504 MR. G. H. DARWIN ON THE PRECESSION OF A VISCOUS SPHEROID, 
If therefore we put x— '(/ft, we must stop tlie integration at the point where 
n=2x 3 sec i, x being given by the equation 
sec i 
— I +P 
1 — 
yn 0 
And if we assume 7=14°, x is given by 
ad— \n Q cos 14°(l+/a)cc+ — cos 14 =0 
because /x= 1-f-sw 0 /2 0 \ 
Now at the end of the third period of integration, which is the beginning of the 
new period, I found 
log n 0 =3*84753, log g=9*82338 —10, and log s=5*39378 —10 
The unit of time being the present tropical year. 
Hence the equation is 
ad—5690a+ 19580 = 0 
The required root is nearly ^/5690, and a second approximation gives x=S2' = 16703 
(16*51 would have been more accurate). 
But /2y= 8*616. Hence we desire to stop the integration when 
t /'A»Y 8-616 
?= ^ ) = —= ol6. 
n 
16-70.: 
Now /x = *6659 ; hence when |=*516, A=l'32*2. 
In order to integrate the equation of obliquity by quadratures, I assume the four 
equidistant values, 
A= 1-000, 1*107, 1*214, 1*321 
And by means of the equation 1 — (y—'^ = 1 — (A--l)(l*502) the corresponding 
values of £ are found to be 
1*000, *8393, *6786, *5179 
Then by means of the formula— = — the corresponding values of are found 
to be 
n n n i 
Nf 
*0909, *1388, *2395, *4951 
I assumed conjecturally four values of 7 lying between 7 0 = 15° 22' and i— 1 4°, which 
I knew would be very nearly the final value of 7; and then computed four equidistant 
cl 
values of — -— log 10 tan 
The values were 
*19381, *16230, *11882, -*00684. 
The fact that the last value is negative shows that the integration is carried a little 
beyond the point when n cos 7=2/2, but this is unimportant. 
