84 C. V. L. Gliailier 



(62**) — C'A'{S^^ + Egg T21 + hi T31) (^12 T12 + h2 T22 + =32 Ï32) 



A C^i^igTll ^23Ï21 "i" ^33 ^3x) (^13Tl2 ^~ ^23^22 ~l~ ^33^32)' 



where 



C = A'(Si, + Sgl Yg3 + T33)2 

 (62*-^=*) 4 S'(s,gTi3+S2Ï23 + ^32T33r 



13Ï13 ^23T23 ^ssTss) ■ 



The values of J^, jB^ and /''i may be considered as known for every square. 

 The cosines of direction — Sy — may he expressed through three independent 

 variables (e. g. the angles of Euler), say 6, cp, ^. Hence there are six unknown 

 quantities 



A', B\ G\ e, (p, f 



For their determination we ought to have the values of A^, B^ and I\ known 

 for — theoretically — two squares. 



The analytical treatment of these equations seems, however, to be little pro- 

 mising. 



According to (55) our equations may also be written in the following form : 



A^C^B'C cos^X'Y^ C'A' cos" Y' Y + A' B' cos^ZT, 

 *(63) B,C=B'C' cos^ X'X + C'A' cos' YX + A B' cos' Z'X, 



F^C^ — B'C cos X'X cos X' Y 



~ C A' cos T X cos Y Y • 



— cos Z'X cos ZT, 



where 



C=A' cos' X'Z + B' cos' Y'Z C cos' ZZ. 



23. A graphical representation of the lines of symmetry on a sphere makes 

 it evident that the velocity sphseroid is very nearly a sphseroid of revolution. It is 

 hence allowed, with Schwarzschild, to treat the problem under the assumption that 

 two of the axes of the spheeroid have the same value. Suppose 



(64) A' = B'. 

 The formula' (63) now take the form: 



A^C== B'(C' + [B' — C) cos'Z Y\ 



(65) B, C = B'(C' + [B' — C) cos' Z'X), 



F,G = — B'{B' — C) cos ZYcos Z X, 



if regard is taken to the relations 



eos^ XT + cos^ FT + cos^ ZY=1, 

 cos^ X'X + cos^rX + cos'' Z'X = 1, 

 cos X'X cos XT + cos FX cos Y Y + cos ZX cos Z'Y^O. 



Further we have 

 (65*) G^ B' — {B' - C') cos' ZZ. 



