Rotatory Motion, the Gyroscope, ^c. 147 



directed upwards, are in a horizontal plane. He says that in experi- 

 menting with the gyroscope, the rotatory velocity usually given to the 

 fly-wheel is so great that the cycloidal oscillations of the spindle are so 

 exceedingly minute, that, to the eye, the axis seems to move horizontally with- 

 out any oscillation at all ! He does not, however, explain why we do not 

 see these oscillations gradually increasing in amplitude, as they ought 

 to do, according to his and Poisson's theory, as the rotatory motion 

 gradually becomes less. With a well made Bohnenberger gyroscope, 

 the weight continues sustained and moving round horizontally without 

 oscillation when the rotatory velocity of the fly-wheel has diminished 

 to a veiy low rate, — when the circumstances, indeed, become such, 

 that, according to their theory, the weight ought to move through 

 cycloidal curves almost lying in a vertical plane through the point of 

 support. The assumption, that in the ordinary experiments, the cycloi- 

 dal oscillations ai'e present, but too minute to be noticed by the eye, 

 will appear very unsatisfactory also, when we consider that by the 

 theory the oscillations shown by a given instrument are greater or less 

 accordingly as the rotatory velocity of the flj'' -wheel is less or greater ; 

 but the greater the rotatory velocity of the fly-wheel is, the less rapid 

 is the precessional motion ; and for the oscillations to be infinitely 

 small, the rotatory velocity must be infinitely great, and the preces- 

 sional motion nil. Now, the precessional motion usually exhibited 

 indicates that the rotatory velocity is very far from being infinitely 

 great, and therefore the oscillations must be far from being infinitely 

 small. At the least, these considerations would lead us to expect that, 

 if the theory is correct, the gyroscope could easily be arranged so as 

 to show the oscillations in a marked and unmistakeable manner. I 

 must here remark that oscillations can be produced in the Bohnen- 

 berger gyroscope even when the wheel I'otates very rapidly, — namely, 

 by fixing a small weight to one side of the wheel rim ; but there is no 

 mistaking these for the cycloidal oscillations, as they increase with an 

 increase in the rotatory velocity and vice versa, whilst the cycloidal 

 oscillations should vary inversely as the rotatory velocity. 



The analysis of Major Barnard is not of such general application as 

 he seems to have supposed. The case considered by me at pages 135 

 and 136, fulfils the conditions assumed as the foundation of his analysis. 

 The sphere is a solid of revolution ; with a weight applied to the pole of 

 the original rotation, the axis of that rotation passes through the point 

 of support (the centre of the sphere) and the centre of gravity of the 

 entire mass, and corresponds to the geometric axis ; it is supported 

 at a point in what corresponds to the geometric axis, at a given distance 

 from the centre of gravit}"^ ; and gravitation tends to turn the body so 



