52H 
PROFI-:SSOR a. H. DATi^VTX OX RRLIPSOTDAI. HARMOXIC AXATA'SIS. 
(1 ~ ^+ iy^ + + hps + I'V]!' + (^ + cos 2(^, 
= i + o2h + ni]} {1 + (1 + 2/3/)3 -\- ^/3)cos2^}. 
Now both for sines and cosines, to the order iiecessary for onr present pui’pose. 
Ji, 2}. Tlierefore, introducingj for 1(2 -j- 1), 
=i j I 1 2/+fi8) ; s 1 -[1 +m-i/S] cos 2,y,; 1 
(C')= 
> • (‘sy 
(I—Pens 2(p)i 
'i''! l+iy^+ + 1 — 8/^/ + 2 / 5 ]COS 2(f )!' j 
()hserve thatjFy/^ and do not involve cos 2(f>, and are of the first order in p. 
Hence, as far as material for the pre.^enf portion of the work. 
(\-Pem 2 (f,fi “ ^(]-Pens 2 </))i “ sfo + i-P ' 
(73). 
Also, to the first order, from (3 / ) 
1 
It 
,(sin) 
— * 
~(cos) 
-1-AA 
Therefore as far as necessarv 
Hence 
{]-Pens 2 (f )4 
(Cf)- 
(I —/3 ens 20 f 
-1/3). 
P ( S,' )- [(i/)=- ( p,‘)-]<-n= I’f) 't!: ( 1 -;8)! (I -1^) {i/3 (,/-2 ( -'/+1) + 4) 
+ T2¥)^' [■“ + ~ • + 1- )] A 
7i'8/3'(./■+1<:y+Hfo)] 
+’cu'2pli-ii3+m .(’J)- 
Ida- S;‘ we have only to replace the factor I — ]-/3 hy and find 
I ns.-)^ LW)—( IV)in= {i /3 (^• + 4 )-yb/ 3 H,r-:! 2 /- 84 ){ 
i— 1 ■ 
(74). 
