486 MR, G. H. DARWIN ON THE PRECESSION OF A VISCOUS SPHEROID, 
Since the tidal reaction on the sun is neglected, t / is a constant, and since r varies as 
fl~ (and therefore as | r_G ); hence 
t~ n Q u - t/ n 0 0 tt / n 0 uu t 
g?i n | 12 ’ g» n ' ’ g?i £ 6 
Let p be equal to , where a is the coefficient of viscosity of the earth. Then 
according to the theory developed in my paper on tides" 
, o 2 % , 71 „ 2/2 
tan 2e= —, tan e = -, tan 2e = 
P P P 
(64) 
To simplify the work, terms involving the fourth power of the sine of the obliquity 
will be neglected. 
Now let 
P=£ l°gio V Q = f sin 3 i lo gio e, R= -TeZ^rj log 10 e=£Q sec i 
bUb 0 
u=£ sin 3 i log 10 e, V = 1 IpJ, log 10 e \ • • ( 6 ■ 5 ) 
W=^ cos' 3 i, X=T sin 3 i cos i, Z=^ sin 3 i cos 3 i 
Also let snJ 2a=-, — — JV ; 
Q 
6 * — “5 
/* 
and it may be called to mind that 
The terms depending on the semi-annual tide will be omitted throughout. 
With this notation the equation of obliquity (35) and (36) may be written, 
cli 
logi 0 e — = sin i cos i{ 1 — f sin 3 i) 
yp+^/)(P sin 4e+Q sin 2e) 
—' ~ (U sin 4e+V sin 2e') — ,P sin 4e' 
( 66 ) 
The equation (43) of friction becomes 
—f = (f + “' ! ) (W si “ 4£+Xs “ 2e ') + f z si " 2£ ’ ■ • • • w 
And by (58), Section 14, the equation of reaction becomes 
=~—(W sin 4e + X sin 2e) .(68) 
* Phil. Trans., 1879, Part I. 
