 4- 58
4472 10 o*o — 34 16 690 -j- 18 + 48 + 1 48 89 132 259 4" I7°
4685 23-8 — 32 46 8-32 4-22 — 44 — 25 51 240 127 256 -f- 16
4716 27-2 — 32 44 8*64 4-22 — 31 — 53 61 210 127 255 4" 45
4735 290 - 33 7 87ö 4" 22 | - 24 - 13 27 241 126 255 4- 14
4882 44*6 - 33 11 779 +24-111 - 33 120 252 123 254 + 2
5063 11 46 - 31 53 8 55 4" 26 - 5 - 41 41 187 118 251 4- 64
5261 26-3 - 30 17 8-95 -f- 30 | — 87 - 17 89 259 114 249 - 10 5286 29*6 - 34 6 8*31 4" 26 ; - 7 4- 13 15 332 114 250 - 82 5300 30 5 - 33 57 772 4- 26 j - 278 j -f 88 290 288 114 249 - 39 5331 33'5 - 34 16 8*i8 + 27 , - 27 j — 17 32 237 113 249 + 12 5352 35 5 - 3i 48 ! 5*57 + 28 | - 28 ! - 65 71 203 112 ! 248 -f 45 1 , 1 i L i i i 



TAfcLË 1.
Taylor - 30° to — 35°.
Nr" 1875 .875 PmT' 1875 "• M * V 1 X *~V
ft fft 0 ' ° " " " O O © 0
5572 12 5*2 — 29 54 770 + 32 —0*079 +0-017 0*o8l 282 106 244 — 38
5693 20*8 — 32 5 8*63 --30 - 80 — 6 80 266 104 244 — 22
5952 520 - 32 43 898 -(-30 - 39 - 39 55 225 98 240 + 15
5977 56*2 - 33 37 7 8o 4-29+5-46 46 174 98 240 + 66
6007 13 o*i - 33 27 7 39 +29-5-83 83 183 96 239 + 56
|
6908 14 45*2 — 33 7 8*03 + 23 ! + 38 — 18 42 115 80 225 + 110
7547 16 n*6 - 30 36 5*47 +I3 + 72 - 32 79 "4 67 208 + 94
7750 41*2 — 33 47 7 25 +6—30—60 67 207 67 201 — 6
7854 54-4 - 33 5 7*50 +6+29 - 119 120 166 64 199 + 33
8i39 17 33'5 - 33 3 8*08 - 1 + 75 - 13 76 100 62 189 + 89
8352 18 o*o — 31 1 8*u — 6 — 31 — 3 31 264 61 183 — 81
8402 7-5 - 33 8 7-04 -8 + 13-20 24 147 63 183 + 36
8479 21*8 — 33 37 8-24 — 11 — 20 — 6 21 253 64 170 — 75
8480 21*8 — 33 34 8*24 — 11 — 20 — 15 25 233 64 178 — 55 8499 24*2 - 33 2 7-52 - 11 — 3 — 11 11 195 63 177 - 18
8517 25-8 - 33 3 7'°5 - 12 - 9+14 17 327 63 177 - 150
8559 33*o — 30 38 7*98 — 12 — 13 — 61 62 192 61 174 — 18
9038 19 37*i — 32 5 7*84 —25+62 — 11 63 100 65 160 + 60
9636 20 48-1 — 32 2 7-80 — 40 j + 18 — 48 51 159 72 145 — 14
9657 50'8 - 32 n 8-46 - 41 j + 53 - 49 72 133 72 145 + 12
9717 57*5 - 32 51 846 - 42 | - 10 + 4 11 292 73 144 — 148
10400 22 24*4 — 33 o 4-48 — 60 j + 83 — 23 86 106 87 129 + 23
10438 29*6 — 32 18 748 — 61 ' — 81 — 28 86 251 87 128 — 123
10820 34*5 — 32 46 7-35 j — 62 ! + 82 +52 97 58 89 127 + 69
10915 50*0 — 30 12 7*89 | — 65 s — 4 — 52 52 184 89 126 — 58
i i 1
Newcomb —40° to — 52°.
21 O 20*1 — 42 59 2*6 — 74 +O23I —0-403 0460 150 III III - 39 I
91 1 22*9 — 43 58 3-5 — 71 ! — 5 — 225 230 181 122 102 — 79
187 2 53-5 - 40 48 3 2 - 60 - 2 +24 24 355 139 90+95
216 3 217 — 42 5 67 — 54 + 16 + 7 17 66 143 84 + 18
297 4 36*5 — 42 6 4 8 — 40 — 138 — 107 180 232 157 63 — 169
39° 5 55*3 — 42 49 4*2 ' — 26 + 70 — 42 82 121 166 15 — 106
395 6 0*9 — 45 2 66 | — 68 + 224 230 342 164 10 + 28
429 6 339 - 43 5 3*4 -19 + 36 - 19 41 "8 165 340 - 138
483 7 25*3 - 43 3 3*2 i —11 - 52 +180 190 344 159 307 - 37
508 7 47*9 — 40 15 3 9 - 6 + 5 + 11 12 24 158 291 - 93
525 8 57 — 46 58 2*i —7+24 — 11 27 115 152 299 - 176
553 8 36*5 - 46 12 3*9 -2 - 48 - 27 55 240 147 288 + 48
585 9 3*4 - 42 56 2*5 + 4 ; + 10 - 7 12 125 143 277 + 152
645 10 9*5 — 41 30 4-2 +13 — 144 + 32 150 281 132 265 — 16
675 10 321 - 47 35 4-2 + 9 157 - 52 170 253 128 266 + 13
760 12 1*9 — 50 2 3-0 +12 — 22 — 30 37 216 114 252 + 36
800 12 34-6 — 48 16 2-6 -- 15 — 169 — 19 170 263 108 245 — 18
864 13 42*0 — 41 4 3*7 +20-51 — 22 56 247 94 234 — 13
865 13 42*1 - 41 51 3*5 + 19 - 8 - 21 22 201 95 234 + 33 871 13 47*8 - 46 40 3 0 +14 -45 - 64 78 215 97 233 + 18



f ABLE 1.
Newcomb —40° to —52°.
I : ! | i
vr. a d Photom. b ! » . ,
Nr" 1875 1875 mag. 1875 j « " V >■ X X-V
h tn O / O tf HU O O O O
903 14 i8'i — 44 39 4.8 4" *5 —0*008 —0-030 0*031 195 91 228 4~ 33
914 14 27*6 — 41 36 2 9 -- 17 — 10 — 32 34 197 88 226 -f 29
920 14 33 6 — 46 51 27 + 11 — *6 — 35 38 205 91 224 4- 19
948 14 50-3 — 42 38 2 9 -f-14 — 50 — 62 80 219 86 223 -- 4
949 14 510 — 4i 36 3*5 +15 4" 30 — 26 40 130 85 223 + 93
958 15 3'3 — 48 16 4*4 +8 — 97 — 62 115 237 88 219 — 18
959 15 3'3 — 5* 37 37 + 5 —■ 91 — 65 112 235 91 219 — 16 969 15 13*2 — 40 12 3*6 -f" 14 4" 39 — 24 46 122 81 219 4" 97 984 15 26 8 — 40 45 3*2 4- 12 4" 4 — 49 49 175 81 216 4" 41
1032 16 105 — 49 51 4-4 o — 184 — 62 190 252 84 206 — 46
io93 17 3*2 — 43 4 3'6 — 3 4" 5° — 306 310 171 74 195 4- 24
1115 17 22 2 — 49 46 3-1 — 9 — 9—83 83 186 80 190 4- 4
1121 17 28 3 — 42 55 2-2 — 5 4- 16 — 9 18 119 73 189 4- 70
1135 17 38 8 — 40 5 3 3 — 6 4- 32 — 8 33 104 70 188 4- 84
1162 18 i*9 — 45 58 47 — 13 — 43 — 45 62 224 76 183 — 41
1245 19 13-6 — 44 41 4-3 — 24 4~ 20 — 24 31 140 76 167 4~ 27
1396 21 127 — 41 20 5-2 — 45 4- 57 4- 5 57 85 82 142 -f 57
1451 22 0*3 — 47 34 2-i — 53 4- 137 — 175 220 141 92 133 — 8
! i
Gill — 40° to — 52°.
4 23 59-5 — 42 27 7*4 — 73 4-°'°92 —0090 0*129 *34 io7 "4 — 20
25 o 3*1 — 46 26 4*02 — 69 -j- I29 — 190 230 146 110 112 — 34
38 5-6 — 42 52 6-2 — 73 — 105 — 60 120 240 108 113 — 127
78 12-5 — 43 56 6-52 — 73 48 00 48 90 110 112 4" 22
110 i8*6 — 51 44 6*8 — 65 4" 534 — 25° 59° "5 114 109 — 6
119 20'0 — 44 25 4*12 — 72 4" 101 4" 3° 100 73 111 111 4" 38
131 227 — 51 13 6*2 — 66 -- 139 — 20 140 98 114 108 4- 10
138 23-2 — 41 21 68 — 76 4" 4 — 3° 3° 172 in iii — 61
142 24*3 — 41 38 6*2 — 75 I — 8 4- 20 22 338 in III 4" *33
143 243 — 40 12 685 — 77 4- 37 — 80 88 155 110 III — 44
144 24*4 — 48 54 564 — 68 4- H5 — 120 160 137 114 108 — 29 165 28-3 — 43 7 6-8 — 74 4" 80 4* 20 83 76 113 110 4- 34 173 297 — 48 41 5-62 — 69 4- 46 — 130 140 161 115 108 — 53 I97 33*9 — 45 29 6 2 — 72 4" 26 — 10 28 111 114 107 — 4 201 34-9 — 41 13 8*3 — 76 — 30 — 20 36 236 113 110 — 126
203 35-4 — 46 46 478 — 70 — 15 — 20 25 217 115 107 — 110
225 39-0 — 43 21 6-2 . — 74 — 94 — 120 150 218 115 108 — 110
228 39*5 — 49 31 7-4 — 68 4* 4^ — 10 47 102 116 105 4- 3
235 39'9 — 48 14 5'88 — 69 4" Ï86 4~ 7° 200 70 116 106 -- 36
246 43*i — 47 23 6-28 — 70 — 24 4- 20 31 310 116 106 J 4- 156
253 44'2 — 44 5 6-48 — 73 — 6 00 6 270 115 108 — 162
262 450 — 51 40 5*17 — 65 4- 63 4-30 70 64 118 104 4- 40
304 53-2 — 51 56 8*o — 65 4" 54 00 54 90 119 102 4" 12
330 57*2 — 47 4 5*35 — 7° 4* 6 00 6 90 118 104 -- 14
347 1 o*5 — 47 23 3*56 — 69 — 24 4- 10 26 293 119 103 4" I7°



TABLE t.
Gill — 40° to - 52°.
1 1 1" ri,lT" II ||
No- .875 ««75 'MJ" >875 M " V 1 1 *~~V'
Jf fff O / OM H 0 O O O O
355 I r8 —42 25 6*8 —74 4"o i69 —0*090 0*190 118 118 106 — 12
418 13*2 — 43 59 6*8 — 72 — 17 4- 10 20 300 120 107 -4- 167
435 16'1 — 45 48 7*1 — 70 4- 151 4- 50 160 72 121 101 4- 29
440 16*9 —44 15 6*2 — 72 + 102 + 4° 110 68 121 102 ~r 34
446 i8*i — 41 36 6-8 — 74 — 29 — 90 95 198 120 103 — 95
452 19*3 — 45 11 6*49 — 71 — 6 — 30 31 191 121 101 — 90
484 260 — 49 43 409 — 66 + 133 + 140 190 43 "4 98 + 55
485 26*1 — 50 33 7*2 — 65 — 40 — 80 89 207 125 98 — 109 487 263 — 46 13 5 7 — 69 — 15 o 15 270 123 100 — 170 504 290 — 46 20 77 — 69 + 119 + 90 150 53 124 99 -f- 46
516 317 — 49 27 6-8 _ 66 — 43 + 2o 47 295 124 97 -f 167
522 32*8 — 46 43 T1 — 68 -f- 36 — 10 37 106 123 98—8
526 33 2 — 43 34 6.8 — 71 — 71 — 30 77 247 123 100 — 147
542 367 — 50 40 6*9 — 65 — 21 — 20 29 226 126 106 — 120
564 4*'2 — 51 26 5*57 — 63 +45 — 30 54 «4 127 93 — 31
571 42-0 —4223 62 -7» + 15 '+ 30 34 27 124 100 -f 73
587 45 3 - 48 26 5 7 — 65 -f 136 + 50 150 70 126 96 + 26
592 46*1 — 40 27 6*2 — 71 + 26 — 40 48 147 125 101 — 46
607 48*6 — 46 55 4 28 —66 — 86—90 124 224 127 95 — 129
609 492 — 43 7 5'»2 — 69 — 39 — 50 63 218 126 98 — 120
629 52*2 — 48 o 4*82 — 65 -f 116 -f 20 120 80 128 94 4* 14
632 53-2 — 41 47 6*8 — 69 -j- 48 — 30 57 122 127 98 — 24
642 54 5 — 42 38 5 52 — 68 — 51 — 110 120 204 127 98 — 106
652 567 — 45 19 5*08 — 67 — 16 — 50 52 198 127 96 — 102
685 2 3-0 — 42 28 6'2 — 68 — 18 — 30 35 211 129 97 — 114
695 47 — 4i 27 62 — 68 + 48 — 30 57 i" 130 97 — 25
698 5-1 — 44 24 62 — 66 -f 47 — 2o 5* 113 130 95 — *8
701 5*5 — 51 26 6*2 —61 +2"I5° -f" 660 2200 71 130 89 -f" 18
754 15 5 — 44 38 8>o — 65 + 5 + 10 12 27 131 94 -f 67
766 17 3 — 43 46 6*5 — 65 +91 +50 104 61 132 94 4- 33
774 18*5 — 51 40 57 —60 — 20 4-70 73 344 132 86 4- 102
780 19-5 — 41 25 57 — 65 4- 272 4" 120 300 66 132 95 4" 29
795 22*4 — 48 16 445 — 61 -f- 16 — 20 26 141 132 88 — 53
823 27.6 — 46 25 76 — 62 — 46 — 20 50 246 133 90 — 156
835 29*6 — 51 39 6-2 — 58 4- 7 — 30 31 167 134 84 — 83
865 35*0 — 43 26 4*89 — 62 4- 80 — 60 100 127 135 91 — 36
869 357 —4023 4*09 —63 -- 129 — 40 140 107 134 94 — 13
884 38*3 — 5» 2© 5'48 — 57 + 308 4- 220 380 55 135 82 + 27
888 38'5 — 41 4 6*2 — 62 4- 15 4" 10 18 56 134 93 4" 37
901 40*8 — 46 49 6-8 — 60 — 5 — 30 30 189 136 85 — 104
902 40*8 — 43 22 6*8 — 61 4" 26 — 60 65 157 136 90 — 67 922 44*4 ~ 46 52 78 — 59 4- 36 — 20 41 1*9 136 85 — 34 927 45 6 — 40 27 6*49 — 62 4- 83 — 10 84 97 135 93 —4 941 480 — 41 54 6*2 — 60 4- 48 — 30 57 122 136 90 — 32 982 55*5 — 42 22 7-0 -59 t 4 — 30 30 i72 138 89 — 83
995 57*6 — 48 3 7*4 — 56 — 64 o 64 270 139 81 4- 171 1000 587 — 47 28 5'84 — 56 4" 36 ~~ 10 37 106 139 82 ~~ 24 1010 3 o*6 — 51 49 7*4 — 54 -- 100 4- 80 130 51 138 76 4- 25 1040 64 — 49 12 6* 16 — 55 4- 36 — 30 47 130 140 78 — 52 1048 8*o — 44 53 6*04 — 56 -f 1,1 — 20 110 100 140 83 — 17 III



TABLE I.
Gill — 40° to — 52°.
xr a 6 Photom. b , ,
Nr- 1875 1875 mag. 1875 M » V l X X~V
ft VI ° ' O I " II H O O O O
1054 3 87 — 4> 51 6-8 — 56 —0-018 — 0*010 0*021 241 140 87 — 154
1066 107 — 41 42 8*o — 56 — 7 + >0 12 325 141 86 4- 121
1079 134 — 48 13 601 — 54 + 6 + 30 31 11 141 78 -- 67
1087 15-0 — 43 33 444 — 55 +3045 -- 74© 3100 77 142 84 -- 7
1122 209 — 51 30 62 — 52 4* 7 + 30 3i 13 141 73 4* 60
"39 23*4 — 44 17 7 » — 53 + 47 + 20 51 67 143 81 + 14
1153 26-6 — 47 48 611 — 52+96 o 96 90 143 76 — 14
1167 289 — 5048 576 — 5' + 82 + 80 115 46 144 70+24
1181 3»*6 — 44 8 6-9 — 52 I + 37 -f 10 38 75 144 79+4
1188 32 6 — 40 41 4*65 — 53 | — 8 — 40 41 191 145 83 — 108
1212 367 — 41 10 7*i — 52 — 8 — 20 22 202 146 82 — 120
1221 38 2 — 46 22 64 — 50 j — 67 o 67 270 145 73 + 163
1232 397 — 41 3 6*2 — 51 j -+ 37 — 100 110 160 147 82 — 78
1239 414 — 47 45 577 — 50 — 4 — 20 20 191 145 72 — 119
1267 45*6 — 43 6 7° — 49 — 18 — 40 44 204 147 78 — 126
1291 49*1 — 41 36 71 —49-I- 4 -f 60 60 4 147 80+76
1292 497 — 47 16 72 — 48 + 36 — 50 62 145 147 70 — 75 1295 50-0 — 40 44 5 72 — 49 + 15 — 30 >34 153 149 79 — 74 1297 507 —4647 71 —48 — 5 — 30 30 189 147 70 — 119 1322 547 — 49 58 7 27 — 47 +36 +20 41 61 147 65 + 4
1368 4 3*3 — 49 58 7"4i — 46 + 55 + 10 56 80 148 62 — 18
1379 47 — 46 12 639 — 46 -f 77 -J- 10 78 83 150 67 — 16
1399 8 5 — 44 41 6 90 — 45 -f 37 o 37 90 151 68 — 22
1406 9*3 — 40 41 6-2 — 45 -- 15 o 15 90 152 76 — 14
1410 98 — 42 36 396 — 45 + 59 — 230 240 165 152 72 — 93
1441 15 3 — 44 34 5.22 — 44 +69 — 50 85 126 153 67 — 59
1468 1 20'6 — 46 56 71 — 43 — 15 — 20 25 217 152 60 — 157
1469 I 206 — 44 19 8 3 — 43 -j- 5 — 10 11 153 153 66 — 87 1474 > 2i*4 — 44 27 6*8 —43+i5+6o 62 14 153 65 + 51 1490 j 23*4 — 47 13 6 39 — 42 -f- 67 — 290 300 166 153 58 — 108
1496 240 — 42 14 71 — 43 — 29 — 10 31 251 155 67 + 176
1500 25*6 — 46 48 649 — 42 +36 +20 41 61 153 58 — 3
1509 27*0 — 45 14 5*45 — 42 — 6 — 10 12 211 154 60 — 151
1541 33*3 — 42 8 62 — 41 +37 +4© 55 43 156 64 + 21
1561 37-2 — 48 47 6 8 — 40 + 6 + 20 21 17 154 52 + 35
1574 396 — 50 43 5*45 — 40 — 31 +40 51 322 154 47 + 85
1578 39'6 — 41 18 6*8 — 40 + 15 + 10 18 56 157 63 + 7
1607 447 — 44 12 6-8 —39+26 + 20 33 52 157 57 + 5
1632 48-4 — 51 56 6 5 — 38 ; — 11 — 10 15 228 152 42 + 174
1667 56-2 — 49 39 7 1 — 37 + 16 + 10 19 58 155 43 — 15
1693 59 5 — 49 20 5'61 — 37 — 33 o 33 270 156 42 + 132
1701 5 17 — 49 45 5 08 — 37 | + 36 o 36 90 156 41 — 49
1721 4 5 — 41 23 7-1 — 35 | — 86 + 280 290 343 162 55 + 72
1727 5 9 —4429 7*5 — 36 i + 26 + 110 110 13 160 48 + 35
1789 166 —47 10 72 — 34 — 5 — 10 11 207 159 37 — 170
1801 17-8 — 44 30 8*3 — 33 — 27 + 10 29 291 161 42 +110
1804 184 — 51 42 7-0 — 33+26 + 30 40 41 156 30 — 11
1821 212 — 44 20 6 5 — 33 — 6 — 20 21 197 161 39 — 158
>833 23 5 — 44 58 7 39 — 32 i + 5+40 40 7 161 36 + 29
I 1853 26-4 — 47 10 6*9 — 32 - + 36 — 40 54 138 160 31 — 107



TABLE I.
Gill — 40° to — 52°.
Nr ® ^ Photom. b > „ w X 7 1 — V
1875 1875 mag. 1875
, Of OO tl H O O O O
ft in
1887 5 327 — 47 23 6 8 — 31 —0045 —0040 0-060 228 160 27 4-159
1938 401 — 45 53 6-8 —30+26+80 84 18 163 23 + 5
1950 43-o — 46 38 5*29 — 28 — 36 -j- 10 37 286 162 22+96
1956 43*5 — 4» 38 6-8 — 28 — 7 — 30 31 «93 167 27 — 166
1994 49'9 — 47 59 7'4 — 28 — 14 — 3° 33 205 160 15 + 170
2027 56*1 — 51 14 7*4 — 28 — 2+10 10 349 158 10+21
2059 6 ro — 51 5 7*8 — 27 + 7 o 7 90 158 7 — 83
2062 1*5 — 48 27 6*8 — 27 — 114 — 40 120 251 161 7 + 116
2066 26 — 45 48 77 — 25 +36 — 70 79 «53 «64 7 — 146
2069 3*4 — 45 5 6-51 —25+79+30 85 69 164 8 — 61
2071 35 — 46 11 7-5 — 25 — 98 — 30 102 253 163 7 +114
2077 4.0 — 42 8 570 — 24 — 29 — 30 42 224 167 8 + 14*
2078 4*i - 44 43 703 — 25 — 17 +20 26 320 164 7+47 2092 6*i — 40 20 570 — 24 — 20 +50 54 338 169 7 --29 2096 7*1 — 45 15 6*37 — 25 — 16 — 20 26 219 164 4 + 145
2147 157 — 50 18 705 — 25+7 + 10 12 35 159 357 — 38
2190 22*4 — 48 6 6*15 — 23 — 14 — 30 33 205 160 353 + 148
2201 23-8 — 41 3 8*o — 21 +15 +90 91 9 167 347 — 22
2207 25*1 — 40 17 8*o — 20 -- 26 o 26 90 167 345 — 105
2226 284 — 51 44 5-85 — 23 +100 +90 130 48 157 35' — 57
2229 287 — 45 13 7'37 — 21 +26 — 40 48 147 163 346 — f61
2244 30*2 — 42 o 7*5 — 20 — 18 — 60 63 197 166 342 + 145
2258 33-4 — 50 13 7' 41 — 22 +26 + 140 140 10 158 347 — 23
2269 34 5 — 49 25 6-9 - 21 — 72 + 20 75 286 159 346 + 60
2285 372 — 40 11 8 12 — 18 — 8—40 41 191 166 332 + 141
2286 37*4 — 47 30 7*1 — 20 — 4 0 4 270 161 343 + 73 2323 43*4 — 47 40 7*4 — 20 + 26 — 10 28 iii 160 338 — 133 2331 44*5 — 43 40 7*4 — 18 — 6 + 50 50 353 165 331 — 22 2348 46*9 — 50 28 2 93 — 20 + 36 — 80 88 156 158 339 — 177 2359 487 — 42 21 7'6 — 17 — 7 — 20 21 199 165 326 + 127
2371 50*5 — 42 13 6*2 — 16 +37 +10 38 75 165 325 — 110
2375 51*0 — 50 28 7'i — 19 — 40 +210 210 349 158 336 — 13
23851 53 0 — 48 34 5'o8 —18+6 + 10 12 31 160 333 — 58
2412 ! 571 —4858 7.1 — 18 ! + 6 — 30 31 169 159 332 + 163
2421 | 58*3 — 43 13 6-8 — 15 + 4 — 4° 40 '74 164 322 + 148
2442 7 2*o — 42 8 6*8 — 15 — 29 + 10 31 289 164 317 + 28
2458 4'2 — 51 46 6*21 — 18 — 21 +50 54 337 >56 33» — 6
2471 6'i — 40 10 87 — 13 — 54 — 20 58 250 165 310 +60
2490 90 — 46 33 471 — 15 — 147 + 90 170 301 160 321 + 20
2497 9 5 —44 58 5*25 — 14 — 6—120 120 183 161 320 + 137
2500 97 —44 26 5 4 — 14 | + 112 + 320 340 19 162 317 — 62
2509 n-2 —4638 601 —15!—15 — 30 34 207 160 320 + 113
2524 I3'9 — 46 46 7*4 — 14 i — 35 + 56o 560 357 159 3'8 — 39
2534 15*9 — 46 59 77 — 14 | — 45 — ,0 46 257 158 319 + 62
2577 23*2 — 50 46 5*21 — 15 — 12 o 12 270 155 320 + 50
2605 27*2 — 50 21 69 — 14 — 2+10 10 349 155 318 — 31
2624 302 — 50 19 6*96 — 13 — 22 o 22 270 154 318 + 48
2631 30*9 — 44 1 6*8 — 11 + 4 o 4 90 158 306 — 144
2643' 33 2 — 48 33 6#o8 — 12 — 24 o 24 270 155 314 + 44
2651 j 34*8 — 48 19 578 — 12 — 14 0 !4 270 155 312 + 42



TABLE I.
Gill — 40° to — 52°.
« £ Photom. b , .
' 1875 1875 mag. 1875 N ** V> 1 X X — V
km O / o U H H OOO O
2662 7 35*8 — 48 46 7*0 — 12 4- 0*006 4-°'030 0*031 11 155 313 — 58
2679 39*0 — 44 51 5'25 — 10 — 59 — 570 570 186 156 305 4- 119
2083 39.5 — 40 38 5*27 — 7 -}- 151 — 190 240 142 158 294 -- 152
2710 43*i 47 48 7*6 — 10 — 14 10 17 306 155 308 -- 2
27*5 437 — 46 18 5*45 — 9 — 5 — 10 11 207 156 304 -- 97
2730 45*4 — 46 3 4*28 — 9 — 5 — 10 11 207 156 304 4- 97
2734 47'Q — 50 11 6*02 — 11 — 32 — 50 59 212 152 310 4- 98
2755 49'5 49 *7 4'98 — 10 4* *6 4~ 10 19 58 153 308 — 110
2782 539 — 45 14 5*31 — 7 — 6 -j- 20 21 343 1 SS 299 — 44
2813 58*4 — 44 19 7*2 — 6 — 6 o 6 270 154 296 -f 26
2o22 0 599 — 49 9 ïl ~ 9 ~~ 43 + 10 44 283 152 304 + 21
2828 8 1*2 50 14 6*21 — 9 —' 22 — 10 24 245 151 305 -- 60
2834 1*5 — 46 38 7*0 — 7 — 25 o 25 270 153 299 -f* 29
2846 4'o 48 39 6*8 — 8 -f- 46 — 10 27 102 151 301 — 161
2860 5-9 47 34 5-55 — 7 _f_ 6 — 20 21 163 152 299 -j- !3ö
2925 15-2 — 47 49 7'i — 6 — 4 — 20 20 191 151 297 -f- 106
2935 i6'5 — 51 33 7'i — 8 — 30 +50 58 329 148 301 — 28
2947 187 — 48 6 5*00 — 5-f- 6 — 10 12 149 149 297 4- 148
*974 22*8 49 5 7'* — 6-|~ 6 — 10 12 149 148 298 -- 149
2989 245 — 42 10 6*2 — 1 — 29 — 20 35 235 151 285 -- 50
2998 25*6 — 45 55 6*8 — 3 — 25 — 10 27 248 149 292 + 44
3001 26*0 40 6 7-4 o I — 54 _|_ 10 55 281 151 281 o
3°i6 28-9 47 11 7-2 — 4 — 35 — 30 46 229 148 292 4- 63
3033 317 — 51 23 7*6 — 6 — 40 4* 40 57 315 146 297 — 18
3036 32*1 50 32 6 2 — 5 — 12 — 20 23 211 146 296 -f" 85
3064 36*3 — 44 45 579 — 1 _j_ 26 o 26 90 148 288 — 162
3069 37* 1 — 48 28 6*2 — 4 — 14 4_ io 17 jog ,47 2gi — 15
3°7° 37*1 46 52 4*98 — 3 — 15 — 10 18 236 147 290 4" 54
3°73 377 — 44 58 5*38 — 1 — 6 — 20 21 197 148 288 -- 91
3075 38 2 — 47 39 5 65 — 3 — 35 — 20 40 240 147 290 4- 5°
3089 397 — 49 22 5 41 — 4 4* 16 o 16 90 145 289 — 161
3107 43'' — 45 42 7'i — 1 — 36 — 20 41 241 146 286 4- 45
3I27 45'4 — 44 51 5'*ï o j — 16 o 16 270 147 287 -- 17
3'33 46*3 — 46 3 5'40 — 1 ! — 5 — 40 40 187 145 287 4" 100
3140 47*3 — 40 31 6 8 — 3 j — 19 — 10 21 242 147 276 -- 34
3156 49*6 — 47 3 57 — 1 ! — 15 — 50 52 197 145 285 4" 88
3166 50*9 — 44 34 68 4~ 1 ] — '7 o 17 270 147 281 -- 11
3181 538 — 48 5 6*2 — 1 — 14 — 20 24 215 144 286 4" 71
3'9° 54'6 — 46 45 5-38 o — 107 4" 3° no 285 144 285 o
3191 55'2 — 47 48 77 o — 24 — 40 47 211 144 286 4" 75
3196 567 — 5' 4 7' 4 — 3 — 30 —'- 30 42 225 143 290 4~ 65
3203 57*8 — 51 42 5*58 — 3 — 20 4" IO 22 297 142 290 — 7
3223 59-8 — 46 36 3*91 4- 1 — 46 — 40 61 229 143 282 4" 53
3243 9 3*2 — 5° 43 7'1 — 2 — 2 — 10 10 191 141 286 -- 95
3266 6*3 — 42 45 6*8 4~ 4 4~ 4 — 60 60 176 143 277 -- 101
3281 8*6 — 41 46 6 8 4- 6 — 41 4-30 51 306 143 275 — 31
3283 9*2 — 46 50 6*2 4* 2 — 25 — 10 27 248 142 281 4" 33
3296 107 45 2 666 4- 3 — 38 — 30 48 232 142 279 4* 47
3302 ii*8 — 43 45 5*II 4"4 — 28 — 30 41 223 142 277 -- 54
33»6 13*9 — SQ 32 5*51 o — 31 4- 10 33 288 141 284 — 4



TABLE I.
Gill — 40° to — 52®.
N°- .875 •»» Ph£T 4 * V 1 * i *_V
m ° > ou hu o o o o
3339 9 17*8 — 45 31 7'2 + 4 —0005 + 0*010 0011 333 141 277 — 56
3352 190 - 47 45 71 +2+6-10 12 149 141 281 + 132
3369 22-2 — 50 38 8*4 + I — 31 O 31 270 139 283 -j- 13
3392 25*8 — 50 58 5*78 I — 12 O 12 270 138 283 -- 13
3402 27*4 — 40 6 5*54 -j" 9 4" '5 — 10 ,24 *39 270 + 146
3419 29 8 — 50 42 5 35 +1+7—20 21 161 137 280 + 119
3432 31*9 — 48 12 6-8 + 3 — 24 — 40 47 211 138 279 -- 68
3437 32 3 — 48 48 4*58 +3 — 122 + 10 120 275 138 278 + 3
3444 33*2 -4238 558 +8 + 26-60 65 157 138 271 +H4
3479 39'° — 50 41 1 6'9 + 2 — 12 o 12 270 136 278 + 8
3501 41*7 — 44 11 ) 5'9i 8 — 6 — 10 12 211 136 271 -- 60
3516 44*2 — 42 54 7*1 --9 — 18 — 10 21 241 137 270 -- 29
3521 45*1 — 45 9 5*47 --7 — '6 — • 20 26 219 136 272 + 53
3531 46'5 — 45 37 578 +7—26 + 10 28 291 135 271 — 20
3533 46'9 — 45 58 4*62 +7 — 36 — 40 54 222 135 272 + 50
3549 49*3 — 5° 34 6*2 +4 — 2 — 20 20 186 135 276 -- 90
3558 50*2 — 49 39 602 +4 — 32 o 32 270 135 275 + 5
3576 52*9 — 47 49 62 --6 — 25 — 40 47 212 135 274 -- 62
3610 584 — 46 2 6*6 +8—46 — 20 50 246 134 270 + 24
3623 598 — 51 12 77 + 4 — 30 — 20 36 236 133 275 + 39
3625 10 01 — 41 34 6-8 +12 + 26 o 26 90 133 266 + 176
3626 0*3 — 50 43 6 2 + 4 — 3i — 10 33 252 133 274 + 22 3632 12 — 46 46 5 37 + 8 + 57 — 70 90 141 133 271 + 130 3649 4*2 — 51 12 5*33 +4+7—1Q 12 145 132 274 + 129 3675 8 6 — 50 37 573 + 5 — 3I— 50 59 212 132 273 + 61
36 77 8 7 — 51 8 5 7 + 5 — 59 + ïo 60 280 132 274 — 6
3707 13*1 — 41 3 6*2 -- 14 — 19 — 10 21 242 131 263 + 21
3717 152 — 47 4 579 + 9 + 16 — 30 34 152 13' 269 + 117
3729 169 — 41 1 5*05 +14 — 4* +40 57 3*4 *30 262 — 52
3754 I9'9 — 4* 50 57 + >3 — 7 — 20 21 199 130 263 + 64
3795 27*2 — 43 59 6*8 + 12 — 17 — 40 43 203 128 264 -- 61
3818 306 — 48 35 7*6 + 9 — 23 — 40 46 210 128 267 + 57
3832 33-3 — 42 6 62 +15—29 — 30 42 224 127 261 + 37
3879 41-4 — 48 46 2 98 +9 + 75—6o 96 129 126 265 + 136
3892 43*2 — 47 5 77 +11—76+20 79 285 126 263 — 22
3912 470 — 45 33 8*1 + 12 — 26 — 30 40 221 125 261 -- 40
3930 49"8 — 42 21 6'5 --16 — 40 — 10 41 256 124 259 -- 3
3957 54*3 — 43 8 6*29 -- 15 — 28 — 10 30 250 123 259 + 9
3958 54*4 — 41 33 4 75 +17 + 26—20 33 128 123 258 + 130 3988 589 — 47 o 609 +12 — 117 + 10 120 275 123 261 — 14
4002 11 01 — 46 46 7*5 + 13 i — *5 — 10 18 236 123 260 +24
4011 1*9 — 47 58 7*0 +11—24 o 24 270 123 261 — 9
4014 27 — 51 44 70 + 8 — 39 + 100 110 338 124 263 — 75
4038 6*4 — 45 35 6-8 + 14 — 57 o 57 270 122 258 — 12
4042 6*9 — 48 25 57 + n — 104^ + 10 100 276 122 260 — 16
4102 16*4 — 43 57 7'2 +16 — 7» — 5o 87 235 119 256 + 21
4115 i8'4 —41 59 62 +18 — 18 — 30 35 211 119 255 + 44
4125 19*5 — 41 59 77 +18 — 29 — 10 31 251 119 255 + 4
4158 24*9 — 41 14 6-8 +19 — 64 — 40 75 238 118 253 + 15
4188 29 2 — 46 41 5-88 +14 — 86 — 30 9' 251 118 255 + 4



TABLE I.
Gilt — 40° to — 52°.
I j ——————■——-—y—■
*t_ « ! S Photom. b \ .. i , !
Nr' 1875 | 1875 mag- 1875 \ hi M f V i j * X-V
1 I 1 ' I 
hm I ° ' o 1 // 11 11 000 o
4192 11 29-91 - 46 57 5-62 -(- 14 j + 0*026 —0060 0-065 157 118 256 + 99
4214 33 8 - 49 47 6 96 + 11 ; - 42 - 10 43 256 117 257 4- 1
4252 396 — 45 o 5 59 -f l& - 69 — 10 70 262 116 253 — 9
4281 44*9 - 44 29 476 -j- 17 — 81 — 10 82 263 115 253 — 10
4282 450 - 43 14 66 +19 - 28 — 30 41 223 115 251 + 28
4318 50-8! — 51 24 6 8 + 10 +82 — 20 84 104 116 255 + I51
4331 529: - 51 0 6*4 -f 11 - 12 — 10 16 230 115 254 -f 24
4335 53*2 j - 45 56 7 4 -f 16 +47 - 20 51 113 114 252 + 139
4385 12 1*81 - 48 o 5*82 -f- 14 — 4—40 40 186 113 251 -f- 65
4388 2*4 i - 43 38 6*20 +18 — 50 — 70 86 216 112 249 + 33
4424 85 — 40 26 8-o + 22 - 350 — 110 370 252 110 247 — 5
4441 iro — 48 14 77 +14 - 274 - 60 280 257 112 249 — 8
4444 115 - 51 37 6-8 -- 11 - 2 o 2 270 112 250 — 20
4484 185 — 41 49 6*35 +21 - 119 — 40 130 252 108 246 — 6
4492 19 8 — 50 45 5*24 +12 - 50 - 40 64 231 111 249 -f- 18
4496 202 — 48 13 62 +14 — 604 — 90 610 261 110 248 — 13
4502 213 - 49 32 431 +13 - 23 - 40 46 210 iii 249 -f- 39
4546 290 — 40 20 5*65 -f- 22 — 122 — 30 120 256 106 244 — 12
4560 309 — 47 51 4*16 -- 15 — 206 — 20 210 264 108 246 - 18
4586 357 — 48 7 4-80 + 15 — 94 — 40 102 247 107 245 - 2
4661 48 0 — 43 28 '6 2 -f* 19 ~ 225 — 250 330 222 104 242 4- 20
4666 48-4 — 42 14 5-57 4~ 20 1 — 41 — 5° 65 219 103 242 -- 23
4676 49'9 - 50 31 5 38 +12 - 21 - 30 37 215 107 244 4- 29
4721 57-8 — 40 31 6-8 4" 22 — 31 — 40 51 218 101 241 4- 23
4734 59*5 - 4° 55 60 4" 21 4" 3 — 40 40 176 101 240 + 64
4763 13 4*0 - 41 34 5*95 4-21 - 86 - 40 95 245 100 239 - 6
4765 4'3 — 42 42 5*25 4- 20 — 118 — 60 130 243 101 239 — 4
4778 60 — 50 2 616 -- 12-41 - 30 51 234 104 241 + 7
4812 ii I — 50 37 6-2 4" 12 — 21 — 30 37 215 103 240 -|- 25
4854 188 — 48 8 7*2 4- 14 — 24 — 40 47 211 101 239 4" 28
4858 196 - 40 51 5*89 4"2i — 8—40 41 191 98 237 4- 46
4868 21*8 — 50 31 5*51 --11 — 2 — 20 20 186 102 239 4" 53
4911 291 — 41 46 6-8 -- 20 — 30 — 10 32 252 96 236 — 16
4913 296 - 43 30 6*2 4-18 - 61 - 40 73 237 97 236 - 1
4916 29 8 - 45 47 6*o -f 16 + 5 - 40 40 173 98 236 + 63
4934 32'3 - 49 19 6-5 +12 - III o 110 270 101 237 - 33
4959 362 — 41 26 6*2 4-20 —30 — 10 32 252 95 235 - 17
4972 38 7 — 50 48 478 -- 11 | 4" 7 — 40 41 170 100 236 4- 66
5003 44-0 - 46 17 6 02 4" 15 ! — 5 ~ 5° 50 186 97 234 4- 48
5019 46-2 — 46 31 6*8 -f" 15 - 46 — 20 50 246 96 233 — 13
5044 51-0 - 44 12 4*22 + 17 j - 17 - 30 34 210 95 233 + 23
5065 53 4 - 43 36 6-8 4- !7 | — 105 - 70 120 236 94 232 - 4
5066 53'9 - 45 o 4-67 +16-6-40 40 189 95 232 + 43 5085 58 4 — 40 35 476 + 20 - 20 — 40 45 207 91 231 + 24 5094 596 - 48 7 6-8 + 13 - 54 - 40 67 233 96 231 - 2
5124 14 52 — 41 3 6-8 +19 —41 — 20 46 244 90 230 — 14
5170 12 7 - 44 37 4 98 + 15 | + 15 - 110 110 172 91 229 + 57
5208 18-1 — 44 49 4-52 + 15 — 17 — 20 26 220 91 228 + 8
5220 19 8 - 43 46 7 4 -- 15 — 39 — 70 80 209 90 228 + 19
5249 24 2 — 49 54 478 + 9 ; — 42 — 20 46 244 94 227 - 17



TABLE I
Gill - 40° to — 52°.
| 1 ||! 1 
Nr* Jtc I«7C M V 1 \ x \ X — V
1875 1875 mag. 1875
[ >
~1
h fff 0 ' 0 " * * O O O 0
5259 14 26*2 —41 33 6.8 4- 17 —0*019 —0*030 0036 212 88 227 -- 15
5268 27-6 — 40 58 6*2 -f 17 — 8 — 30 31 195 88 226 4- 31
5278 29*5 — 48 53 4*21 — 10 j — 23 — 40 46 210 93 226 -- 16
5279 29*6 — 42 34 7*4 16 I — 29 — 30 42 224 88 226 4* 2 5288 31-0 — 46 2 6*8 -f 13 | — 202 — 250 320 219 91 226 -j- 7
5332 38*1 — 46 55 6*8 -f- 11 | — 45 — 40 60 228 91 225 — 3
5336 39*4 — 43 2 6*8 4- 15 ; — 18 — 20 27 222 87 223 -f 1
5362 42*9 — 42 18 6*8 -- 15 : — 52 — 30 60 240 86 224 — 16
5440 566 — 46 34 4*oi -- 10 | — 15 — 4° 43 201 88 221 -j- 20
5470 15 o*5 — 44 48 4*51 + 11 | — 17 — 3° 34 210 86 220 10
5490 4*5 — 44 1 5*14 + 11 i — 28 — 40 49 2Ï5 85 219 -f 4
5504 7*2 — 47 36 7*2 8 + 16 — 50 52 162 87 2i9 -f" 57
5509 7*9 — 41 1 5*36 --13 ~~ 4 — i° 11 158 82 220 -- 62
5510 7*9 — 43 1 6*8 -- 12 — 62 — 30 69 244 84 219 — 25 5529 io*8 — 40 20 5*86 -f- 14 j — 20 — 3° ! 36 2i4 81 219 5
5545 13*3 — 47 5i 68 -f 7 — 1640 — 270 j 1*700 259 87 218 — 41
5547 13*4 — 47 28 5*15 4-81—115 — 140 ! 180 218 87 218 o
5618 25*1 — 40 4 6-8 4- 13 | 4- 37 — 70 ! 79 I52 79 2i7 4" 65
5631 27*3 — 44 32 4*93 4"9 — ^ — 5° 5° 187 83 214 4~ 27
5647 297 — 42 9 4-21 4" i° — Ï52 4" 5° 16° 288 81 216 — 72
5666 32*6 — 44 15 4*68 4-8 — 189 — 260 320 216 83 215 — 1
5723 41*5 — 45 1 6*35 --7 4" 58 — 4° 7° I25 82 212 -|- 87
5735 43'6 — 50 14 6*47 --3 4" 0 1^ 9° 86 211 4" i2ï
5772 49*7 — 43 43 6*8 7 — 62 — 60 86 226 80 211 — 15
5779 5i'° — 4i 23 5'°4 4* 9 ~ 4i — 20 46 244 78 211 — 33
5816 577 — 44 50 4'95 4- 5 4" 15 I 4- 20 25 37 81 209 4- 172
5822 58*3 — 48 5 6-8 4- 2 4* 16 — 40 43 158 83 208 4- 50
5846 16 2 8 — 40 47 6*2 4-7 — HO — 14° ï8o 218 76 209 — 9
5853 3*8 — 49 34 7'2 4- 1 — 43 — 2° 47 245 83 207 — 38
5888 io*6 — 42 21 5-81 4- 5 4- 4 — 20 20 169 77 207 4- 38
5899 12*2 — 47 53 679 4" 1 — 4 — 3° 3° 188 82 206 -- 18
5905 13*1 — 49 16 5*57 o 4" 6 — 3° 31 169 83 206 4~ 37
5907 13*7 — 43 36 6*2 4"4 — 61 — 30 68 244 77 207 — 37
5981 25*3 — 49 8 7*1 — 1 — 14 — 20 24 215 82 204 — 11
. 5996 27*6 — 42 36 570 4" 3 — 7 — 3° 31 193 76 205 4~ i2
6014 31*3 — 48 30 7*4 — 1 { 4" ^ — i° 12 x49 81 203 4" 54
6044 36-1 — 40 36 5-85 + 3 j — 20 — 60 63 198 73 201 4- 3
6087 43*8 — 40 30 6*8 ~h 2 \ — 20 — 4° 45 207 72 200 — 7
6090 44*0 — 41 34 8*i -- 2 ! — 19 — 20 28 224 73 200 — 24
6098 45*2 — 42 9 5*13 4- 1 | 4" 37 — 30 48 129 74 199 + 7°
6108 46*5 — 50 28 6*5 — 4 ! — 2 — 30 30 184 82 198 4- 14
6109 466 — 43 7 6*8 o i — 28 — 20 34 234 79 198 — 36 6116 47*9 — 40 37 6*8 4- 1 ! 4- 3—20 20 171 72 199 4- 28 6169 56*8 — 43 56 6*2 — 2 | 4- 15 4" i° 18 56 76 197 4- 141 6190 17 0*5 — 46 52 7*4 — 4 ; — 15 4- 10 18 3°4 78 196 — 108
6193 1*7 — 44 24 5*io — 3 — 27 — 50 57 208 75 196 — 12
6271 15*2 — 44 2 57 — 5 — 28 — 30 41 223 75 194 — 29
6287 17*0 — 51 50 6*8 — 9 — 11 — 30 32 2oo 83 192 — 8
6290 17-5 — 50 31 5.6 — 9 i — 12 — 30 32 202 80 192 — 10
6318 226 — 45 57 7*i —7 I — 67 — 20 70 253 77 190 — 63
i 1 | j 



TABLE I.
Gill — 40° to — 52°.
wmtftmmÊÊÊÊmm
XT a i Photom. b i , „ t/> ü y ï — v
Nr' 1875 1875 mag. 1875 f*m M XXV
km 0 ' o « * 000 o
6328 17 24*8 - 4.8 26 j 6-8 - 9 -0*024 -f0050 0055 335 78 190 - 145
6338 26 3 - 46 25 j 471 -8-25-40 47 212 77 190 - 22
6365 30*8; - 49 20 ! 5 02 — 10 4* 114 - 180 210 148 80 189 -f 41
6384 344 - 45 54 7*1 -9-5-10 11 207 76 187 - 20
6428 41-4 - 40 3 5*06 - 7 | 4* 3 — 30 30 '74 7° l87 + '3
6431 42*5 — 45 33 6*8 — 9 | — 16 — 10 19 238 75 187 — 51
6459 47*6 — 44 19 5*04 — 9 ! — 38 — 20 43 242 74 180 — 56
6469 48 9 - 41 42 4-88 - 9 ; - 19 - 20 28 224 72 185 - 39
6510 56*9 — 50 6 401 — 14 — 3 — 3° 3° 186 79 184 ~ 2
6514 57*8 - 43 26 5.34 - 11 + 15 - 120 120 173 73 183 + i°
6535 18 i*6 — 47 32 6*2 — 13 — 14 — 4° 42 199 77 1^3 16
6546 3*2 — 50 35 7'2 — 15 i — 2i — 80 83 195 80 182 — 13
6568 6-8 - 44 15 5*54 - 13 ! + 5» + 20 61 71 74 182 -f 111
6572 7*2 — 51 6 6*2 — 16 ; — 21 — 5° 54 203 81 182 — 21
6585 97 - 42 20 6*5 - 13 j + 4 - 30 30 172 72 182 + 10
6619 15*2 — 44 10 5*62 — 14 | -f- 15 — 3° 34 153 74 180 27
6634 177 - 46 2 3*86 - 15 ! - 5-50 50 186 76 179 - 7
6646 192 - 49 8 4-17 - 17 j + 155 - 260 300 149 79 178 29
6661 22-5 - 46 o 5*23 -16-5-50 50 186 76 178 - 8
6703 29 8 - 48 1 6 2 _ 18 ; + 26 -f 20 33 52 78 176 + 124
6745 37-3 — 50 13 6*66 — 20 i -f" 36 ~~ 4° 54 138 80 176 4" 38
6748 37*8 - 49 45 7 7 - 20 | - 32 - 10 33 253 80 175 - 78
6754 39*0 — 40 32 5*30 — 17 ; — 20 — 30 36 214 7° 172 - 42
6758 39*8 - 43 49 5-86 - 18 i -f 26 - 20 33 128 73 174 4* 46
6774 43-1 - 46 44 5 61 - 20 -f 26 - 20 33 128 77 173 4- 45
6776 43 4 - 41 51 6-8 _ 18 7 - 30 31 193 72 173 - 20
6794 47*o - 49 9 7'0 — 21 Ji — 33 ~~ 5® 60 213 79 172 41
6821 51*2 — 48 27 77 — 21 — 24 — 40 47 211 78 172—39
6845 55*2 — 48 35 7*o — 22 I 4* 36 _ 4° 54 138 78 *7° + 32
6856 57*3 — 50 30 62 -22 -31 - 40 51 218 80 170 — 48
6901 19 5*5 - 45 24 605 - 23 4-89 -70 113 128 76 168 4- 40
6909 7 2 - 45 41 5*45 - 23 - 5 - 10 11 207 76 168 - 39
6943 12*9 — 51 28 62 — 26 4" 64 4- 10 65 81 82 167 4" 86
6956 15*2 — 40 51 4-30 — 23 4" 26 — 14° 14° 17° 72 166 — 4
7006 24-3 — 45 32 5*89 — 26 - 16 — 40 43 202 77 163 — 39
7015 25*9 — 48 22 512 — 27 | — 14 - 3° 33 205 80 165 — 40
7100 41*1 — 47 52 6'8 — 29 ] — 14 — 4° 42 199 80 160 — 39
7103 42 0 — 42 M 8-o — 29 4" 37 - 3° 48 129 74 159 30
7115 43 4 - 40 12 5*55 — 29 ; 4" 49 — 3° 58 122 72 160 -- 38
7131 466 — 42 12 4*25 — 29 4~ 4 4" 4° 4° 6 74 158 4" 152
7162 517 — 43 23 6*2 — 30 4" 15 0 15 9° 76 159 4" 69
7163 519 - 45 27 5*99 - 31 4" 5 - 30 30 171 7| 159 - 12 7219 20 i*4 - 44 15 7 ° - 32 4" 4 0 4 90 78 156 4- 66 7237 3 8 - 43 8 60 - 33 - 18 - 120 120 189 77 155 7 34 7272 10*2 — 44 55 80 — 34 4" 47 4" 3° 56 57 79 *54 4" 97
7282 12*6 — 50 23 5*9 — 35 _ 335 — 250 410 233 84 154 — 79
7292 14*0 — 42 26 5*9° — 35 H~ 59 — 110 130 151 77 154 4* 3
7297 15*4 — 42 49 5*90 —35|-i8 o 18 270 77 153 — 117
7357 25-3 — 44 56 5*29 — 37 | 4" 15 " 4° 43 !59 80 152 — 7
7177 28-8 — 47 43 3*37 — 38 !i 4" 56 4~4° 69 54 83 150 4~ 96
4- 96



TABLE t.
Gill — 40° to —52°.
No ? o Photom. b > $ ^ y, x x X~V
1875 1875 mag. 1875
i
^ fff o I OU H H OOOO
7393 20 31*6 — 47 16 8-2 — 38 —0-005 — 0-020 0021 194 83 150 — 44
7404 33*7 — 45 20 7*13 — 39 — 6 + 10 12 329 81 149 — 180
7437 38-8 — 46 19 7*4 — 39 — »5 — 10 '8 236 82 149 — 87
7452 40-9 — 46 41 5*07 — 39 4* 47 4" 10 48 78 83 <48 -+■ 70
7461 42*4 — 52 4 5*27 — 39 4" *7 — 20 26 '4° 88 148 + 8
7478 45*5 — 40 17 5*49 — 40 4" 60 — 100 120 '49 77 '47 — 2
7500 494 — 44 35 6 2 — 42 — 552 — 980 i 120 209 81 14C — 63
7508 51-4 — 51 45 601 —41 — 87 4- 130 160 325 89 147 1— *78
7509 517 — 43 3° 7'1 — 4* 4" !5 4" 10 f8 5^ 81 146 + 90 7544 58*3 — 41 53 572 — 43 4- 26 — 20 33 128 81 144 + 10
755° 59"2 — 49 2® 6*2 — 43 4" 26 — 5° 56 '53 87 144 9
755' 59*4 — 45 53 5*7 — 43 4" 26 — 40 48 147 84 144 3
7563 21 1*9 — 43 53 6*8 — 43 — 7 — 40 4* '9° 83 144 46
7602 9*4 — 49 '4 6-8 — 44 — 33 — 9° 96 200 88 143 — 57
7614 1 ro — 47 34 6*2 — 44 -[* 26 — 5° 56 153 87 142 11
7638 16-0 — 47 9 5*7 — 45 4-67 — 40 78 121 87 141 4 2
7645 16*4 — 41 32 6*04 — 46 4- 15 -f 10 18 56 83 141 + 85
7662 19*0 — 43 5 573 — 46 — 61 o 61 270 84 141 — 129
7690 24*2 — 41 44 5*53 —48—8 + 10 13 321 84 140 -j- 179
77 52 35*1 — 44 4 68 —49 -f 210 — 80 230 111 87 137 4 26
7770 38*1 — 47 58 8*o — 49 — 14 0 '4 270 90 137 133
7783 40*2 — 47 52 5*86 — 5° 4" *46 — 320 350 155 90 136 19
7785 40*5 — 48 21 6*8 — 49 — 14 — 10 '7 234 90 136 98
7791 417 — 47 11 77 — 5° 4" 26 — 60 65 157 9° !36 21
7930 22 7*i — 41 59 6.2 — 55 4" 559 — 800 980 145 89 132 13
7981 15-4 — 46 33 5 98 — 56 4- 232 — 7o 240 107 93 131 + 24
8017 22*3 — 44 23 4'43 — 57 — 38 o 38 270 93 129 — 141
8037 248 — 43 54 74 _ 58 — 6 4- 10 12 329 94 «29 4* 160
8057 291 — 48 57 6*8 — 57 4~ 46 — 30 55 123 97 128 4- 5
8059 29*2 — 41 14 6*29 — 60 4~ «5 — 80 81 169 92 128 41
8066 306 — 47 21 74 — 58 4- I27 — 70 150 119 96 128 4 9
8075 32*5 — 50 15 7*47 — 57 4~ 64 — 7° 95 *38 98 128 10
8090 35*2 — 47 51 62 — 58 4- 6 — 340 350 170 98 127 — 43
8091 35*2 — 47 33 2*26 — 58 4" *67 — 3° 17° 100 97 127 4* 27 8093 35*4 — 44 54 6-43 — 59 4~ 37 4" 3® 48 5» 95 127 4* 76
8097 36*3 — 42 4 5'°o — 60 4" 4 — 100 100 177 94 127 5°
8108 38*3 — 47 12 5-50 — 59 — 45 — 20 49 246 97 127 — 119
8(12 38*6 — 49 38 6-2 — 58 4- 210 — 50 220 104 98 127 4- 23
8117 39#o — 50 20 6*67 — 57 -- 111 — 270 290 158 99 126 32
8126 41*0 — 51 59 3*86 — 57 4" 128 — 60 140 115 100 126 4- "
8157 46 2 —49 16 57 — 59 4" 232 — 90 250 112 99 ,125 4- 13
8214 570 — 42 9 5*97 — 64 — 41 4" 60 73 326 97 124 4-158
8233 59*8 — 44 12 4*57 — 63 — 28 — 30 41 223 99 123 — 100
8234 59*9 — 50 17 6*59 — 60 4" 36 — 10 37 106 102 122 4" «6
8246 23 30 — 43 32 6*o6 — 65 — 355 — 30 35° 265 99 122 — 143
8247 3*2 — 41 16 6*19 — 66 4" 26 — 60 65 157 97 123 34 8249 3*3 — 45 55 4*23 — 63 4" l6i — 5° *7° 107 100 122 4" *5 8274 8*i — 41 47 5*90 — 67 -- 93 — 120 150 143 98 122 — 21 8306 13*8 — 51 o 6-15 — 61 4- 35 — 90 97 159 104 120 — 39 8321 16*5 — 42 17 6*9 — 67 — 41 — 10 42 256 100 121 I — 135



TABLE I.
Gill — 40° to — 52°.
Nr a ^ Photom. b # w X XX — V
1875 1875 mag. 1875 ™
1
Jl m O I O O H H O O O O
8323 23 16*9 — 43 49 6 8 — 66 + 0004 —0-030 0*030 172 101 120 — 52
8345 20*3 — 50 51 6-42 — 62 -- 17 O 17 90 105 119 + 29
8351 22-2 — 45 11 673 — 66 + 15 — 40 43 *59 102 119 — 40
8363 23*8 — 42 41 6 5 — 69 — 84 — 100 130 220 101 120 — 100
8366 247 — 45 32 600 — 67 +26 — 20 33 128 102 119 — 9
8387 282 — 43 19 504 — 68 + 37 — 30 48 129 103 118 — 11
8427 35*3 — 42 58 To — 69 + 15 — 60 62 166 104 117 — 49
8438 37'3 — 45 47 5*9 — 67 +309 +20 310 86 105 117 4- 31
8451 39*4 — 40 53 645 — 7« + 93 — 40 101 113 103 lis + 5
8458 40*6 — 50 55 5 52 — 64 i + 7 — 20 21 161 108 115 — 46
8479 44*0 — 48 5 6-8 — 66 ! — 14+20 24 325 I0^ !I® -j- !5!
8495 47.1 — 50 8 78 — 65 +93 + 10 93 84 109 114 4" 30
8542 546 - 49 30 575 — 66 — 3 o 3 27o 109 113 — 157
8544 549 — 5i 2 5*45 — 65 —30 + 10 32 288 110 113 — 175
8546! 55*3 —4051 6-8 — 73 + 37 — 30 48 129 106 116 — 13 I I
Auwers —52° to —90°.
4 o 13 61 — 65 36 4 45 — 51 i + 1*675 ! + 1*147 j 2*000 56 117 ! 102 + 4ó
5 19 5 — 77 58 3*06 j — 39 + 2-202 | + 311 i 2-200 82 119 95 + 13 10 28 5 — 53 4 5"6i ! — 64 i + 183 j + 15 ! 180 86 116 106 + 20 13 37*7 — 58 9 4*66 ! — 59 — !5 — 5 16 252 118 102 — 150
16 44*2 — 75 37 5-12 — 42 + 97 + 3 97 88 120 91 + 3
17 50*4 — 70 12 5*54 —47 — 5° — 45 67 228 123 92 — 136 19 56*8 — 57 41 6*03 — 60 — 62 + 5 62 275 120 98 — 177 21 1 2*3 — 62 27 5-40 — 55 + 50 — 5 50 96 121 95 — 1 24 207 — 65 1 5*93 — 52 — 18 — 15 23 230 123 89 — 141 28 329 — 79 8 6" 16 — 38 — 40 — 145 150 196 122 76 — 120
I 33'i — 57 52 0.68 — 59 + 74 — 35 82 115 125 89 — 26
31 41-3 — 79 47 6 23 — 37 + 38 + 15 4i 68 123 74+6
.32 41*4 — 54 9 5'24 — 61 | + 81 + 52 96 57 127 92 + 35
34 512 — 52 14 379 — 62 + 618 + 261 670 67 127 91 + 24
35 51-8 — 68 16 482 — 48 +64+57 86 48 126 80 + 32
37 54*9 — 62 11 3*13 — 53 | + 240 + 15 240 87 127 82—5
43 2 19-5 — 69 14 4*41 — 46 — 65 + 11 66 280 128 72 + 152
44 214 — 60 52 5-52 — 52 — 71 — 136 160 207 130 78 — 129
48 344 — 79 39 5-44 — 37 + 102 — 34 100 109 125 60—49
49 33*3 — 53 5 5"28 — 57 +20 — 45 49 156 135 81 — 75
i
51 37-6 — 68 48 4*34 — 45 + 79 | + 2 79 89 129 67 — 22
54 56'5 — 64 34 515 — 47 — 1 — 36 36 182 133 65 — 117
57 3 o*7 — 60 14 5*23 — 50 ; — 88 — 55 104 238 136 68 — 170
58 20 — 72 24 5*53 — 41 j + 13 + 1 13 86 130 57 — 29 60 9*4 — 57 47 5*88 — 50 — 19 — 28 28 224 137 68 — 156
63 19*0 — 77 51 5*70 — 36 | + 102 + 63 120 57 128 49 — 8
64 27*6 — 63 22 4*97 — 45 i + 320 + 353 480 42 137 62 + 20 70 42 6 — 65 12 3 93 — 43 ! + 289 + 60 300 78 137 51 — 27
72 49 2 — 74 37 3*29 — 37 i; + 37 + ">5 ">0 *6 *3i 42 + 26
73 5i*3 — 53 3 6*46 — 47 — 1 — 57 57 181 145 62 — 119



TABLE I.
Auwers — 52° to —90°.
nZ ö d Photom. b , N fi l X * —V I
No* 1875 1875 mag. 1875 \
I 7 ~m "° ' o " " " ! o o o öj
75 3 567 —6145 4*48 — 43 —0021 -0021 0030 225 140 50 *75 I
I 78 4 12*8 — 62 47 3*52 — 41 i + 22 *4- 49 54 24 Ï41 44 j" I
L 206 - 63 41 5-35 - 40 : + 70 4 145 160 26 141 41+15
I 83 26*5 — 80 30 579 — 32 4* » 4 88 8? 7 l27 30 4 3 1
I 86 31*3 — 55 18 37O — 40 !+ 34 — 8 35 io3 '48 46 57 I
I fin A2'£ co c8 5*58 — 38 — 9 14" 42 43 348 145 36 4" 48 I
£ £.f _ ft 9 5-92 - 35 - 7 1+ 34 35 348 j .36 29 +4.
I 93 5 3'4 — 57 39 4'87 — 36 — 74 4 "O li° 326 J49 30 4 4 I
I qj a*x 71 2Q ('42 — 34 22 -|" 41 47 33^ l37 49 I
£ ,3-1 - C 1! 603 - 30 | - 29 T ■ 29 , 272 | .26 .7 + .05
I 96 13*8 — 67 19 4'92 — 33 | — 7 4 37 38 349 !4i 21 4 32 I
I 103 32-6 — 62 34 3*87 — 32 ! — 17 4 '7 24 l 315 '46 17 4 62 I
I 104 368 — 76 26 5.14 — 30 | 4- 83 4 323 330 14 i 133 j j .li
07 44-6 - 65 47 466 - 3» - 53 - *4 55 255 143 " 4 »6
no 47*6 -5612 4-46 -29 4- 46 - 70 84 147 153 11 -136
I 112 587 — 79 23 570 — 29 ~ 39 4 97 io5 338 130 4 4 26 I
u\ 6 59 -62 8 5* 14 -28 - 2-80 80 181 147 2 - 179
I li 7-8 — KA. <7 60I — 27 — 47 — 20 51 247 154 2 4 115 I
I IV 21*2 — 52 38 -079 — 24 + 11 4 7 13 58 156 355 — 3 I
I 121 26-5 — 69 37 5'6i — 27 — 14 4 2°9 2i° 357 !4Q 35^ I
I I2, 3r3 — 52 53 463 - 23 — 37 ~ 14 40 249 156 349 4 i°o I
ui 46-1 - 6149 3-46 - 23 - 89 + 277 290 342 147 346 + 4
I 128 504 — 80 41 5 79 — 26 — 19 4 75 77 346 128 350 + 4 I
I 129 52'9 — 70 48 570 — 25 — 9 4 9 13 315 138 346 + 3
I 132 7 2*0 — 56 34 5*48 — 19 — 24 — 21 40 238 151 337 4 99 I
I A A — 79 14 5*63 — 26 — 26 — 22 34 230 130 345 4 "5 I
\\l ,6-1 _ 67 43 4-09 - 22 — 8 - 16 18 207 140 338 4 Ui
li <26 _ 52 ti 5'o8 - 14 1 - I - 32 32 182 153 321 4 139
I 1 Ïvjl —7218 3-99 _ 21 4- II — 2 II 100 136 331 — I29 I
I 149 48-9 — 65 52 6-17 - 18 | - 27 - i2 30 246 140 326 4 80 I
I ia 5v6 52 39 3*73 — 12 — 46 -f" !4 48 287 150 310 23 I
i<6 8 200 — 59 6 191 | - 12 — 33 + 2 33 274 143 3>° + 36
<7 S-3 - 77 5 «6 - 21 - 149 + 17 150 278 130 322 +44
I ic8 243 — 65 43 378 — 15 i — 5° — 184 190 196 138 3>4 + "8 I
& 379 - 59 *9 4'57 - iS | - 4. - 3» 51 234 .42 304 + 7°
I x.a _ CA IC 2-17 — 7 4- 4 — 97 ! 97 178 143 297 4 119 I
66 45-5 — 78 30 5*85 I - 21 i — 54 4 15 ! 56 286 129 317 4" 3i
H frl - 60 10 1.2 - 9 - 23 + 46 ; 5> 334 U9 300 - 34
70 9 o-S - 65 54 4-30 - 12 — 26 - 112 IIO 195 "35 304 + I0?
\7° 9 °| _ 7l 5g 470 - .6 j - 71 + 3 1 7' 272 131 307 + 35
I i7t ir8 — 69 12 1*90 | — 14 — '7® 4 9° 19° 298 133 3°3 5 I
» _ C8 A 241 -6—41-4 41 264 137 294 4" 30
76 18-3] -54^9 276 - 2 - 40 + "I 42 285 138 288 j- 3
Vi 27*5 - 56 29 3 15 - 3 - 53 + 6 53 277 136 286 + 9
1 180 3o4 - 72 32 565 - .5 - 42 - 4 42 264 130 300 + 36
1 181 308 - 58 41 4'35 —4 — 25+6 26 284 136 290 + 61
1 184 41-8 - 61 57 37 - f - 3' + 3 3> 276 33 289 + «3
I VII 44*0 — 64 29 316 — 8 — 26 4 7 27 285 133 90 j- 5 I
I 186 524 — 53 59 3-84 + 1 — 32 — 5 32 261 133 79 + I
I 190 10 107 - 69 25 3-78 - 10 ~ 22 + 2 | 22 | 275 '28 287 + 12 |



TABLE I.
Auwers — 52° to — 90'
w Wfc IV 9V •
Nr a <5 Photom. £ , I
1875 1875 mag. 1875 *** *** f* V> * Z * —V I
h 1» 0 ' ® h * # o o ö 7|
loc IO 2v? ""Ja2! 1-1? 13 ~0,040 -0027 0048 236 126 288 + 52 I
'95 233 —58 O 4 22 O — II — a 12 2CO 120 X I
196 276 - 61 3 379 _ 3 _ 2g _ J " y° g» t J5
™ S? = 2 f? !■?, I 'l - i + » 63 3 \l} l"7 - 9
34 3 54 57 4 57 + 3 — $6 — 6 56 264 127 272 -f" 8 I
vm 403 = 5! 1 f " ~ % ~ ft + * * $ \H Hl ± \l
s sï"si: s t 19 t uit & a «s +s
s ..1: =ss js t: ± u t t ï £ s 2; ='d
iii iS =lit S ! ° = % - m t 21 :n % t :?
210 L, II „ 3 13 ~~ I4<* — !s 15° 266 121 272 -- 6|
9 39 7 66 2 3*94 — 4 — 121 -I- 25 120 282 120 26* 10 I
2» 40 5 -6029 4 45 + 2 - 30 I 3? « 224 I "9 26? + 37 I
224 \i?A ~ " H \.TA + ,? I ~ ♦! — " 57 237 117 257 + 201
22c c6-7 ff-, 1-7 5.25 ~~ 5 " '9 56 250 120 267 + 17 I
"9 ,2 8 ? ~ es , ifi T 1 - '57 - 25 160 261 118 259 - 2
229 12 85 — 58 3 3-25 + 4 — 52 _ ,2 ei 2<7 \ 116 2CA — 3 I
230 ,0-8 - 67 .6 432 - 5 - 2I3 - 35 £ 262 u7 257 = 5
231 11 V 78 37 4-51 — 16 — 52 4- 14 54 281; 110 26a — 21 I IX \ïï ~ P 42 3 70 + 3 - + 8° 2?o 293 ? 254 _ 39
S. s=M 3 ±i ±f ES 1 1 ■:! Ig is
242 38-6 - 67 25 3-43 - 4 - 53 - " 56 25Ó Ü4 l\i f *1
537 -705° 3'77 - 8 + 28 Z J? ,£ ^ Jg t '53
248 ,3 0-3 -5247 606 + 9 - l! _ f, 77 243 I 106 2S3 + "
250 6'8 = I? ;j «X + 1 I - 73 - 35 8. 244 .09 243 - I
2C7 c 4 1°8 ~ 4 ! — 20 ~ 25 32 219 112 246 + 27I
257 28 5 — 75 3 672 —I3 —32 — C «2 261 II* *A7 _ I» I
26* fi2 50 275 +9—40 — 36 54 228 103 237 4- 9 I
263 486 -63 4 4-93 - «| - 56 - 85 102 213 106 236 Ijl 2?
268 ,4sï°7 zg* ±| z ? z li\ ft v* 1n t jj
270 11*6 — cc >10 i<(i 1 e > J' «17 I15 230 21 I
271 1 A*y kl fa a. ! 4 — 44 ^4 22^ 100 23° + 4 1 XII -12 ^ 7 j 41 — 44 60 223 107 232 -- 9 I
39 19 0 37 0 | ~~ 3 604 — 737 3700 259 101 227 — 32 I
277 U i — 78 f lï 4 I ~ "I 245 330 222 103 2*6 4- 4 I
278 35't - 62 21 s-?2 'Jj 7 ? ~ 37 45 2I5 "2 232 + 17 I
281 \ l.l — 2\ + 47 — 104 I 110 153 101 226 + 73 I
282 AC'O L ,2 5 54 15 —66 — 4 | 66 266 110 228 — 38 I 2 459 - 59 36 5 50 0 -169 - 134 210 232 98 223 - 9
280 7-7 fa 13 3 9 ' — 42 82 239 103 220 — 19 I
9 7*7 —5820 4-17 — 1 1 — Il8 _ 162 200 217 06 220 4- ?l
292 17 9 - 72 57 578 - 14 - 8 - 43 44 191 i^6 2^2 I 21
296 29*6 — Tl ?8 ?-c7 T 8 + 14 ~~ 88 89 171 101 216 + 45 I
5 5 5 57 | -f- 2 jj 49 — 63 | 80 218 89 214 — 4 I



TABLE I
Auwers — 52° to — 90°.
„ a d Photom. b * ,
No- 1875 .875 mag. ,875 M" M " f l X X~V
k fH 0 ' ° " HU 000 O
298 IS 44*1 — 63 3 3-26 — 7 — 0-197 —0407 0-460 206 97 212 + 6
304 16 3-6 — 54 18 5-27 — 3 — 45 — 53 7o 220 88 207 — 13
305 4.1 —63 22 4-21 — 9 — 11 — 18 22 210 96 207 — 3
309 15 0 — 69 48 5-16 — 14 -|- 175 + 108 200 58 102 206 + 148
310 14-3 — 78 36 4*11 — 20 — 131 — 79 150 238 110 208 — 30
311 197 — 61 21 528 —9—51—26 57 243 94 204 — 39 315 25-2 — 77 15 4*39 — 19 — 310 — 342 460 222 108 204 — 18
317 35*4 — 68 48 206 — 15 4- 12 — 49 5© 166 100 201 -I- 35
318 38*9 — 58 49 377 — 9 4" 9 — 43 44 168 91 201 + 33 322 48 2 — 55 47 3-19 — 8 — 48 — 46 67 226 87 199 — 27
324 49-6 — 52 58 4*34 —7—26+3 26 277 85 198 — 79
328 17 8-2 — 70 o 578 — 18 — 24 — 41 47 210 100 194 — 16
XVII 14-9 — 56 16 3*59 — 11 — 19 — 11 22 240 86 193 — 47
331 14-9 — 55 25 2*89 — 11 — 16 — 23 28 215 85 193 — 22
334 19*9 — 60 35 3*93 — !4 — 69 — 111 130 212 91 192 — 20
338 27 8 — 54 25 5-39 — 12 — 97 — 161 190 212 84 189 — 23
341 33-4 —6440 368 — 18 — 28 — 46 54 211 95 188 — 23
347 56 5 — 63 40 4*56 — 20 + 7 — 220 220 178 94 184 -f- 6
351 18 6-6 — 56 4 5*65 — 18 — 60 — 20 63 252 86 182 — 70
353 "7 —61 33 4-32 — 20 — 31 + 10 33 288 91 180 — 108
357 16-9 -F- 74 2 5-94 — 24 — 2 — 115 110 181 104 179 — 2
360 28-4 — 71 32 4-21 — 25 — 30 — 169 170 190 101 176 — 14
363 34*3 — 73 7 637 — 25 — 32 +11 34 289 103 174 — 115
365 40*6 — 62 20 4-52 — 24 — 41 — 54 68 217 92 174 — 43
367 44-0 — 67 23 4-0 — 25 — 50 + 14 52 286 97 174 — 112
369 48-5 — 53 6 5-03 — 22 — 11 -f 11 16 315 83 172 — 143
372 56-4 — 52 31 5'2i — 23 — 20 — 114 110 189 83 170 — 19
376 19 4*6 — 66 52 5*80 — 27 — 17 4- n 20 303 97 168 — 135
379 17*8 — 54 35 5*6o — 27 — 72 4-22 75 287 85 166 — 121
383 35'° — 72 48 5*66 — 30 — 24 4- 34 42 325 104 162 — 163
385 37*8 — 56 40 577 — 30 4- 38 — 148 160 165 88 162 — 3
387 43-8 — 61 30 6*34 — 31 — 8+22 23 340 92 161 — 179
389 46-1 — 73 14 4-21 — 31 4" 65 — 132 150 153 104 159 + 6
393 56 5 — 66 30 373 — 32 + 1162 — 1*144 1600 133 97 158 -j- 25
394 577 — 53 14 4*99 — 33 — 65 4- 13 66 281 85 158 — 123
397 20 157 — 57 8 2-21 — 35 — 5 — 77 77 184 90 154 — 30
399 271 — 61 57 519 — 36 4- 13 — 37 39 161 96 151 — 10
400 26-6 — 76 37 6-29 — 33 4" I9i — 23 190 97 109 150 4- 53
403 33 7 — 66 39 371 — 36 — 53 — 10 54 259 100 149 — 110
404 34-9 — 52 22 4-90 —38 + 144 — 69 170 116 88 149 4" 33
408 450 — 58 55 3 83 — 39 — 7 — 8 11 221 94 148 — 73
410 49*5 — 77 30 5 48 — 34 — 20 — 366 370 183 109 144 — 39
414 21 1-5 — 70 38 5-21 — 37 + 15 — 35 38 157 104 143 — 14
415 6-8 — 53 47 5*97 — 43 — 19 — 36 41 208 92 143 — 65
418 i6-I — 65 55 4-34 — 40 4- 73 4- 793 790 6 102 140 + 134
419 17*3 — 55 12 636 —44—19+28 34 326 93 140 + 174
422 281 — 65 23 6*45 — 42 — 7 + 4 8 300 102 138 — 162
423 27-5 — 77 56 3-90 — 35 + 19 — 258 260 176 iii 135 — 41 426 40-2 — 70 12 572 — 40 — 55 — 21 59 249 106 134 — 115 428 494 — 55 35 4-68 — 48 + 33 — 37 50 138 97 135 — 3



TABLE I.
Auwers —52° to —QO°.
Nr* j 1875 187$ Pmigm' 1875 M * V * \ X \ Z-V'
i | i ! i I 
i ; I II
\ h m i 0 ' I 0 " " " o o 0 o
430 21 54*0 — 57 19 4 96 - 48 -f- 3*847 -2 600 4 600 124 98 134 + 10
435 ! 22 5-9 - 81 3 | 5-33 - 34 -j- 23 - 55 60 157 "5 125 - 32
437 ; 9*8 j — 60 53 3*07 — 48 87 - 50 100 240 102 130 — 110
438 io-o | — 54 14 5-61 i — 52 -}- 410 — 665 780 148 97 130 — 18
439 I3'9 — 72 52 5'6i - 40 + 1260 — 722 1*500 118 110 127 + 9
443 24*5 — 62 37 i 4*97 - 48 1 + 14 - 28 31 153 i°5 127 - 26
447 33'! — 82 2 | 4*52 i — 34 ' — 68 - 4 68 267 118 120 — 147
451 44 o | - 63 51 6*i6 I — 49 | — 10 I — 45 i 46 193 107 123 I - 70
453 45'9 - 70 44 6'44 - 43 | - 7* 4" 61 94 3" m 121 + 170
454 ! 53 5 | - 53 25 4-3© — 58 ; — 88 — 7 88 j 265 I 103 123 - 142
455 | 56'5 — 69 30 571 — 46 j -f- I4 + 67 68 j 12 111 119 + 107
460 ! 23 9*4 - 62 41 5*82 — 51 -f 151 — 45 160 | 107 109 117 + 19
461 10*2 — 58 55 4*15 - 55 — 63 + 80 102 ï 322 108 118 j -f 156
465 196 - 53 25 5*69 - 60 - 17 -f *35 140 | 353 105 118 + 125
466 21*8 - 63 48 5*79 - 51 -f- 10 — 15 018 j 146 iii 115 — 31
467 25 2 - 78 5 5*94 - 39 - 7 4. 5 9 305 116 109 -f- 164 473 37'3 - 7i » 613 - 45 + 227 -j- 85 250 70 115 109 + 39
477 52*4 53 27 529 - 63 + 4 -f- 50 50 5 iii 113 -f- 108
478 534 - 66 17 481 | - 51 -f 29 - 38 48 143 115 107 - 36
479 55'2 — 77 45 479 j — 39 i — 93 — 155 170 210 118 101 - 109
480 58-3 - 72 8 573 1-45 + 16-27 31 149 117 103 - 46 A o 12*8 — 89 4 7-39 |—28 -f- i° + 5 n 63 119 91+28 B 1 448 - 85 24 5*81 - 32 +23 -j- 35 42 33 121 70 + 37 C 2 39*4 - 86 16 7*93 - 31 - 3+4 5 323 122 54 + 91 D 3 187 — 88 40 8-52 — 29 — 21 — 26 33 219 120 44 — 175
E 4 37'5 — 83 10 692 — 31 —22 + 22 31 315 126 25 + 70
F 5 54*5 - 84 5i j 6*42 — 28 — 18 +61 64 344 124 5+21
G 6 12*7 — 85 56 i 6-95 — 28 — 21 o 21 270 123 o+9°
H 7 30*21 — 86 49 ! 6 51 | — 27 + 4 — 2 4 117 122 340 — 137
I 8 n*41 — 88 30 i 7-92 — 27 — 10 + 18 21 331 121 329 — 2
K 9 14*41 - 85 10 ; 5 63 - 24 - 120 | + 46 130 294 123 313 + 19
L 10 38*1 - 85 26 69 | — 24 : — 8 — 25 26 198 121 291 -- 93
M 11 o*i ! — 83 55 6 39 — 22 j — 71 l — 5 71 266 121 285 + 19
N 12 421 j - 84 26 5*54 - 22 + 59 + 25 64 67 119 259 — 168
O 13 210 i — 85 8 5-85 — 22 I — 89 ; — 30 94 251 118 251 o
! ill
P 14 287, — 87 39 671 — 25 — 112 — 64 130 240 118 236 — 4
Q 15 14*8 - 84 2 5 87 | - 23 + 134 i + 77 150 60 115 223 + 163
R 16 147 — 86 7 6*21 j — 25 + 5 — 2 5 112 I 116 209 + 97
S 17 41-2 - 87 40 ; 5*41 j — 27 - 58 j — 125 130 205 | 118 188 — 17
T 18 17-1 — 89 17 5 64 — 27 | + 25 j — 4 25 99 I 119 179 + 80
U 19 32*9 — 81 40 6*49 — 29 + 6 + 2 | 6 72 i 112 162 + 90
V 20 12-2 - 84 49 7-26 - 29 + 47 + 33 | 58 55 j 115 151 + 96
W | 21 9-3 — 89 26 j 678 — 28 + 2 — 31 ' 31 176 119 135 — 41
X j 22 7*2 — 86 36 i 5*86 — 30 i — 37 + 70 79 332 118 123 + 151
U ! 23 8-5! - 88 10 j 575 - 29 | + 10 + 15 | 18 34 ! 119 108 + 74
! 1 : 1, . 1 1



TABLE II.
1
f =
CQ*
i | j ! | I ! j
90° 95° |IOO°'IO5° iio° 1150 120° 1250 130° 1350 140°! 14501150°| 1550; 160° 165°1170° 1750 180°
90° 85° 8o° 750 70° 65° 6o° 550 50° 450 40° 350 30° I 250 ; 20° 150 | io° j 50 o°
•+- '
o 10*82 082 0*82 083 0*83 084 085 086 088 0-90 0-92 0-94 096 098 roi 1*04 1*07 no 1*13
5 |o*82 0 82 0*82 0*83 0*83 0-84 0 85 0 86 o*88 0 90 0*92 0 94 0 96 0*98 1 01 1*04 1*07 rio 1*13
10 0*82 0 82 0*82 0*83 0 84 0*85 0 86 0*87 0 88 0*90 0-92 0*94 0 96 098 roi 104 107 no 113
15 0*83 0 83 0*83 0*83 0 84 0 85 0 86 0 87 0-89 091 093 0*95 097 099 roi 1*04 1*07 rio 113
20 0*83 0-83 0*84 084 0-85 086 087 088 0-89 091 093 0*95 097 0*99 102 1*04 1*07 no 1-13
25 0*84 0-84 0*85 085 o-86 086 087 o*88 090 0*91 093 095 097 0*99 102 rc>5 ro8 no ri3
30 085 085 o*86 o-86 0-87 0*87 o*88 089 091 0*92 0*94 0*96 098 roo 103 rc>5 108 no 113
35 o*86 o*86 087 087 o-88 o*88 0-89 090 092 093 095 097 0*99 roi 103 1*05 1*08 ru 1*13
40 088 o*88 088 o*88 089 090 091 092 093 0*94 0-96 098 roo 1*02 1-04 ro6 f09 ru 113
45 0-90 0*90 0*90 0*90 0*91 091 0*92 093 094 095 097 0*99 roi 1*03 1*05 1-07 ■ 1*09 ru 113
50 092 0*92 0*92 0*92 093 093 0*04 0*95 0*96 0*97 0-99 1*00 102 103 1*05 ro7 1*09 rji 1*13
55 0*94 0*94 0*94 0*94 0-95 095 096 097 098 0-99 roo roi 1-03 1*04 ro6 1*07 109 ru 1 13
60 0-96 096 0*96 0*96 0*97 097 098 0*99 roo roi 1*02 1*03 1*04 105 1-07 ro8 no 1*11 113
65 0-98 0*98 098 0*98 099 099 roo roi 1*02 ro2 1*03 1*04 1*05 106 ro8 1*09 rio ru 1*13
70 roi roi i*oi! i'oi i"02 ro2 1*03 1*03 1*04 1-04 1*05 106 107 ro8 109 rio ru ri2 113
75 ro4 104 104 104 1-04 rc4 1-05 1*05 ro6 1-07 1-07 107 ro8 1*09 rio rio ru 112 113
80 1-07 1*07 1-07 1-07 1*07 ro8 ro8 ro8 1*09 1*09 109 109 rio rio ru ru 112 112 1*13
85 rio rio no no rio rio rio ru ru ru ru ru ru ru 1*12 1*12 1 12 112 113
90 113 1-13 113 1-13 n* ri? n* 1*13 1*13 1-13 1*13 rn 1*13 1*13 rn 113 1*13 1*13 1*13
95 1-17 j 1*17 1*17 1*17 ri6 1*16 1*16,1*16 n6 ri6 1*15 1*15 115 1*15 1*14 1*14 1*14 1*14 1*13
! |
100 120 120 i-20 120 1*19 1*19 1*19' 1*19 I*I8 1*18 1-17 1-17 116 116 1*15 115 114 1*14 113
105 1*23 123 I'23 1*23 1*22 I'22 1*22 j 1*21 I 2l 1*20 II9 1*19 I*l8 I*l8 l'lj I*l6 1*15 I'I4 1-I3
110 126 1*26 1*26 1*26 1*25 125 1*24 1*24 1*23 i*22 1*21 i*2i i*2o 119 I*I8 117 1*15 1*14 1*13
115 1*30 130 1*30 130 129 i*28 1*27 1*27 126 1*25 1*23 i*22 1*21 120 1*19 n8 i*i6 1*15 ri3
120 1*33 1-33 1*33 i*33 1*32 i'ji 1*30 1*29 128 127 1*25 124 1*22 1*21 1*20 ri8 ri6 115 1*13
125 1*36 136 1*36 1*36 1*35 134 1*33 1-321 1*31 1*29 127 1*26 1*24 1*23 i*2i 119 1*17 115 1*13
130 1*38 1*38 1*38 1*38i i*37 1*36 1*35 1*34:1*33 1*31 1*29 1*27 1*25 123 i*2i 1*19 117 1-15 1*13
135 1*41 1*41 1*40 1-40j 139 138 i'37 1*36 1*35 133 131 129 1*27 1 25 1*22 1*20 118 ri6 1*13
140 i*43; 1*43 1*42 142 i'4i 140 i*39i 1*38, i*3ö i'35 i*33 i*3i 1*28 126 123 i*2j 118 1*16 1*13
145 1*46 j 1*46 1*45 1*44 1*43 142 1*41 1*40 j 1*38 136 1*34 1*32 129 1*27 1*24 1*21 119 116 1*13
150 1*48 1*48 1*47 1*46 1*45 1*44 142 1*411 1*39 1*37 1*35 133 1*30 127 1*24 122 119 116 1*13
155 i'So i'5o i*49 1*48 1*47 1*46 1*44 1 *42; 1*40 1*39 136 1*34 1*31 128 1*25 122 119 n6 1*13
160 1-51 1*51 1*51 i'5o 148 147 145 1*43 1*41 1*39 1*37 1*35 132 129 1*25 1*22 119 i*i6 1I3
165 1*53 153 1*52 r5i'1*50 148 146 144 1*42 1*40 1*38 1*36 1-33 130 i'26 123 120 117 1*13
170 1*54 1*54 1-53 1*52 r$i 1*49 147 1-45j 1-42 1*40 138 136 1*33 1*30 i'26 1*23 120 117 113 !
17S i'55 ï-55 i*54 i'53 **5i *'5o 1*48 146 1*43 141 138 136 133 i'3o 126 1*23 120 117 1*13
180 1*55 1.55 1*54 1*53 1 *51 1*50 148 1*46 143 1*41 138 i'36 133 130 126 1 23 120 1*17 n3



TABLE III.
1 — COS® 8 cos8 a.
\ ohom cfi 30111 ih ora ih 30111 2h o™ 2h30m 3h o™ 3h30m 4h om 4h3om 5bom 5h3om 6hom
\ 0 + + + + + + + + + + ++ +
\ 12ho'u nh30m nhom i0h30m iohom 9h3om 911 om 8h30m 8hom 7h3om 7hom 6h30m óko™
\ _ + + + _ + + + + + + ± + + +
\ i2hom I2h30m i3hom I3h30m i4hom I4h30m i5hom I5h30m i6hom i6h30m i7hom I7h30m i8ho,n
\ 4~ 4" 4* jh -h + 4~ 4- 4* 4- 4- 4-4-
d \ 24hOm 23h 30™ 23hOm 22h 30m 22hOm 2Ih30m 2IhOm 20h30m 20h0m IQ1130m IQhOm l8h30m 18h om
\ 4- 4-4- 4-4- + 4- 4-4- + 4- + 4-
± j
O O'OOO 0019 0*007 0*148 0250 0*371 0*500 0*629 0*750 0*852 0*933 0081 I'OOO
5 0*008 0027 0*074 0*154 0*256 0*376 0*504 0*632 0752 0853 0934 0*981 i*ooo
10 0030 0049 0095 0173 0*273 0*390 0515 0*640 0*758 0856 0*935 0*981 i*ooo
15 0*067 0085 0130 0*204 0-300 0*413 o* 5 34 0*654 o 767 0*862 0*937 0982 i*ooo
20 0*116 0*133 0-175 0*246 0*337 0*444 0558 0*672 0*779 0*869 o*94* 0*983 rooo
25 0179 0195 0234 0*300 0*384 0483 0*590 0*695 0795 0*878 0*945 0984 i'ooo
30 0*250 0*265 0300 0360 0*438 0530 0*625 °'721 0*813 0*889 0*950 0986 i'ooo
35 0*329 0341 0374 0*428 0*497 0*578 0665 0*751 0832 0*900 0*955 0*987 rooo
40 0*413 0424 0*452 0*499 0*560 0630 0707 0782 0853 0*913 0*961 0988 1*000
45 0*500 0509 0*534 0*574 0625 o*686 0750 0815 0*875 0*926 0*967 0*990 rooo
50 0*587 0594 0*615 0648 0690 0740 0794 0*846 0*897 0*939 0*972 0992 1000
55 0*671 0*677 0-693 0719 0753 0793 0836 0*878 0*918 0*951 0*978 0*993 rooo
60 0*750 0755 0*767 0*787 0813 0*842 0-875 0-907 0*938 0*963 0-983 0995 rooo
65 0-821 0*824 0*833 °'847 0*866 0887 0-911 0-933 0955 0*973 i 0*988 0*997 1*000
70 0*883 0 885 0*891 0*900 0 912 0*926 0*942 0*957 0*971 0*982 ! 0-992 0*997 rooo
75 0933 0934 0937 0943 0*950 0*958 0*967 0975 0-983 0*990 | 0*996 0998 rooo
80 0*970 0*970 0*972 0*974 0*978 0*981 0985 0*989 0993 0*995 0*998 0999 rooo
85 0992 0*992 0*993 0993 0994 0995 0-996 0*997 0*998 0*999 °'999 1000 rooo
90 rooo rooo rooo 1000 rooo rooo rooo rooo rooo rooo rooo 1*000 rooo
______
1 — cos2 8 sin2«.
ohom oh 30™ : ih om ih 3om j 2h om 2b 30111 3hom 3h 30™ 4h om 4h 3om 5hom 5h 30111 6hom
\ " + + + ++ + + + + + + + +
\ 1211 om 11 h 30111 nhom ioh 30m 1 oh om 9h 30™ 911 om 8h30m 8hom 7h 30111 7hom 6h 30m 6hom
\ + - + + + + + + + + + + +
\ i2hom i2h30ra i3hom I3h30na i4hom i4h30m i5hom I5h30m i6hom i6h30m i7hom i7h30m i8hom
\ 4- 4*4-4-4- 4-4-4-4- + 4-4-4-
d \ 24hOm 23h 30™ 23hOm 22h 30™ 22liOm 21h30m 2IhOn> 20h 30m 20h Om I9h 30m I9hOm l8h 30m l8hOm
\4-4-4-4-4-4-4-4-4-4-4-4-4-
±
o i'ooo 0981 0*933 0852 0750 0-629 0-500 0-371 0-250 0*148 0067 0019 0-000
5 i'ooo 0981 0-934 0*853 0752 0632 0*504 0*376 0*256 0*154 0-074 0*027 0008
10 i*ooo 0*981 0*935 0856 0758 0*640 0*515 0*390 0*273 0*173 0*095 0*049 0*030
15 rooo | 0*982 0*937 0*862 0767 0654 0*534 0-413 0-300 C204 0-130 0 085 0*067
20 rooo 0-983 0-941 0869 0779 0*672 0*558 0*444 0*337 0*246 0175 0*133 0*116
25 rooo 0984 0-945 0*878 0795 0*695 0-590 0*483 0*384 0*300 0*234 0195 0*179
30 1000 0986 0950 0*889 0*813 0*721 0*625 0*530 0*438 0*360 0*300 0*265 0*250
35 rooo 0987 0*955 0*900 0*832 0*751 0*665 °'578 0*497 0428 0*374 0341 0*329
40 i*ooo 0988 0961 0-913 0-853 0782 0-707 0-630 0-560 0*499 0*452 0424 0*413
45 1*000 0*990 0-967 0*926 0*875 0*815 0'750 0*686 0*625 0*574 0*534 0509 0500
50 rooo 0*992 0*972 0939 0*897 0*846 0*794 0*740 0*690 0*648 0615 0-594 0*587
55 i'ooo 0*993 0*978 0-951 0*918 0*878 0-836 0793 0753 0719 0*693 0677 0*671
60 i*ooo 0*995 0*983 0*963 0*938 0*907 0-875 0-842 0*813 0787 0*767 0755 0*750
65 i*ooo 0*997 0*988 0*973 0955 0*933 0*911 0*887 o-866 0*847 0*833 0*824 0*821
70 rooo 0*997 0-992 0*982 0-971 0*957 0942 0*926 0-912 0*900 0*891 0*885 0*883
75 rooo 0*998 0-996 0990 0-983 0*975 0*967 0*958 0*950 0*943 0*937 0934 0*933
80 i*ooo 0*999 0*998 0*995 0*993 0*989 0*985 0*981 0*978 0*974 0*972 0*970 0*970
85 i*ooo i*ooo C999 0*999 0*998 0*997 0*996 0*995 0*994 0*993 0*993 0*992 0*992
90 rooo i*ooo rooo rooo rooo rooo rooo rooo rooo rooo rooo rooo rooo



TABLE III.
cos9 8 sin « cos u.
\ ohom oh30m ih o™ ih 30111 2bom 2h 30™ 3hom 3h30m 4h om 4h 30111 5h om 5h3om 6hom
\ ° 4 4 + 4 4- 4- 4 4- + 4 4 4- 4
\ i2hom iib30m nhom i0h30m iohO™ 9h 30111 911 om 8h 30111 8h o™ 7h 30111 7hom 6h3om 6hom
\ i2hom I2h30m i3hom I3h30m 14®1 o™ I4h30m i5hom I5h30m i6hom i6h30m i7hom I7h30m i8hom
\ 4 + 4" 4 4- 4* 4 4 4-44 + 4
ö \ 24hom 23h30m 23hom 22h30m 22hom 2ih30m 2ihom 201130m 20h0m 191130™ I9hOm i8h30™ l8hOm ±
o o-ooo 0129 0*250 0352 0-433 0481 0*500 0481 0433 0352 0*250 0129 0000
5 0000 0128 0-248 0-349 0*430 0*477 0496 0-477 0*430 0349 0248 0-128 0000
10 o-ooo 0-125 0242 0-341 0-420 0-467 0-485 0-467 0-420 0341 0-242 0*125 0000
15 o*ooo o* 120 0233 0*328 0*404 0-449 0*466 0-449 0404 0*328 0233 0120 0000
20 OOOO 0*114 0-22I 0-311 0*383 0*425 0-442 0425 0*383 0*311 0*221 0*114 0000
25 0000 0105 0*205 0*289 0*355 0*395 0*410 0395 0*355 0*289 0205 0105 0000
30 o*ooo 0*096 0*187 0*264 0-325 0*361 0-375 0*361 0-325 0*264 0-187 0096 OOOO
35 0*000 0*086 0*168 0*236 0-291 0-323 0-335 0323 0291 0236 0168 0086 0*000
40 o*ooo 0*075 °'I47 0*206 0-254 0*282 0-293 0*282 0*254 0*206 0*147 0*075 0*000
45 o-ooo 0064 0-125 o*175 0*216 0-240 0*250 0240 0216 0*175 0*125 0*064 0000
50 0000 0*053 0*103 0,I45 0*179 0*199 0*206 0*199 0*179 0*145 0*103 0053 0*000
55 o*ooo 0*042 0*082 o*n6 0*142 0158 0*164 0-158 0*142 0*116 0082 0*042 0*000
60 0*000 0*032 0*062 0*088 o* 108 o-120 0*125 o* 120 o-108 0088 0-062 0032 o-ooo
65 o-ooo 0*023 0"°45 0-063 0-078 0086 0-089 0*086 0-078 0063 ' 0-045 0023 o-ooo
70 o*ooo 0*015 0029 0*041 0051 0056 0058 0056 0*051 0041 i 0029 0015 0*000
75 0000 0*008 0*017 0-024 0029 0032 0033 0032 0*029 0*024 ; 0*017 0008 0*000
80 O'OOO 0*004 0-007 o-oio 0*013 0-014 0*015 0014 0*013 O'OIO 0*007 0004 OOOO
85 O'OOO OOOI 0*002 0003 0003 0*004 0*004 0004 0*003 0003 ! 0*002 0*001 OOOO
90 O'OOO o-ooo O-OOO O'OOO O'OOO O OOO O'OOO 0*000 O OOO O-OOO ! O OOO O OOO O'OOO
cos 8 sin S cos «.
\ oh om oh 30™ ihom ih 30111 2hom 2h 30111 3hom | 3h 30111 4hom 4h3oni 5hom 5h3om 6hom
\ « ± ±± ±± ± ± ± ± ± ± ± ±
\ i2hom nh30m nhom ioh 30m iohom 9h30m 9hom 8h30m 8hom 7h3om 7hom 6h3om 6hom
\ T -F 4- -F -f- -+- -F -F-+- + + + +
\ i2hom i2h30m i3hom I3h30m i4hom i4h30m i5hom i5h30m i6hom i6h3om i7hora i7h3om i8hom
\ =F =F T =F _=F =F =F + + =F + =F +
d \ 24hOm 23h30m 23hOm 22h30m 22hOm 2Ih30m 2IhOm 201130m 20h0m I9h 30m I9hOm l8h30m l8hOm
\± ±± ±± ±± ±± ±±
±
O O'OOO O'OOO O'OOO OOOO O'OOO O'OOO O'OOO O'OOO O'OOO O'OOO O'OOO OOOO O'OOO
5 0-087 0087 0*084 0*081 0-075 0-069 0*062 0*053 0*043 0*033 0*023 0*012 0*000
IO 0*171 0-169 0-165 0158 0*148 0*136 0*121 0*104 0*085 0*065 0*044 0*023 O'OOO
15 0*250 0*248 0*241 0*231 0*216 0*198 0-177 0*152 0*125 0*096 0-065 0*033 0*000
20 0-321 0-318 0-310 0*297 0*278 0*255 0*227 °'i95 o* 160 0123 0*083 0-042 0-000
25 0*383 0-379 0-370 0*354 0-332 0-304 0-271 0233 0-191 0-147 0*099 0*050 o-ooo
30 0*433 0*429 0418 0*400 0*375 0*344 0*306 0*264 0216 0-166 0-112 0057 0*000
35 0*470 0466 0*454 0*434 0*407 0*373 0-332 0*286 0*235 0*180 0*122 0*062 0000
40 0*493 0-489 0-476 0-455 °'427 0391 0*349 0,3°0 0*246 0*189 0*128 0*065 °'ooo
45 0-500 0-495 O*483 0-462 0*433 0-396 0*353 0*304 0*250 0*191 0*129 0065 o*ooo
50 0-493 0*489 0-476 0*455 0427 0391 0*349 0*300 0-246 0-189 0128 0065 0*000
55 0*470 0*466 0*454 0*434 0*407 0-373 0-332 0*286 0*235 0-180 0-122 0*062 0000
60 0-433 0*429 0*418 0400 0-375 °'344 0*306 0*264 0216 0*166 0*112 0057 0000
65 0*383 0*379 0*370 0*354 0-332 0-304 0*271 0-233 0*191 0-147 0099 0*050 0*000
70 0-321 0-318 0-310 0-297 0-278 0-255 0*227 OI95 o-160 0*123 0-083 0*042 0*000
75 0*250 0*248 0*241 0231 0-216 0-198 0-177 0-152 0-125 0-096 0065 0*033 O'OOO
80 0*171 0*169 0*165 OI58 0*148 0*136 0*121 0*104 0*085 0*065 OO44 0*023 O'OOO
85 0*087 0*087 0-084 0*081 0*075 0-069 0-062 0-053 0043 0-033 0023 0-012 OOOO
90 0*000 O'OOO O'OOO O'OOO O'OOO O'OOO O'OOO O-OOO OOOO O'OOO OOOO O'OOO OOOO



TABLE III.
cos 8 sin 9 sin <*.
\ Qh Qm Qh ^ora ih om ih30m 2hom 2b 30™ 3hom 3h 30111 4h 30® ShQpl 5h30,n 611 om
\ « ± ± ± ± ± ± ± ± ± ± dt ± ±
\ i2hom nh32m i^o™ io^o™ io*om 9h30m 8h30ni 811©™ 7h3om 7hom &30111 6hom
\ ± ±±± ±±±±±±±±±
\ i2hom I2h30m ^o™ I3h30m i4hom I4h30m ^o110 I5h30m ióko™ i6h3om I7h0m I7h30m I81*©111 \ T TTTTTTTTTTTT
<5 \ 24hOm 23h30m 23hOm 22h30m 22hOm 21h30m 2IhOm 2CÏ130"1 20h0m ig^o™ i^o"1 l8h30m l8hOm
\ T =F
"o O-000 0000 0.000 0000 0*000 o-ooo 0.000 0000 0000 0000 0000 0000 0000
5 O'OOO O'OI 2 0*023 0*033 0*043 0053 0.062 0069 0*075 0081 0084 0087 0087
IO OOOO 0023 0.044 0065 0085 0104 O* 121 0.136 0148 0158 0165 0-169 0*171
15 o*ooo 0*033 0*065 0*096 0*125 0152 0*177 0*198 0*216 0*231 0*241 0*248 0*250
20 0000 0*042 0*083 0123 0*160 0195 0*227 0*255 0*278 0*297 0*310 0*318 0*321
25 0*000 0*050 0*099 0*147 0*191 0*233 0*271 0304 0*332 0*354 0*370 0379 0383
30 O'OOO 0*057 o* 112 0*166 0*216 0264 0*306 0*344 0*375 0*400 0*418 0*429 0*433
35 o*ooo 0*062 0122 0180 0235 0*286 0*332 o*373 0*407 0434 0-454 0466 0470
40 0*000 0065 0*128 0-189 0*246 0300 o* 349 0*391 0*427 0*455 0476 0*489 0*493
45 0000 0065 0129 0*191 0*250 0*304 0353 0*396 0*433 0462 0483 0495 0*500
50 0000 0065 0128 0189 0246 0300 0349 0391 0427 0455 0*476 0*489 0*493
55 0*000 0062 0122 o-180 0235 0*286 0332 0373 0407 0-434 0454 0-466 0470
60 o-ooo 0*057 0112 0166 0-160 0264 0-306 0344 0*375 0400 0*418 0*429 0*433
65 0000 0.050 0099 0147 0191 0233 0.271 0*304 0-332 0*354 0-370 0*379 0*383
70 o-ooo 0.042 0*083 0.123 0160 0195 0227 0-255 0-278 0*297 o*3io 0318 0321
75 o-ooo 0033 0065 0096 0125 0-152 0-177 0198 0-216 0-231 0-241 0*248 0-250
80 o-ooo 0-023 0-044 9065 0-085 0-104 o-i2i 0*136 0-148 0*158 0*165 0169 0-171
85 o-ooo o*oi 2 0*023 0-033 0043 0*053 0-062 0-069 0-075 0-081 0-084 0087 0-087
90 O-OOO O-OOO OOOO OOOO O'OOO O'OOO O'OOO OOOO O'OOO OOOO O'OOO O'OOO o-ooo
sin S cos cc.
\ ohom 0h30m ihom Ih30m 2bom 2h30m 3hom 3h30m 4hom 4h30m 5hom s^o111 6hom
\ « ± ± ± ± ± ±±±±±±±±
\ i2hom nh30m nhom i0h30m iohom 9h30m 9hom 8h30m 8hom 7h3om 7hom 6h30m 611©111
+ ^ + T -F ~F
\ I2hom i2h30m i3hom i3h30m i4hom I4h30m is11©01 i5h30m i6hom i6h30m i7hom I7h30m IS11©00
+ + + + T- T T T
5 \ 24hom 23h30m 23hom 22h3om 22hom 2ih30m 2ihom 20h30m 20h0m 191130111 ^O™ i8h30m 18*0"
\±±±±±±± ± ± ± ± ± ±
O O'OOO O-OOO O'OOO O'OOO O'OOO O-OOO O'OOO O-OOO OOOO OOOO O-OOO O-OOO o-ooo
5 0087 0087 0084 0081 0-075 0069 0062 0*053 0-043 0-034 0-023 0-012 o-ooo
10 0174 0172 0168 0161 0-151 0-138 0-123 0*106 0087 0067 0-045 0023 0000
15 0*259 °'25 7 0*250 0-239 0*224 0*205 0*183 0*158 0*129 o* 100 0*067 0*034 0-000
20 0*342 0-340 0*330 0-316 0*296 0-271 0.242 0-208 0*171 0*131 0*089 0*045 0-000
25 0-423 0 419 0 409 0 391 0 366 0-335 0 299 0 258 0-2II 0-162 O-I IO 0*056 O-OOO
30 0-500 0-495 0-483 0-462 0433 0-396 0-353 0304 0*250 0*191 0129 0-065 o*ooo
35 o* 5 74 0569 0554 0530 0497 0455 0*406 0*349 0*287 0*220 0*149 0*°75 O'Ooo
40 0643 0637 0-621 o* 594 0*570 0510 0*455 0391 0*321 0-246 0-167 0*084 0000
45 0-707 0700 0-683 0-653 0612 0561 0500 0-431 0353 0271 0183 0093 OOOO
50 0766 0*759 0740 0707 0*663 0607 0*552 0467 0-383 0-293 0*198 o-100 o*ooo
55 0*819 0*812 0*791 0*756 0*709 0*649 0-579 0*499 0-409 O-313 0*212 0*107 O'OOO
60 o*866 0*858 0*837 o799 o75o 0686 0612 °'527 0433 0*331 0224 0*113 0000
65 0*906 0-897 0-875 0837 0785 0718 0-641 0552 0-453 0-347 0-235 O*II8 0000
70 0*940 0931 0908 o-868 0814 0745 0-655 0-572 0470 0*360 0-243 0123 0000
75 0966 0-957 0-933 0892 0837 0766 0-683 0-588 0483 0*370 0250 0126 o-ooo
80 0985 0976 0-952 0909 0853 0-781 0-696 0599 0492 0-377 0-255 0*128 0000
185 0*996 0987 0-962 0-919 0-863 0790 0704 0*606 0498 0-381 0258 0-130 o-ooo
90 1*000 0991 0966 0923 o*866 0793 0707 0-609 0500 0382 0-259 0*131 0000



TABLE III.
sin sin <*.
\ o^o™ o1130m ihom i^o™ 2b o111 2h3om 3hom 3h30m 4hom 4*30™ s11^ 5h3om 6hom
\ a ± ± ± ± ± ±±±±±±±±
\ I2h0m Iih30m Iih0m I0h30m io*1 om 9h3oB0 9hom 8h30m 8hom 7h30m 7hom 6h30m 6hom
\ ± ± ± ± ± ± ± ± ± ± ± ± ±
\ i2hom I2h30m i3hom I3h30m i4hom h^o™ i5hom i5h30m i6hom i6h30m i7hom i7h30in i8hom
\ T =F T T T =F TT T T T T T
d \ 24hOm 23h30m 23hOm 22h 30m 22hOm 21h30m 2IhOm 201130m 20h0m I9h 30™ I9hOm l8h30m l8hOm
\zfjfiTTTTTTTTTTT
± r~~_~l
O O'OOO O'OOO 0*000 OOOO O'OOO OOOO O'OOO OOOO OOOO OOOO O'OOO OOOO OOOO
5 o'ooo 0'0i2 0*023 0*034 0*043 0*053 0*062 0*069 0*075 0*081 0*084 0*087 0*087
10 0*000 0*023 0*045 0*067 0*087 o* 106 0*123 0.138 • 0*151 o*i6i 0*168 0*172 0*174
15 O'OOO 0*034 0*067 O'IOO O'129 0*158 0*183 0*205 0*224 0*239 0*250 0.257 0*259
20 o*ooo 0*045 0*089 0*131 0*171 0208 0-242 0271 0-296 0*316 0330 0*340 0*342
25 o-ooo 0*056 o-i 10 0*162 o*2i 1 0*258 0-299 0*335 0*366 0*391 0-409 0*419 0*423
30 o*ooo 0*065 0*129 0*191 0*250 0304 0*353 0*396 0*433 0*462 0*483 0*495 0500
35 o-ooo 0-075 o* >49 0-220 0*287 0*349 0*406 0-455 0*497 0*530 0-554 0.569 0*574
40 o*ooo 0-084 0*167 0-246 0321 0-391 0455 0510 0-557 o* 594 0*621 0*637 0*643
45 o*ooo 0-093 0*183 0271 o'353 0431 0-500 0561 0*612 0653 0683 0700 0707
50 0*000 0*100 0*198 0*293 0*383 0*467 o*542 0*607 0*663 0*707 0*74° o*759 0*766
55 o*ooo 0*107 0*212 0*313 0*409 0*499 0*579 6649 0709 0*756 0*791 0*812 0*819
60 o'ooo CI13 0224 0*331 0*433 0*527 0612 0'686 o'75° 0799 0*837 0*858 o*866
65 0000 0118 0235 o* 347 0*453 0552 0641 0718 0785 0837 0*875 °"897 0*906
70 O'OOO 0*123 0*243 0-360 0*470 0*572 0665 0*745 0*814 0*868 0*908 0*931 0*940
75 o*ooo 0*126 0*250 0*370 0*483 0588 0*683 0*766 0837 0*892 0*933 0*957 0*966
80 0000 0*128 0*255 °'377 o'492 0599 0*696 0781 0*853 0*909 0*952 0976 0985
85 o*ooo 0*130 0-258 0*381 0*498 0606 0*704 0-790 6*863 0*919 0*962 0*987 0*996
90 0000 0*131 0*259 0382 0500 0*609 0707 0*793 o*866 0923 0966 0-991 1000



TABLE IV.
Gal. lat. A | B C DEFPQRN
Bradley + 90° to + 52°.
— 20° to -j- 20° + 135 50 -J- 14071 4- 3179 o-oo + 4203 + 2'65 — 4«6 — 2586 + 439 *54 -f20 to--4o -j- 9I'65 + 837° -- 12-64 — 2*26 — 6*42 — 3*ii — 338 — 1772 -j- 80 94 + 40 to + 90 -f- 38*44 + 46*5» + 1304 — 1*62 —18-95 + 3*43 + 399 867 -j- 322 49
Allstarstogether 265*59 + 270*92 + 57*47 — 3*88 -f-16*66 -f" 2'97 — 355 — 5225 + 841 297
Bradley + 52° to — 20°.
— 90°t0 —40° + 67-11 + 27986 + 32°94 +17*06 — 152 4- 5*69 — 179 — 5215 4" 4833 334
— 40 to — 20 4- 180*42 4" 184*22 4" 283*30 + I3'42 4"53'°6 4-19-41 — 608 — 4761 4" 566o 324
— 20 to 4-20 -- 586*64 -- 229*49 -- 539*77 —68 29 77*36 --17*17 —2665 — 6772 -- 7675 678 4-20 to -|- 40 -- 20898 -- 123-30 -- 251-68 —20-34 —13-36 4-12'36 4" 110 — 4224 -- 4387 292 4-40 to 4-90 4- 177*06 4- 389*42 4- 407 44 +15*63 —93*45 — 3*53 + 1738 —12010 + 6376 487
All stars together + 1220-21 +1206*29 +1803*13 —4252 +22*09 +51*10 —1604 —32982 +28931 2115
Bradley South, of — 20°.
— 90°t0 —40° + 15*33 + 24*24 + 28-42 — 502 — 9-90 + 20 7 + 68 — 438 + 287 34
— 40 to—20 + 868 + 3*02 + 830 — 184 — 1*39 + 136 — 46 — 92 -- 68 10
— 20 to + 20 + 52*51 + 12*60 + 4687 — 2*49 + 2*50 + 9*13 + 30 — 634 + 603 56 + 20 to + 40 + I7'56 + 2912 + 31.33 + 7*68 +12*50 + 5*68 + 23 — 951 + 849 39
All stars together + 94*08 + 68*98 + 114*92 — 1*67 + 371 +18*24 + 75 — 2115 + 1807 139
Newcomb —20° to —40°.
— 9o°to —40° + 18-65 + 27*16 + 28*19 + 109 — 11*93 — 1*65 + 118 — 685 + 347 37
— 40 to — 20 + 15-01 + 5*74 + 13*25 — 202 — 1*90 — ro8 + 36 — 18 -- 369 17
— 20 to + 20 + 39 58 + 14*97 + 33*44 — 2*02 + 3*98 + 601 + 86 — 774 + 807 44 + 20 to + 40 + 610 + 13-52 + 12-38 + 2*32 + 5*79 + 1*47 — 184 — 285 + 496 16
All stars together + 79*34 + 61*39 + 87*26 — 0*63 — 4*06 + 475 + 56 — 1762 + 2019. 114
Taylor — 20° to — 35°.
— 90°t0 —40° + 2612 + 45*67 + 48*20 — 969 —19*15 + 4*77 + 76 — 343 + 1040 60
— 40 to —20 + 15*92 + 8*73 + 17*34 — 6*27 — 4*07 + 4*34 — 283 — 274 + 148 21
— 20 to + 20 + 6635 + 20*47 + 57*16 — 2*89 + 4*18 +11*91 + 250 — 651 + 1601 72 + 20 to + 40 + 17*03 + 35*42 + 33*55 + 5*oi +15*35 + 3*i8 — 433 - 1054 + 720 43 + 40 to + 90 + 0-25 + 200 + 176 + 0*02 + 0-65 + o*oi — 24 + 45 + 61 2
All stars together + 125*67 + 112*29 + 158*01 —13*82 — 3*04 +24*21 — 414 — 2277 + 3570 198
Newcomb —40° to —52°.
— 90°t0—400 + 477 + 5*49 + 3*74 + 0.48 — 2*61 — 0*83 + 34 — 105 + 99 7
— 40 to — 20 + 2*95 + 1*52 + i*54 — 0*16 — 0*17 — 0*67 — 4 — 59 — 15 3
— 20 to + 20 + 21*65 + 20*22 + 14*14 + 1*85 + 8-40 + 3-67 — 133 — 635 + 390 28
AU stars together + 2937 + 27*23 + 1942 + 2-17 + 5*62 + 2-17 — 103 — 799 + 474 38



TABLE IV.
Gal. lat. A B C DEFP Q RN
Gill—40°to—52°.
— 90°t0 — 40° -4- 114*2 + >45-80 -f 84*00 10*65 —69*01 —1869 4-2376 — 3289 4- 1747 172
— 40 to — 20 + 68 32 -f 4139 -f- 34 29 — 4 97 — 7*53 — 5 47 — 19 — 765 -f 436 72
— 20 to + 20 -j-18469 -[-17857 +11476 — 7*89 +7279 — 397 —2466 — 5232 + 3490 239 + 20 to-f-40 -|- 3 22 -j- 680 -(- 399 4- 075 4- 3*3714- 068 •— 101 — 358 4- 171 7
AU stars together 4" 37° 44 4~ 372'56 4" 237 04 — 146 — 0 381 — 27-45 — 210 — 9644 4" 5844 490
Combination Newcomb—Gill.
— 90° to — 40° 4" I29'33 4- i64*«9 4" 95'68 -f 10*08 — 77 79 — 18*35 4- 2524 — 3719 4- 2116
— 40 to —20 4- 81-92 4- 5°'39 4- 4'"69 — 7'49 —1087 4* 1*37 — *3 — >133 -f 669
— 20 to 4~ 20 4-21609 4-206*00 4" 135*36 — 047 4*8274 4- «4*33 —2381 — 6430 4* 4311 4-20 to 4-40 4" 3 22 4* 6 80 4- 3-99 + 075 -f 3*37 4~ °'68 — 101 — 358 4- l7l
AU stars together 4-43°'56 4" 4*7 38 4-27672 4" 2*87 — 2-55 — 1-97 4- 29 —11640 -|- 7267
Auwers — 52° to — 90°-
— 90°t0 —40° 4* 4272 4- 4770 4" »*58 4" 076 —1705 — 2-85 4- 286 — 921 -f 95 51
— 40 to —20 -- 84-45 4* 7802 4* 9*5i — 1*59 — 4*83 + 0*37 — 192 — 1774 4- 124 86
— 20 to 4* 20 4" 77'04 4" 79'9i 4" !9*04 — 0*05 -f 24*65 + 3'56 — 648 — 2823 4~ 732 88
AU stars together 4" 204*21 4" 205*63 4" 4OI3 — °'88 4* 2'77 + 1 08 — 554 —' 5518 4- 951 225



TABLE V.
Bradley.
Corrections depending on the
declination. TABLE VI.
Deel. A/tj
Southern 4- o"ooo35 o" 0004
o° to 200 -- 23 — 17
200 to 40° 4* 16 — 25
40° to 6o° o — 12
6o° to 90° — 10 -f- 55
Corrections depending on the rightascension.
AR Afia A/ji#
o»» 4-°8'000°5 4"0,/00°5
ih 4- 8 o
2h + 2 + 1
3h — 8 o
4h — 12 — 5
5h — 13 — 12
6h — 16 — 9
7h — 16 — 6
8h — 11 o
gp — 6 -f- 10
io11 — 6 4" 16
uh — 8 -f 7
I2h — 15 — 2
I3h — 16 4- 7
I4h — 4 -f 18
I5h 4- 6 4- «4
i6h 4- 3 + 7
I7h o — 1
i8h 4-IO — 4
I9h -j- 18 — 2
2<P +14 — 2
21h + 7 + 2
22h — I IO
23h — 3 4- 11
Gal. lat. A? AQ AR
Bradley.
— 90° to— 40° — 8 —1787 — '9
— 40 to — 20 — 325 — 1019 4" 5*4
— 20 to 4" 20 —1290 — 915 4" !442
4-20 to 4-40 — 365 + 486 4" !5
+ 40 to-fgo — 103 + 702 -f- 189
AU stars together — 2091 — 2533 -f- 2141
Newcomb — 20° to — 40°.
— 90° to — 40° — 40 — 6 — 88
— 40 to — 20 — 7 — 3 — 41
— 20 to4*20 4* 18 +32 — 167 4-20 to-j-40 4" 12 4" 3 — 23
All stars together — 17 4" 26 — 319
Taylor — 20° to — 35°.
— 90°t0— 40° — 98 4-27 — 233
— 40 to — 20 — 22 +26 — 87
— 20 to 4* 20 4-24 +77 — 365 -}- 20 to 4- 4° + 89 -f- 19 — 200 4*40 to + 90 4" 9 o — 16
All stars together 4" 2 4" !49 — 901
Newcomb — 40° to — 52°-
— 90°to—40° — 15 _ 5 — !9
— 40 to — 20 — 1 — 3 — 8
— 20 to 4"20 4" 5° 4" 24 — 83
All stars together 4" 34 + 16 — 110
Giil — 40° to — 52°.
— 90°t0 — 40° — 534 — *45 — 639
— 40 to—20 — 78 — 60 — 377
— 20 to 4-20 + 77° — 42 —1221 4-20 to -f 40 4-20 4- 4 — 20
All stars together 4" !78 — 243 — 2257



TABLE VII.
Groups of different galactic latitude.
Gal. lat. A B • C D E F P Q R
— 90 to — 40° 4- 190*85 4- 444*92 4- 44i'»3 +16-89 — 73*77 — 4*29 4" io37 —10496 4" 6243
— 40 to — 20 -- 28742 -- 256*38 -- 332-61 -j- 4-56 4- 42 42 4-17*55 —"76 — 73i6 4- 6654
— 20 to +20 - 983 33 4- 552*35 -- 747*20 —75*63 --18402 4-41*40 —5424 —16453 4-12916
t20 to 4-40 -f 330*i6 4" 26189 -- 318*41 —1098 -f 4'°3 4*'7*54 — 868 — 7178 -- 6009
40 to -j-9° t 215-56 4- 43643 4- 420-92 4-H'Oi —112*24 — o-io -f2030 —12164 4* 6898
AU groups together 4-2007-32 4-1951-97 4-226027 —51*15 4" 44*46 4-72-10 —4401 —53607 4-38720
TABLE VIII.
Groups of different type of spectrum.
Type. A B CDEFPQR
I 4- 741*99 4- 637-10 4- 858-78 —17*75 4" 36*42 4~30*96 —1746 —18049 4-13192
II 4- 625-51 4- 695-27 4- 809-01 4- 622 4- 10-27 4-25*07 —1330 —19278 +14704
TABLE IX.
All stars together (definitive results).
A B CDEFPQR
4-2404*75 4-233005 4*2506-39 +5079—33*8o—86*97 —4525 —64017 4-43502







STELLINGEN
I.
Aan de eigenbewegingen in declinatie volgens Newcomb's fundamentaalcatalogus van de sterren zuidelijk van — 20° declinatie moeten waarschijnlijk positieve systematische correcties worden aangebracht.
II.
Het traagheidsprincipe is geen zuivere ervaringswet.
III.
Het theorema van het arithmetisch gemiddelde moet niet als een axioma worden opgevat.
IV.
De onderstelling, dat bij gasvormige hemellichamen in eikaars nabijheid vloedgolven worden opgewekt aan de naar elkaar toegekeerde en van elkaar afgekeerde zijden is niet algemeen juist.
V.
De spectrographische methode van Küstner ter bepaling van de zonsparallax verdient naast de andere methoden ter bepaling van deze grootheid in aanmerking te komen.



VI.
De hypothese van Pickering ter verklaring van de retrograde beweging van Phoebe uit een oorspronkelijk retrograde omwentelingsbeweging van Saturnus (Harv. Ann. 53) is niet aannemelijk.
VII.
De grondeigenschap, gewoonlijk als axioma in de rekenkunde vooropgesteld, is een bewijsbare eigenschap.
VIII.
Ten onrechte ziet Poincaré in de mogelijkheid van het bestaan van een niet-Euclidische meetkunde een argument tegen de opvatting van de meetkundige axioma s als synthetische oordeelen a priori (la Science et l'Hypothèse pag. 64).
IX.
De bewering van Poincaré, dat het aanvaarden van de meetkundige axioma's slechts berust op een overeenkomst op eenvoudigheidsoverwegingen gebaseerd, is onjuist, (la Science et l'Hypothèse pag. 66.)
X.
De invoering van het begrip differentiaal in overeenstemming met de wijze, waarop Newton de differentiaalrekening baseert, verdient de voorkeur boven die volgens de methode van Leibnitz.
XI.
Door de onderstelling, dat voor electronen met een snelheid grooter dan die van het licht de traagheidswet niet geldt, wordt aan het traagheidsprincipe in theoretisch-mechanischen zin niet te kort gedaan.



XII.
Ten onrechte beweert Lippmann, dat de opvatting van een electrischen stroom als een beweging van electronen eischt, dat aan het begrip absolute beweging een physische beteekenis wordt toegekend.
XIII
De studie van de Erkenntnisstheorie is van belang voor de beoefenaars der natuurwetenschap.
XIV.
Uitgezonderd voor de pharmaceuten zou één algemeen candidaatsexamen in de faculteit der wis- en natuurkunde gewenscht zijn.