68 J. G. Barnard on the Motion of the Gyroscope. 
these two extreme cases (for moderate rotary velocities) the un- | 
dulations of the axis, will be large and sensible. : 
I have likewise shown that whenever, to the axis of a rotating 
solid, an angular velocity is imparted, a force which I have — 
called “ the dejlecting force” acting perpendicular to the plane of — 
motion of that axis, is developed, whose intensity is proportional 
to this angular velocity, and likewise to the rotary velocity of 
the body; and that it is this deflecting force which is the imme- 
diate sustaining agent, in the gyroscope 
In the above deductions of analysis is found the full and com- 
plete solution of the “self-sustaining power of the gyroscope.” 
make the character of the motion indicated by analysis, — 
sensible to the eye, it is only necessary to attach to the ordinary | 
gyroscope, in the prolongation of the axis, an arm of five or six — 
inches in length, and having an universal joint at its extremity, 
and to swing the instrument as a pendulum; or, the extremity — 
of an arm of such a length may be rested in the usual way, — 
upon the point of the standard, when, with the centre of gyra- _ 
tion removed at so great a distance from the point of support, — 
the undulatory motion becomes very evident. 
_ But it cannot fail to be observed that the motion preserves — 
this peculiar feature but for a very short period. The undula- — 
tions speedily disappear; instead of periodical moments of rest — 
(which the theory requires at each cusp) the gyratory velocity — 
becomes continuous, and nearly uniform and horizontal; andit | 
increases as the axis (owing to the retarding influences of friction | 
and the resistance of the air) slowly falls. In short, the axis — 
soon seems to move upon a descending spiral described about a — 
vertical through the point of support. eo. 
The experimental gyroscope, in its simplest form consists of — 
two distinct masses, the rotating disk, and the mounting (or ring — 
in which the disk turns). The point of support in the latter, — 
though it gives free motion about a vertical axis, constrains 
more or less, the motion of the combined mass about any other — 
The rotating disk turns at the extremities of its axle, upod — 
points or surfaces in the mass of the mounting, with friction ; it 
is rare, too, that the point of support, of the mounting, is ag 
justed in the exact prolongation of the axis of the disk. 
Without attempting to subject to analysis causes so difficult — 
_ to grasp as these, I shall first attempt to show, by general con 
siderations, what would be the immediate influence of the Te — 
tarding forces of friction and the resistance of the air upon our 
theoretical solid; and then point out the further effect due to the 
discrepancies of figure, above indicated. Leaving out of con 
sideration the minute effect of friction at the point of support 
these forces exert their influence, mainly in retarding the rolary 
velocity of the disk. Friction—at the extremities of the axle 
