140 
PROFESSOR C. RIVEN OR THE CONDUCTION 
and hence, dividing by the expression for —, we find 
CL, 
r+l 
t I ^ Pr +2 \ i v 
— , up to e J 
«, \<f>" r+1 ' f *, +1 f r+s 
(51) 
In a similar manner 
j}\ • o • 
r+2 C h±~ _ 
But 
— ^0 • * • ^/-l• <£/•+]{ <f>r + iSj[• </>, + e fi+iSo^),-■ 
P>- | P*+l\ I 
(52) 
r +1 S ] = l -_ 1 S 1 + (f^+ J , jS 
and 
^V—1 ^V+l/ 
C< _ a I ^ ( P r i P''+l\ a Pr-\Pr 
r+1^2 — -'-1^+7 7 r V , -iOj —7 77 —. 
(pr\(p,—l 9 »'+l/ 9''-29 r-l 9 '- 
Putting these values into the series on the right-hand side of (52) it becomes, up to e 5 , 
ei Pr+\Pr+% 
j/% j/ 9 
(p ;•+!</> ;-+2 
and finally 
and therefore 
_ o 
C.,. </> r+lty i'+2 
1 
(53) 
^•+3_P I 
°V i r+2-4>'r+3 J 
The series for C( — — 3 can be easily found ; for 
a r ’ a r a,. J 
_ epr _ 1 — ,.- 2 S 1 e 3 + ■ ■ ■ _ ep 
Ci r (f>r-l 1—)--lS 1 e 3 + . . . 4>"r- 1 
-•[i+(,_ 1 s 1 -,_ 3 s 1 K+.-.], 
and therefore, 
CL, 
'»'-l 
a. 
—p,e 
o Pr -1 
'■ Wr- X ' 
_ o 
— =PrPr-ie'. . 7- 
C( r (p r—\(p r- 
Expanding these expressions in powers of e, we obtain 
