Mb. Edmukd Hunt on Rotatory Motion. 205 



At page 70, Major Barnard says — "This sustaining power being 

 directly proportional to the rotatory velocity of the disc, as well as to 

 the angular velocity of the axis, diminishes with the former ; and as it 

 diminishes, the axis must descend, acquiring angular velocity due to the 

 height of fall ; hence the rapid gyration and the descending spiral 

 motion which accompanies the loss of rotatory velocity." This sentence 

 contains several errors : in the first place, theoretically, the sustaining 

 power is absolute for all rotatory velocities — that is, the gyroscope 

 always retains or recovers its original elevation, whatever the rotatory 

 velocity may be ; secondly, the descent of the axis is entirely due to 

 the resistance experienced to the precessional motion ; thirdly, the 

 angular or precessional velocity increases as the rotatory velocity de- 

 creases, and there cannot be any increase of it due to the descent ; if 

 an undulatory curve is being described, the descent will make it more 

 prolate ; but any tendency to increase the precessional motion will 

 immediately check the descent. 



At page 75, Major Barnard speaking of the top, saj's — " This rolling 

 speedily imparts an angular motion to the axis, greater than the hori- 

 zontal gyration due to gravity" — (there is a tendency to increase the 

 gyratory motion, but it takes effect in lifting up the top ; the gyratory 

 or precessional motion cannot be increased, unless the top is in some 

 way prevented from rising). " The deflecting force becomes in excess 

 and the top rises." Also, page 71, — "The addition to this gyratory 

 velocity, caused by friction, when the axis is inclined upwards, puts the 

 deflecting force in excess, and the axis is raised." Here we have the 

 mystical " deflecting " force figuring in quite a new way. If v/e do 

 assume that a " deflecting force " acts in producing the undulatory 

 motion, we cannot consider it as doing more than altering the direction 

 of motion, just as the connection between the pendulum bob and its 

 point of support makes the former move in a curve. If an undulatory 

 curve is being described, any additional forward impulse merely makes 

 the curve more prolate ; if the gyroscope or top is moving horizontally 

 there is no " deflecting force " in action, so that it cannot be excess of 

 that which causes a rise. In either case, the rise is derived from the 

 horizontal impulse in precisely the same way as the horizontal gyratory 

 or precessional motion is derived from the downward pressure of gravity. 



At page 74, Major Barnard says — "But these little undulations 

 speedily disappear, through the retarding influence of friction and 

 resistance of the air." In the case in which the top point is so free 

 from friction that the centre of gravity remains always in the same 

 vertical line, that friction must be quite unable to make the undulations 

 disappear. As to the resistance of the air doing so, the top may be so 



