14^ ]Mr. E. Hunt on certain Phenomena connected with 



put a weight on the opposite end of the lever to lessen the downward 

 force of gravity on the gyroscope, so that the latter may not descend 

 inconveniently low. The lever b can turn on horizontal pivots in a ring 

 D fixed on the top of a tube e. The ring and tube turn freely round 

 the fixed pillar f, resting on a point, close under the ring, whilst anti- 

 friction wheels carried by the tube bear on the lower part of the pillar. 

 The phenomena shown by the apparatus arranged in this way may be 

 very beautifully varied. Thus, if the wheel is spun and then left free 

 with the lever in a horizontal position, care being taken not to impart 

 an impulse of any kind on removing the hand, we shall have a case of 

 two forces — the rotatory momentum of the wheel, and the downward 

 pressure of gravity. In this case, the centre of the wheel describes a 

 curve, indicated by dotted lines in fig. 14, resembling the common 

 cycloid, or more correctly, a spherical epicycloid, the cusps of the curve 

 being directed upwards. If, at starting, a forward horizontal impulse is 

 imparted by the hand, the case becomes one of three forces, — this 

 impulse being added to the rotatory momentum of the wheel and the 

 downward pressure of gravity — and the result is. that the curve described 

 becomes prolate, the cusps disappearing. If this forward impulse is of 

 a certain precise force, corresponding to the other two forces, it will 

 cause the precessional motion to be quite horizontal. In a third case, 

 a backwai-d horizontal impulse is given by the hand, and has the effect 

 of making the curve curtate or looped. 



An insight is gained mto the second and thii'd cases by considering 

 the effect of first compounding two of the three forces — the rotatory 

 momentum of the wheel, and the horizontal impulse given by the hand, 

 — and then as it were superadding the downwai'd pressure of gravitj'. 

 In the second case, the forward impulse, combining with the original 

 rotation, would tend to produce rotation about an axis passing above the 

 centre of the wheel, so that the superadded action of gravity would be 

 the same as that of a weight attached to a point beJoiv the pole of 

 original rotation of a sphere supported at its centre. Similarly in the 

 third case, the backwai'd impulse, combining with the original rotation, 

 would tend to produce rotation about an axis passing beloio the centre 

 of the wheel, and the superadded action of gravity would be the same 

 as that of a weight attached to a point above the pole of original rota- 

 tion of a sphere. It will thus be seen that the circumstances in the 

 three cases are varied in a manner analogous to the variation of those 

 under which the several forms of plane cycloids are described, by a point, 

 carried by a disc, rolling along a straight line. 



In the gyroscope the curves are prevented from being true spherical 

 epicj'cloids by the varying leverage of the weight, and also by tlie action 



