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).