700 
ME. HOPKINS ON THE THEOET OF THE MOTION OF GLACIEES. 
C E 
it is meant that the ratios jr and |r are small ratios. This is equivalent to the assuming 
that the force on any element parallel to the axis of z is small, and that the couple 
Avith reference to an axis parallel to that of y, is also small. The condition D=0 signi- 
fies, as in the first approximation, the absence of a couple on every element, vrith refer- 
ence to an axis parallel to that of cc. 
Hence putting D=0 in our general cubic, we have 
or 
{(A— ^)(B— ^)— F^}(C— ^)=E^(B— ^). 
Putting C=0 and E=0, we have, as before, for the three first approximate values of^, 
p,=i{A-fB+y(A-B)^+4P}, 
P2='2'{^“1“® — — B/+4E®}, 
P3=C. 
To proceed to a second approximation, put 
in the cubic, and we obtain 
{d\) 
or 
{(A— ^1— ^^l)(B— ^1 — ro-i)— E"}(C— ?7,)=(B— ^1— a7,)E", 
{(A— ^,XB— F"— (A— ^,-l-B— 
The first approximation gives 
(A— ^,XB— pi)— F"=0 ; 
and the preceding equation shows that must be of the order E^. We may therefore 
neglect terms in Wi E^ and and we then obtain 
_(A+B-2p0(C-i).K = (B-^.)E^ 
jOj — B . 
and 
itt/ 1 
or, since C is small, 
A+B — 2j!?j — 
Pi-B 
■2pi-(A + B) 
Ts’a and ra -3 may be found in the same manner. 
23. Again, equations (c.), art. 16, become, if D = 0, 
(A— j)) cosQ5-f-F cos/3+Ecosy=0, 
F cos a-|-(B— cos j3=0, 
E cos a+(C— cos 7=0, 
The two last equations give 
(c".) 
cos a= — 
C-P 
E 
cos 7 , 
o F C-p 
cos (3=^:^ -^cosy. 
