204 Me, Edmui^^d Hunt on Rotatory Motion. 



ning, with the lever horizontal. If now a vertical impulse is imparted 

 to one end of the lever, the wheel will describe a circle ; if the Major's 

 view is right, this circle should become larger and larger ; on the con- 

 trary, however, the circle becomes less and less, owing to the action of 

 the centrifugal resultant. I believe the decrease in the rotatory velo- 

 city of the fly-wheel would of itself tend to make the curves more 

 prolate, but not in the way shown by Major Barnard, nor to anything 

 like the extent actually seen in practice. 



In his first paper Major Barnard endeavours to shov/ that the undu- 

 latory motion is such as would be produced by the combined action of 

 gravity, and what he terms a deflecting force. Supposing there is such 

 a deflecting force, it will be directed to a point travelling along the 

 level of the cusp of the cycloidal curve ; in the sujiposed case in which 

 the rotatory velocity continues uniform, and the cusped cycloid is 

 described, this point travels at such a rate as to coincide with the point 

 describing the curve at each cusp ; but when the rotatory velocity 

 decreases, the point travels faster ; so that on its reaching the point at 

 which the cusp would have occurred, the gyroscope is below it, instead 

 of coincident with it, and the curve is deflected, as shown at a^ (fig. 1, 

 Major Barnard's second paper). The mean motion along the cui-ve is 

 in a certain sense independent of the mean horizontal angular motion — 

 that is, the motion of the point to which I have supposed the " deflect- 

 ing force" to be referred. If the motion along the curve is retarded 

 (which can be done by imparting a forward horizontal impulse), the 

 motion of the " deflection " point is more rapid in comparison, and the 

 curve described is prolate. On the other hand, if the motion along the 

 curve is sufficiently accelerated, the gyroscope will get in advance of the 

 "deflection" point, rise above it, and form a loop round it. The intro- 

 duction of the idea of a '" deflecting force " facilitates the conception of 

 the way in which the curves are modified ; but I think Major Barnard 

 unnecessarily mystifies it. This deflecting force simply corresponds to 

 the radial pressure on the point of support in the case of the ordinary 

 pendulum. What corresponds to the point of support in the common 

 pendulum is in the gyroscope what I have termed the precessional axis, 

 which is continually moving round. In the common pendulum, the 

 bob is at each instant moving in a direction at right angles to the line 

 between it and the point of suppoi't ; and similarly the gyroscope is at 

 each instant moving at right angles to the plane between it and the 

 imaginary precessional axis. 



In my former paper I have endeavoured to explain actions having a 

 much greater influence on the form of the curve than the mere decrease 

 in the rotatory velocity of the fly-wheel. 



