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