342 Mr. J. Bridge on the Gyroscope. 
Also let ia=0, and let ia make an angle yx with the vertical 
circle through 7. Then « being the angular acceleration which 
would result from the given weight if it were applied at right 
angles to the axis at a, we have (Airy’s Tract on Precession, 
art. 12), 
Be Fe Oo gt 10 Ay esa ad 
dy _ atk 
Fp = c@8 sin x 5 por & 2128) Cree 
also 
7 eee ale dp dy 
SID X CosWae + cosy 5 - + + (©) 
since the change in @ arises entirely from the change in position 
of 7, and not from the rotation about 7. And 
ght i ehirdets WML 
6 = 08 cos x cos r= Se (D) 
the change in y resulting in part from the rotation about 7, and 
in part from the change in position of 7. 
By substituting (A) and (B) in (C) and (D), we obtain 
dé 
a. 
ah =n x cos fy 
dy 4 
0 = — 7 c08 x cos + (1+c)o. 
If Ocosy=u and @siny=»v, the preceding may be replaced 
by the system of equations 
du 
7 doi Co +c)v, 
Oy (1+c)u— co 
er @ ame 
db _ a cou 
dé @ cosy’ 
dy _ 
ait se CMU 
Also 
dq’ 
pOP 
cos dp Os 
dy! _ 
