WITH THE TIDES OP A VISCOUS SPHEROID. 
579 
Then if we multiply each of the sines by its appropriate factor given in (63), and 
substitute from (64) for each of them in terms of sin 4e, and collect the results from 
(66), (67), and (68), and express by the symbol S the corrections to be introduced for 
the effects of inertia, we have 
! irC-H|U4(i-M 3 +«i-2x)*-i}TU 4 T;- T r, ] 
dt 
P .W-[ t 2 (1-X) 3 + T/ 2 ] 
clt 
9»o 
9 
9«o 
Now 4(1 — \) ? +4(l— 2X) 3 —i = (l — 2\)(4— 7X+4A. 2 ). Therefore if we add these 
d| 
dt 
di dN . 0 dp 
corrections to the full expressions for —, — (in which I put 1— \Q' — P) and P-ur, given 
clt dt 
,n~ 
in (83) “Precession,” and write K=-^^- for brevity, we have 
dt, N Oy 0 
/»{»»(, -X)+r;+|rr,f+K[(l -X)V+t,“] 
clt 
(■ (69) 
dt n-~ 
— sin 4eP 
r clt “W 
i-A+K(i-a) 3 
The last of these equations may be written approximately 
clt 
^d~f 
J-— sin 4e P( 1 —^ 
' 9^o 
P 
-l 
[l K(i X) 2 ] 
• (70) 
Then if we multiply the two former of equations (69) by (70), and notice that, when 
P is taken as unity, 
(1—2X)(l- : |A+X 3 ) —jl—A)(l —X)—J;A(1 —2X), 
and that 
1 — (1 — X) 2 =X(2 —X) and — £+(1 -X) 3 =l(l — 2\)(3 — 2X). 
we have 
