Bre) Mr. J. Bridge on the Gyroscope. 
Hence the motion of the extremity of the principal axis may be 
considered as compounded of a precessional motion with velocity 
__* _ about a vertical axis, and a nutational motion in a small 
pe di ( p a COS fh Th , a 
circle of radius Tee are e€ expression (+e)o 
represents all which it was required to account for. Also, since 
(1+) =e its value is = ; and aA is proportional to the mo- 
ment of the force applied, so that the expression becomes t) 
which is independent of the moment of inertia about an axis at 
right angles to the axis of figure. 
That the rate of precessional motion does not depend upon 
the moment of inertia about a principal axis at right angles to 
the axis of figure, may be illustrated by means of a simple appa- 
ratus such as the following :—Two equal circular boards are 
made to slide on a steel rod passing perpendicularly through 
their centres. They are placed at equal distances from the 
middle of the rod, where there is a groove running in a socket 
in which it may be made to rotate, and by which it is freely 
suspended. When this is weighted, it will be found that the 
rate of precessional motion is independent of the distance of the 
boards from the groove. This may be best judged of by the 
constancy of the ratio which the square of the number of seconds, 
or ticks of a watch, in which the precessional motion increases by 
a given quantity, bears to the number of turns. 
In the pteceding investigation, the change in the value of @, 
arising from the weight being applied to the principal axis 
instead of the instantaneous axis, is neglected. This will easily 
be seen not to affect the approximate results. 
The Second Problem. 
Let the axis aa! be now free to move only in the plane Aaa’ ; 
this plane will then be pressed upon at the points a, a! in a direc- 
tion perpendicular to the plane, and an equal and opposite pres- 
sure will be exerted on the axis at the points a a’; let the angular 
acceleration due to these pressures be 8, and that due to the 
external force applied in the direction of the plane, a. 
The equations A, B then become 
dp _B 
ae —-—COU, 
dpa 
Wt =——co@v ; 
whence we easily find 
