244 
MR. S. S. HOUGH OH THE APPLICATIOH OF HARMOHIC 
On solving these equations we obtain 
+ 7 L, - "^5.7 4«V 
J ^^72 , _£_ _^2_ 1 ^ Jff2 _ ^3 
7 4a)%2J L. - 5.7 4foV L, - H, - Kg., 
after which we can deduce Og, Cg . . . in succession by means of (32), 
For example, taking 
_ J_ Jl_ _ _! 
20 ’ 4a)2a3 ‘ 30 ’ 
which makes the law of depth for the earth 
(14520 + 9680 sin’^^) feet, 
we find for the lunar-fortnightly tide 
1^2= - -13276, 4 = - -08722, Lg = - *07583, 
Lg = - -07156, Lio = - -06955, = - -0685, 
and 
log ^ 3 % = 4-1437, log = n 6-9549, log 4^70 = 6-9586, 
log ^sVs = 5-4217, log = 5-578, 
whence, if we suppose K ^4 = 0, we obtain in succession, from the formula 
?i 4-1062, 
3-7730 ; 
whence from (33) we find 
Cg = *4719(^3, C 4 = - -185260. 
Again 
log(Cg/Ci.) =log(Kg/77^) =n 2-6976, 
log (Cg/Cg) = log (Kg/ryg) = 2-3910, 
'og (Cio/Cg) = log (Kio/’^s) — 2 - 774 . 
log K ^3 = n 4*75, log K;^q = n 4-583, log Kg = 
log Kg = 4*0758, log = n 3-2025. 
Also 
log Hg = n 3*0206, log ^0 = 2-3707, log 7^2 = 
C3= - 
04= - 
( 33 ), 
