494 MR. 8S. 8. HOUGH ON THE OSCILLATIONS OF A 
we have 
({P Ax, Yyi2, — 0, [ | Pidaapec—105 
\) Pdo yy" = ys mp(p> —_b°) (p? — c*J, &e. 
Therefore, 
[[pP do ye, = — oO,p, ate mp (p? — 2) (p? — 2), 
and the corresponding part of L is 
— y's 7p1- p (p” — b*)* (p* — e*)* (c? — 6") w°O,. 
Similarly the parts of M, N arising from this part of p are 
+ sap. p(p? — BY. (p? = 2) (— c2) o% and 0. 
(c.) Lastly, if 
aa hod ; B, B 
p= pipe a B, {a — y? — 30°?} + Byyy, + a Tae AF a ne | > 

C — is 9 9 9 9\2 9 9 B. in 
c 9 9 9\2 B, 4 
—3@ 8 ies 20 do = + y's 7p,C°p (p* — 6°) (p® — oP = e™, 
b? 9 9 19,2 9 2 5 
(pe —B) {|Pp yx do = — 485 7p,b*p (p* — b*)} (p* — ce”)? Bie™. 
Collecting the different parts, we obtain for the couples, provided there be no 
external disturbing force, 
: 9 9\2 9 9 B, iAt 
=) 35 Tp P(p’ — 0") (po ee — Bb), {08 + Be \ 
9 9\,2 i) 9\2 9 By a 9 
M = + vfs mpi. p(p? — b) (p? — et) e®. |e — 06, 
N = — +57 p,- p (p? — 0”)? (p? — &)' 0. Bye™ 
= (u — ») Bye™ J 
