( 262°) 
We get further: 
do 
Said ( =U dh 
eee 2 je --f dh ) 
2 2 2 2 
ER do je do | ‘dy do ( */d*o\* 
dS ne eden ee ee 1} 
| Cae IS aes Td OT ar NaI 
1 1 1 1 1 
The potential energy per unit of surface becomes: 
2 
( 8 dy oy da? 
Wz —afo? dh +avjm en sf ee dh — aa (Te dh 
l 
1 2 
As zero position we have taken that of the liquid. If we take 
infinite rarefaction as zero position, we get «g,m=0 and so: 
S= — W 
Astronomy. — S. L. VEENSTRA: “On the Systematic Corrections 
of the proper motions of the stars, contained in AUWERS’- 
BRADLEY-Catalogue, and the coordinates of the Apex of the solar 
motion in Space’. (Communicated by Prof. J. C. KAPTEYN.) 
The materials for these investigations have been taken from an 
yet unpublished catalogue, prepared by Prof. Kapreyy. This cata- 
logue contains for all the Bradley-stars, observed in both coordinates 
(with the exception of the Pleiades, the Hyades and the fainter 
components of physical double-stars) the position, the total proper 
motion w, its components v and 7, in the direction from the apex 
and perpendicular to that direction and the quantities A and 7%), 
respectively the distance from star to apex, and the angle between 
the great circle on which this distance is measured and the decli- 
nation-circle. 
The quantities v, 7, 4 and 7 have been calculated with different 
dp, & ; 
1) The differential-quotients WD = etc. are zero outside the separating layer. 
2) In the printed catalogue the quantities have not been included. 
