388 Mr. George J. Axlman's Account of 



Let a, ^, 7 be the direction angles of OT ; a, ^', y\ of OM ; o,, p,, 71, of 

 TS ; and oq, |3o, yo, of the normal to the plane OST ; and let OS, OT, and the 

 angle SOT, be denoted by p, r, and respectively. It will be sufficient to prove, 

 that the component Q of the attraction in the direction of the normal to the 

 plane OST is cypher. 



We shall first find the components X, Y, Z, of the attraction in the directions 

 of the axes, and thence deduce the value of Q. 



Now, 



but, 



dl _ 2(A-I) cos a' dl_ _2(£ - I) cos ^ dl^ _2 (C - I) cosy' 

 dx' ~ ? ' dy' ? ■' U' ~ r' " 



Hence we have 



-^ M , , ^ / I . -n . /-r r T\ I BA COS a 



X = — cos a' + — ^ (.4 + 5 + C - 5/) COS a + 



7 = ^cos/3' + -^J^+5+C-5/)cos/3'+^i^^4pi, (7) 



Y' ■ 2r" 



_3_ 



r- • '2r'- 



Z =^^, cosy' + ~ {A + B+ C - 51) cosy' + 



Now, 



Q = X cos oq + Y cos /3o + Z cos 70 ; 



but, 



sin cos o„ = cos j3 cos 7' — cos 7 cos /3', 



sin cos po = cos 7 cos a' — cos a cos 7', 

 sin cos 7o = cos a cos /3' — cos /3 cos a' ; 



the following relations moreover exist, 



a- cos a = rp cos a, b- cos |3' = rp cos ^, c^ cos 7' = r/> cos 7 ; (8) 



