﻿Disk rotating in a Vacuum. 27 



The agitations to which I ascribe the heating are communi- 

 cated to the disk by the wheel work ; they are due to slight irre- 

 gularities in the working of the axes and wheels, and are snch 

 that the rotating disk and its axis, within the play left to it, is 

 continually moved backwards and forwards. 



Such an oscillation cannot escape observation ; for the radius 

 of the disk amounts to 6 \ inches =165 millims. If, therefore, 

 the axis (which is certaiuly far shorter) moves only the hun- 

 dredth of a millimetre in its bearings, there must be a shaking of 

 the edge, and in rapid rotation an apparent increase in the thick- 

 ness, of the disk. 



Stewart and Tait have, it is true, noticed this phenomenon ; 

 they observed a rising and sinking of the aluminium disk used 

 (which was ^ inch thick) of 0*015 inch, or 0*38 millim., on 

 both sides of the edge*. They explain this, it appears, on the 

 assumption that disk and axis were not fastened to each other 

 exactly at right angles. I consider it not less probable that 

 an oscillation of the axis was the cause. 



If, however, this assumption is correct, it is a necessary con- 

 sequence that the oscillation must be the stronger the lighter the 

 disk. This, in fact, was noticed by Stewart and Tait ; for they 

 found that while the disk of 2 \y inch thickness deviated by 0*015 

 inch, that which was half as thick moved up and down as much 

 as 002 inch. 



It follows, moreover, from this assumption that the vis viva 

 which was communicated to the disk by the wheel work must 

 have been the same in both cases. The quantities of heat re- 

 sulting from these equal vires viva must have been equal; that 

 is, the one of half the thickness must have been twice as hot as 

 the one which was double. This, however, is exactly what has 

 been observed by Stewart and Taitf. 



After this confirmation of the hypothesis, it seemed worth 

 while to calculate the magnitude of the vis viva which is changed 

 into heat by agitations and impulses. 



In this calculation we are concerned both with the number of 

 the impulses and with their strength. 



Since the wheelwork runs with constant velocity, the impulses 

 occur regularly. The axis of the disk rolls, therefore, with re- 

 gularity within the space which its ends have on their bearings. 

 The axis describes a kind of conical surface. After each revo- 

 lution it comes into the same position, or, at all events, into 

 almost the same position ; after each half revolution, into the 

 opposite one. During each revolution, therefore, it is thrown 

 once forward and once backward ; or during each turn it expe- 

 riences two impulses which change its position and direction. 



* Article 20 (2). t Experiments XIII. and XX. Article 18. 



