242 
MR. S. S. HOUGH ON THE APPLICATION OF HARMONIC 
Similarly, when 
h = 
4«2«2 / I 1 
<y UO 4.5 
— sin® 6 1 = (29040 + 15454 sin^ 6), 
fJi / 
I = (5,[-6201P.3 - -1446?^ ; 
when 
]i = i JL Q I — (14520 + 15454 sin- d\ 
rj \^20 ^.0 rj^ I ^ 
I = C5o[- 5018P3 - -ISOrPJ ; 
and when 
h = — i ^ siiP e ) = (7260 + 15454 sin^ 0), 
'j \40 4.5//, / ' 
I = 62[-4095P3 - •2248P,]. 
x4.gain, if we take 
I = 
4cokr 
6.7//, 
= 7218, 
the series for ^ will terminate with a term involving P^, and the values of C^, C,, C 
must be computed from the equations 
“b 
eoC, - L,c, 
- LeCe 
I 4 Ig \ 72 / hg„ 4 lgc,_ , „ 
4a)Ad 7 4«kd/ g “ 7 4 «%"-' 
2.3 
5(7 4«kr 
- • hi 
2.3 Ig, 
5.7 4(o%- 
(5.,. 
= 0; 
from which we find, when 
hg^ 
larii? 
f], = -731662, C, = - - 097862 , Co = -002462. 
Thus for the law of depth 
_ bfdP A _p A Jh gpy ^1 = 58080 + 7218 siiP 6. 
g \o ^ b.l g, J 
^ = 62[-7316P2 - -0978P, + -0024P6]; 
in like manner, when 
li = + A 4k spy 5/1 ^ 29040 + 7218 siiP 9, 
// [10 b.i g^ J 
^ = 62[-5954P.3 - -I426P, + •0064Po] ; 
