4G2 MR. G. H. DARWIN ON THE PRECESSION OP A VISCOUS SPHEROID, 
two equations. But when C — A is neglected compared to C, the integrals of these 
equations are the same as those of 
dm l It dm . 2 Jft dm 2 di 
~dt = O’ ~dt~ cT’ ~di~~C .( 26 ) 
apart from the complementary function, which may obviously be omitted. The two 
former of (26) give the change in the precession and the obliquity of the ecliptic, and 
the last gives the tidal friction. 
§ 7. Precession and change of obliquity. 
Then by (17), (18), and (26) the equations of motion are 
dw l 
dt 
dm. 
dt 
= F sin n -|-G cos n 
-F cos n + G sin n 
y 
and by integration 
OJ 
=-f — F cos n 4-G sin n\ F sin n —G cos ii\ 
oi - 1 A ni L. 
But the geometrical equations (1) give 
di 
dt 
d'yf/' 
dt 
= — aq sin w+ctq cos n 
sm4=-w 1 cos n—a q sm n 
Therefore, as far as concerns non-periodic terms. 
di G dilr . . F 
t =-, ,sinj=- 
dt n dt n 
(27) 
(28) 
(29) 
If we wish to keep all the seven tides distinct (as will have to be done later), w 7 e 
clx cIaIt 
may write down the result for --and — from (15) and (16). 
But it is of more immediate interest to consider the case where the semi-diurnal 
tides are grouped together, as also the diurnal ones. In this case we have by (19) 
f= T fiPQ(l-mZs™^+irQ s E'ame'-IQ 3 E"sm2e'} . . . (30) 
and since sin i=Q 
®=^£iP(l-fences <U-P(\-W)E' cos t'-PW'cos 2e "} . (31) 
