no 
ME. GEOEGE H. DAEWIN ON THE INFLUENCE OF 
of inertia C. Let O be the point where the axis C cuts the earth’s surface, and let 
OX, OY be parallel to the axes of A and B. Then z=l ; and if the earth’s radius be 
taken as unity, x and y will be the coordinates relatively to OX, OY of the point P in 
which the normal to the invariable plane cuts the surface. 
Putting therefore z=l in the preceding equations, we find for the determination of 
x, y that 
and 
u= — £>, V=GT. J 
In these equations we are to regard a, b, u, v as given functions of the time. 
Eliminating y, we have 
a (it) +*=£©-* (4) 
which is a linear equation, from which x may be found by integration ; and then, by the 
first of equations (3), 
i / v-7~A 
(5) 
1 / dx\ 
y=a \ U -di ) 
If B=A, the presence of a in the equations would merely mean that the axes of x 
and y revolve with an angular velocity <r; and so we lose nothing of interest with 
reference to the terrestrial problem by supposing <7=0. If, then, we take A and B 
constant, equation (4) becomes, 
where 
cPx du 
u 2 =ab. 
• (6) 
To integrate this according to the method of variation of parameters, put 
and 
£=P cos od-\-Q sin at (7) 
— Peysin^ + Qiycos^ (8) 
