520 
MR. G. H. DARWIN ON THE PRECESSION OP A VISCOUS SPHEROID, 
Now the force on the moon tano-ential to her orbit, results from a double tidal 
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reaction. By the method employed in Section 14, the tangential force due to the 
earth’s tides is 
rp C T 2 . 
1 =— = --sm 4e, 
r 2r a 
and similarly the tangential force due to the moon’s tides is 
C t~ vftci 
2r a vPa' 
sin 4e\ 
and the whole tangential force is (T-fiT'). 
Hence following the argument of that section, the equation of tidal reaction becomes 
id! 
^ cl t 2 g?i 0 
sin 4ej 
wht 
vPa' 
sin ie\ 
Then taking the moon’s apparent radius as 16', and the ratio of the earth’s mass to 
CL W 
that of the moon as 82, ive have ,= 3'567 and — = T806 (so that taking iv as 5^, the 
specific gravity of the moon is 3), and hence —,= ll - 64. 
At first sight it would appear from this that the effect of the tides in the moon was 
nearly twelve times as important as the effect of those in the earth, as far as concerns 
the influence on the moon’s orbit, and hence it would seem that a grave oversight has 
been made in treating the moon as a simple attractive particle ; a little consideration 
will show, however, that this is by no means the case. 
Suppose that v , v are the coefficients of viscosity of the moon and earth respec¬ 
tively ; then the only tides which exist in each body being those of which the speeds 
are 2(ou —/2), 2(n — fl) in the moon and earth respectively, 
But 
and hence 
, 19u(« — SI) 19y(n — fl) 
tan 2e , =-— and tan 2e, = - 
g a tv gavj 
(j a w —gaw 
wa. 
tan 2e\ 
w—fL v’ 
n — fl v 
tan 2e i 
It will be found that 
wa 
= 41 TO. It is also almost certain that u must for a 
