72 J. G. Barnard on the Motion of the Gyroscope. 
tre as if it were fixed. Calling # the resistance of the ater 
M the —— and Mg the a, of the top, andz the height of © 
the centre of gravity above the plane, we shall have for the q 
equceal ‘of motion of the otitis of gravity* s 
Mae —R— Mg (1.) 
As the angular motion of the body is the same as if the centre 
of gravity was fixed, and as 2 is the only force which operates — 
to produce Se anpie about that centre, if we call C the moment — 
of inertia of the tup about its axis of figure, and A its moment — 
with iitince th a perpendicular axis through ee centre of — 
gravity, and y the distance, GX (fig. ay of the point of support — 
that centre; the equations of rotary motion will become — 
identical with equations (3) (p. 53),+ sbestintite R for Mg 3 
Cdv,=0 a 
Advy,—(C—A)v,1,dt=yaRdt (2.) : 
Adv,+(C—A)vyv.dt= —ybRdt 
The first of — (2) gives us v, as for the gyroscgiiee ;. 
ge ; 
equal a consta 
Multiplying, the 2d and 3d of equations (2) by vy and Ur Te 
spectively, gnc Pages and making the same reduction as on Pe 
53, we shall 
A (vydvy+-v,dv,;)=Ry d.cos 4. | 
* As there are no horizontal forces in action, there can be no horizontal motion 
of the centre of gravity a ie from sien ae ulse, which a here exclude. : 
The references throughout this peg 2 my paper e gyroscope in the 
nal. 
July number of this Jour 
