lis Me. E. Hunt on certain Phenomena connected wUli 



as to make the original axis vertical. In this case my investigation led 

 me to the same result as Major Barnard's analysis ; but this is not the 

 case of the common gyroscope, as I have already shown. The gyro- 

 scope, however, fulfils the conditions contemplated by Major Barnard ; 

 but there is a difference between its conditions and those of the case 

 treated at pages 135 and 186, which is not taken into account in his inves- 

 tigation. The analysis is not complete as apphed to all cases fulfilling 

 his various assumed conditions, and it would only have been so had the 

 first condition been — that the body be a soHd of revolution, such that 

 the centrifugal forces are balanced about whatever axis passing through 

 the point of support it may be turning ; but the condition so worded 

 excludes the common gyroscope. 



Major Barnard's analysis shows at any instant the position of the 

 line passing through the point of support and the centre of gravity, 

 that is, the spindle of the instrument to the end of which the weight 

 is applied. It does not however foUow that this Kne is at every instant 

 the actual axis of rotation, as is assumed by Major Barnard in his 

 interpretation of the analytical results. By the first theorem of the 

 composition of rotatory motions, the body cannot, under the given 

 conditions, rotate about an axis loive)' than its original one, — that is, 

 than the original position of that axis, — and, therefore, if the centre of 

 gravity descends, the line through it ceases to be the actual axis of 

 rotation. Indeed, the analytical residts, if properly interpreted, show 

 that the line through the centre of gravity is not continually the axis 

 of rotation, for what is the movement of this line along the cycloidal 

 curve but a motion of rotation about some other axis which has a 

 horizontal progressive motion ? It being indisputable that the body 

 is continually revolving on a different axis, or at least tending to do so ; 

 the anal^^sis is incomplete as far as regards its application to any body 

 in which the centrifugal forces are not balanced about whatever axis it 

 may be revolving. To make it applicable to the gyroscope, as commonly 

 arranged, it will be necessary to introduce an element which will have 

 the effect of showing how the results are modified by the occurrence of 

 an unbalanced condition of the centrifugal forces when the body tends 

 to rotate about an axis differing from its geometric axis. I have no 

 doubt that the analysis corrected in this way, if it can be done, will 

 show results coinciding with those I have obtained, by a different method 

 of investigation. 



Major Barnard seems to think that if the weight does not actually 

 descend, the horizontal precessional motion cannot take place, except as an 

 effect produced without a cause. But, viewing the matter in this way, 

 what does he gain by making his weight descend — as long as he brings it 



