502 MR. S. S. HOUGH ON THE OSCILLATIONS OF A 

{A +B—C+2AE— qe} + i67,{(A+B—O)(1+E)}—gl,= = 0, | 




i E 
'.{(A + B—C) + 2BE — 904} —i0',{(A-++B—C) (1+ B)} + qq ™ = 0, a 
a {1+q—E} +i-$ (eI) les (aeotn) = 0) 
ae {l-e_—E} —i= (1+E)+6¢,(83+2E) = 0. j 
These equations are correct as far as first powers of €, €, EK only. Solving for the 
ratios of @';, 6’,, B,/Tw*, B,/rw*, we have 




6", mp 
DAO =Osy) Os 0 Pees qCé,, 0 
| 3, Iie i suid) | 0 ea) (i215) 
| 0, {Dy heise, 10 € (8+2E), —i(1+E), 144—E| 
i B,/To" 
7 SOSA Cae AARC a ae, (0 
0, = 8a, i(1+E) 
3€5, 0, 1+e,—E 
aa —B, |r? 
~ |=1@+B=0) (+E), A+B=C+2BE=9Ce, gCe, 
0, Ss, ete = 
Be, 0, —i(1+E) 
or 
a, —i6', —1B,/To* —B,/To? 


GEB=Cye te =4m)  GEEB= Ce na= 4m a 3(es) OB =0) moe Ge=oE 
where the denominators are correct as far as first powers of ¢,, &c., only. 
Replacing E by its value $(e, + €,) (1 + g) we obtain 

Pie es Ws cet ele oe 
Oyo anb) we yee 3 3 
Taking 
6, = de" 
we have 
OY, = 19e" 
and, in the corresponding real motion, 
6, = 2¢ cos (At + 6), 
6, = — 2¢ sin (dt + e). 
The angular displacements, relatively to the fixed axes O€, On, OG at time ¢ are 
