tvOI.UriO FUNCnONIS per rtHBATRICIS ETC. 275 



(E) R= 



a 



-{sin(7-t-2x)-sinjj 





•4-00 



^2 aa'B(''-<)sin(y'— 2x) 



-t-OO 



-iE aa'B('-')sinj> 



(j), (num. 25) ; 



m' , 



3a 

 4^ 



-[cos(3j*2x)H-cos(7-t-2j:)cos-t.2 cos/ ] 



■*-^_oo-^'^W'>'-^2x)*v_^Qfi)cos(;- . ..(f), (num. 26). 



-00 



3« 



-00 



m' (3a 



*'2 ■'''''' (■"2^2'^^'"^ ■^'■**^'^^"^''"^^*2-^)] 



-t-oo \ 

 -^^S_^«'^B(.-2)sin(/r+2x)j („), (num. 21), 



m' 



I 



2 



3a 



4a'2 



.[cos(3r-t-2j:)^.cos( r-f-2x)— acos/)] 



+00 ^(y\ \ 



*^_oo^^^^*=°<'>-^2x)-+-S_^Q(i)cosy' . . . (w) , (num. 28); 



quo pro X, eiy subslituendae erunt (1), (num. 14) quauti- 

 tates (^nt-i-e), (n't — nt-i-e — e). 



30. Denique imaginamus , omnibus quanlitalibus quas ae- 

 quatio (E) sub symI)olo S^^ complectitur, series (num. 5,6) 

 restitui, quae exoriuntur, cum in iis quanlitatibus omnes va- 

 lores integros numero i, ne excepto quidem /=:0 deinceps 

 tribuamur. Ea pars tolius evolulioni.s, quae angulos nt,n tu- 

 na, cum tempore varialjiles non contine]>it, ideoque variatio- 

 nes sive inaequalitates seculares respiciet, liuera F adnotata sit. 

 Statim formam aequationis (E) , vel leviter consideranti , quae- 

 siti termini occorrunt; nequeunt enim ex ullo alio valore nu- 

 mero f, praeter i = 0, derivari. Quapropter erit 

 p_ ( A('')-i-N(3Xe2-t.e'2)M.(N(4)^.N(5))ee'cos(o— o') 

 ~'^*QW(p2-^VQ^^Yp'V^'^)-4aa'B''5(pp'<77') 



Cum autem sit i = 0, erit eliam (13), num. 16), 



