OF ROTATING LIQUID CYLINDERS. 
93 
h + ^ - 
^ ^ ijr] 
500 
27T]^ 343/;"’ ^ 
+ — 6 r^ + 0 .7^“^ + . . .] 
5e-y)^ + oe.^r + 
= So, 
+ Qy] + + hlW + 47 ; + 0 . >7 ^ + . . .] 
9?; 
2 OlJ.^5 
_ 12 7,12 5„3 I .3 12 5 
5 6 7 8 1) () '/ ^ 
78,123 
7“’) - -^27 + 
_I_ 6 7_5. 5 I AIAy,3 _ I r“’:’'’LL i 
T^128^T^6i’? 144/; ^ ‘ 
+ mv^ - + 
+ ^5(fl>r+ llr + fH^ + ; 
21 ,S^j 
Gt; 
0250 
‘V 
.4)00 
+ . . . 
24:07} 
r.A 
+ ^ 3 ( 1 ^" + 4^ + + • • • 
+ <’i(il>) + :;^+...) 
p]<juating the coefficients of the various powers of rj, we obtain 
iii/? —— ii 0 7 jr I aA/7 
8 ‘'j — 1 2 8 T 3 2''5 
2 .5 
0 
"^5 + 
AS — _ 1 5 8,6 2 5 I 2,v 4- IV 
2 *^2 — 8y0 ■ 4 8'"3 W 8''; 
_ 2 5()u„ _ 15. 
2 4 3 1 5 “ 
oVffi ~ 2^3 + ¥^h “ IG 8^ — -|g- + f 1 0^5 + 4(^3 + tv • • 
" 3 - - ""F §2 - = M ooi ^ + Iffi 
(lOG), 
(107) , 
(108) , 
(109). 
Solving the first two of these equations, we obtain 
^5=-F- • • • (110), h=-\W- • ■ . (111). 
Equations (108) and (109) may be written 
-¥r^5-¥(^3 + -nffii)“ 10S,= .(112), 
-¥¥ffi-V(^3 + ¥iei)-¥'^ 82 -lffi= ¥oo'¥- • • (1'3). 
Multiply ( 112 ) and (113) by 20 and 9 respectively, and subtract, and we obtain 
+ 3008, - = ¥i¥.(114). 
From equations (110) and (HI) we obtain 
+ 3008, = W 2 ", 
and hence, by comparison with (114), — 0. 
This vanishing of e_^ .supplies a searching test of the accuracy of the work. 
Equation (112) becomes, after simplification, 
^3 + ¥j^i=-¥tF. (115). 
Our equations do not enable us to determine Cg and separately ; they are, 
however, all satisfied by taking 
(113), 
_ in 
(117) 
