CIECULAE CYLINDEES UNDEE CEETAIN PEACTICAL SYSTEMS OF LOAD. 201 
Now write 
I,! {a) = — 
g,! (a) = — (a) + g, (a), 
//(“)- +/.H, 
where denotes the first four terms of the above series for /«(«), with a similar 
meaning for (a) and_^/'^^ (a). 
Then if we substitute in the equations for 2 . 5 ; Q, we find ; 
(^ zz _ 1-266804 a' - 4-411716 1 i r^r 
ftE 
,4 s. . 8_. r _ V TTf _ 1141 V 1 
-f X 
1 
L 
— cos ■— — ^ , 
1 /r c 1 ?r 
, r. Y ( — 1V‘ nirz 
t 6 S ^ —-c”' cos — 
COS 
C I 
1 ir 
1 )" COS 
nirz 1 ] 
^ 7d f 
Now remembering that 
(-1)" 
uirz 
0 n 
TT" C'' 
4 
]r 
COS 
c 
~ 4 (;2 ““ 
12 
(- IT 
httz 
cos 
6' 
2^ TT'^ 
^ 2 - TT'^ 7 TT'^ 
c'i 48 
' 6-2 24 720 
(- 1)" 
7171.3 
1 
1 
k 
, C5 
z’^ TT® 32 771® 
3177® 
71® 
COS 
c 
c« 1440 
Y 288 6-2 1440 “ 
30240 
we find, using ira/c = 3, 
( 2.3 + 
fiEa^ 
2-493930 
22 ^4 ,G 
- 8-201525 —4- 2-251614” + -00972222 — 
a- 
a” 
!_ V / 1 Vi I 112 /«_ 8 _ 1 7 0 _L 3 3 5 
" vt"! 
(108). 
And, in a similar mannei' 
{(j)ip)r=a 
yLt.Eft'^ 
= - -3842415 4 1-6416832 - - ri284672 
a- 
q-i)”cos'YtAF + fF ^ 
n- 
2 D 
. COS). 
VOL. OXCVIII.—A. 
