ANALYSTS TO THE DYNAMICAL THEORY OF THE TIDES. 243 
when 
h - I™ + i sin= ej = 14520 + 7218 sin"* 6, 
C = gj[-4576P3 - •1821P4 + •0137PJ ; 
and when 
h = j L _i_ L — 7260 + 7218 sin^ 
r/ [40 6.7 ^0 J 
C = (S2[-3457P3 - • 2075 P 4 .+ •0234P,]. 
For other values of I we must employ a method similar to that of the last section. 
The general formulae for the computation of the forced tides due to a disturbing 
potential of the second order are 
where 
T p _L n _ I 4 l'y.2 
leg, 
4 Iq^ 
— ~ 
^4,0^ — LqCj; 4- ^6^8 = 0 
9 f! 
_ hi 
5.7 4«2rt2 
c2_ I _.. \ rc 
4(o^-a- 7 4«%2 1 '-3 
2.3 ^2 
5.7 4:co^a 
2„2 
6.7 
h- • (31), 
iu = 
1 — 91 (n + 1) Ignhw^a? 
{2n + 1) (2« + 3) 
^«-2 
1 — % (71 + 1 ) lg,ilAo)^a“ 
{291 - l)(27t + 1) 
P — 1 , 2{1 — n{9fi+ 1) lg,pw‘’“a~] _ kg„ 
n{n -t .1) (271 — 1) (271 + 3) 4:<jra~ 
Let us introduce the notation 
TT ^ngn ^n — iVn — n 
H„= -- 
— 2 
—2 ^nVn 
T — T 
. - L, ’ 
Then it may be shewn, as in the last sections, that for values of n greater than 2, 
4- 2 / — K,; + ^l’^n 
( 32 ), 
and therefore the first two of equations (31) may be written 
©0 
T p I „ p _ J ^‘^2 I 4 ^5^2 1 
- F3O2 + 773©, _ |^^2^2 + 7 4^2^2| -2. 
fA-(L-K0C,= -|U-g,. 
2 I 2 
