276 
ME. GrEORG-E H. DARWIN ON THE INFLUENCE OE 
Hi — (A-j-atf) a+^i, H 2 — (A-|-b£)/3-|-|^ 2 , H 3 — (C + c t)y-\-^ 3 , 
where ^£h, ^ 2 , ^ 3 , denote those parts of the double areas conserved, which depend only 
on the internal motions accompanying the change of shape. 
Then, if the changes proceed with uniform velocity, a, a, &c. are all constant. 
Corresponding also to the equations of motion are the geometrical equations 
dQ . 
^=9 2 cos i p + sm <p ; 
^7 sin Q=—Q 1 cos <p+ 0 2 sin <p ; 
dtp d^ 
dt'~dt 
COS 0 = 0 3 '. 
Eig. 1. 
z 
In figure 1, A, B, C are the axes, about which the moments of inertia are X 1? A 2 , X 3 ; 
XY is the ecliptic ; and the meaning of the other symbols is sufficiently indicated. 
Substituting, then, for the various symbols in the original equations of motion, it will 
be found that 
C)^ 3 =L — — (b — c) ows + b yu 2 — c/3^| — a*q — { My +%\&> 2 
and two similar equations*. 
Now the terms on the right-hand side are always very small compared to A^ 1 , because 
the time will not run on until they have become large ; hence approximate values may 
be substituted therein. 
* The A is written A' in two places, where it may he taken to stand for B ; and then the other equations 
may be found by cyclic changes of letters and suffixes. 
