80 
4. Method of discussion the results. Solution of the equations. 
In order to render the determination of the constants as simple 
and as systematic as possible, and thereby to be able to conveniently 
make use of the results obtained in a previous research by Dr. 
E. F. v. p. SANDE BAKHUYZEN and myself concerning the influence 
exercised upon the determination of the constant of Precession and 
the systematic Proper-motions by the connection between the value 
of the parallax of the stars and their apparent distance from the 
galactic plane‘), the hourly means were represented by formulae of 
the form: . 
Ac=ae+bdsnatcosa . . » -. 2a 
Ada bana dees o 2,6.) > ee 
and the values of the coefficients were deduced from these equations. 
The same weight is given to all hourly means every where, in spite 
of the sometimes considerably diverse number of stars upon which 
they are founded. By this means we gained the very material 
advantage that all the inequalities depending upon the sines or 
cosines of multiples of @ become eliminated. 
Moreover the centennial variations of the reductions Aa, and 
Ad, of Auwers’s Old Fund. Cat. to his new one were developed in 
formulae of the same form. These expressions, as being probably 
known with sufficient accuracy — which was doubted at first — 
were added to the corresponding terms of the formulae (1) and (2). 
The following table contains the values of the ccetficients of both 
formulae per 100 years; in this the centennial variations of the 
reductions Aa, and Ad, have been taken into account. 
In order to facilitate the further calculations, instead of the coeffi- 
cients 4 and c, the quantities 4 cos dé and c cos d are given in the 
table. The results are all expressed in seconds of arc. 
1) These Proceedings, 18, 683—695. 
