470 MR. G. H. DARWIN ON THE PRECESSION OF A VISCOUS SPHEROID, 
§11. The rate of change of obliquity when the earth is viscous. 
In order to understand the physical meaning of the equations giving the rate of 
change of obliquity (viz.: (35) and (36) if there be two disturbing bodies, or (29) if 
there be only one) it is necessary to use numbers. The subject will be illustrated in 
two cases: first, for the sun, moon, and earth with their present configurations; 
and secondly, for the case of a planet perturbed by a single satellite. For the first 
illustration I accordingly take the following data: e/= 32T9 (feet, seconds), the earth’s 
mean radius « = 20'9 X 10° feet, the sidereal day '9973 m. s. days, the sidereal year 
= 365’256 m. s. days, the moon’s sidereal period 27‘3217 m. s. days, the ratio of the 
earth’s mass to that of the moon v— 82, and the unit of time the tropical year 365'242 
m. s. days. 
Then we have 
‘9973 in radians per m. s. day 
r=|x gV of 47 r-P (month) 2 
r / = § of 47r -P (sidereal year) 2 . 
Then it will be found that 
fUo 
n 
T 
= ‘6598 degrees per million tropical years 
' =-1423 
9Vo 
(39) 
TT 
'= *3064 
These three quantities will henceforth be written nr, u~, uu t . 
For the purpose of analysing the physical meaning of the differential equations for 
C ~ and V no distinction will lie made between — and — , &c., for it is here only 
dt dt\nj g n g« 0 
sought to discover the rates of changes. But when we come to integrate and find the 
total changes in a given time, regard will have to be paid to the fact that both t and 
n are variables. 
For the immediate purpose of this section the numerical values of nr, u~, uu / given 
in (39), will be used. 
I will now apply the foregoing results to the particular case where the earth is a 
viscous splieroid. 
2(jctw 
Let P ~fd h’ 
where v is the coefficient of viscosity. 
