( 99) 



result we tlien reject all terms which do not contain the argument 



u' — u = & -f 180°, 

 or its multiples. We thus find easily 

 <Z J o 3 



<ft 2 



fb x + - <?,#, 



<(« [It — It 



sin 2 (u — u') 



m'l/a' 



my a 



m'l/a' 

 a 0> i B£, -) — aifiB'B'— boABB'+B.B') \sin(u— «' 



,/V 



= — 3»Wi 



eft' 



3 



-f 6n' 

 + 12»' 



— 3m' 



G.B,' + - F.B, 



sin (n — k') 



/"/>' -! -,. '-,/;" 



sin («' — n) 



m\/a 



a ]fi B^ -) — — aoiJ5' — 2h\»B.B' sin2(u—u') 



m ya 



m\ a 



( /,„/>'7>Y + -f-a ,i 85, - l, l>{) (BB l , +B l B') 



m ya 



sin (u — u') 

 ) 



d*Q" 



iri'v/d' 



a lfi B" -\ — — a,,i B"* — 2/., .,B'B" sin 2 (»'— a 



7M ya 



in't/a' 

 a\ fl J! B,' + -JL_. a 2j1 B"B; -b {fi {B'B;' -±B X 'B") 



sin (it — it) 



— 3)////"" 

 -f 6«" 

 + 12»" 



G'.B"-f / '■/.•■ 



in (u'—u) 



sin 2 (a' — n) 



m' l/a' 

 «2,i B"' + v a ]fi B" — 2b- 2 , B'B" 

 m y a 



ui \ a 

 ,i, A B'B," + ((|2 i?'ö l '-^ 1 (//Z? 1 "-f7?.7?') 



in ya iii/ 



sin («' — «) 

 We now put 



sin (u — u') =r sin 0- 

 sin 2 (w — «') = — 2 sin <>. 



Further we introduce the approximate values of B, IV . . . which 

 TlSSERAND gives in the middle of page 22, viz. : 



B' = m CG B; = m" CF B 1 =B" — 0,. . . [yj 

 where 6' is a constant, the value of which is indifferent to our 

 argument, and can easily be derived by comparison with TlSSERAND, 



