344 Mr. Lubbock on the Variation of 



(,12 ft \ 

 :j — p J = i" B cos (i n n t +j" mnt + l"nt). 



These terms give in -, — 

 ° at 



/ d a R \ 8 e &R $_m 

 \de dc) an dco dc an' 

 and therefore 



(**) PM (**)dt + (S4-) [^ ( d -£) at 



\dedc/i/ an \d coj \d(odc/J an \de ) 



and hence the following terms : 



$ CBA sin (i! nt +fmnt + l'n t) 



cos (i n nt + j" mnt + /" n t) 

 (i" +fm + l")n 



, i 1 DBA . ,,. -, , v , w .c 

 H — sm (r nt +j' mnt + V n t) 



cos (i n nt — int -\-j"mnt—jmnt + I" nt — Int) 

 (i" — i +j" m —jm -f I" — I) n 



i ] D B A 



H - sin (i 1 nt + j' mnt + V nt) 



cos (i" nt+ int -\-j n mnt + jmnt + V nt + Int) 

 (j,n _|_ 2 +f m +jm + /" + l)n 



— i" CBA cos (i" n +/' mnt + I" n t) 



sin (if nt 4 f mnt +Vnt) 

 [i! +j'm + V)n 

 ft d jb j£ 



o C0S (*" n t +J n mn t + W n 



sin (? 7 nt — int +f mnt —jm nt + V nt —V n t) 

 (i ] — i -t-j'm —jm + V — I) n 



i n DBA 



cos (jji n i +jii mnt + 1" n t) 



z 



sin (i 1 nt + int +/ mnt +j mnt -f- V nt-\- Int) 

 (i 1 + i + j' m +jm + V + l)n 



The terms multiplied by CBA, which arise from the constant 

 portion of [e 9 co], have already been considered, the rest form four 



