29G 



Messrs. Balfour Stewart and Tait on the Heating [Dec. 



and also time of vibration 



n 250* 



Hence 



%=500x 3-14 = 1570, say, 

 .'• 'OlSx 1570 sin .*. greatest velocity =23*55, 



or say 2 feet per second. 



Hence the energy of this motion in foot pounds, 



= weight of disk in pounds X — 



= weight of disk in pounds through jL- of a foot. 

 But an approximate experiment performed by causing the disk to ring, 

 and noticing how long the sound lasted, would seem to show that probably 

 the energy of vibration of the disk diminishes at first, and therefore con- 

 stantly (if it is maintained) at the rate of the whole in 3 seconds. Hence 

 in 30 seconds it loses 10 times as much as the whole ; that is to say, in 30 

 seconds the heat produced cannot be greater than that due to the energy 

 produced by the disk falling under gravity through ^ of a foot. Re- 

 ducing this to its heat-equivalent, the greatest possible heat effect due to 

 vibration during 30 seconds rapid turning will be less than 



which is a very small fraction of the effect observed. 



(2) The thin aluminium disk was out of truth about -02 inch on each 

 side. Its note of vibration was as nearly as possible one octave lower 

 than that of the thick disk, while its coefficient of viscosity was some- 

 what greater, say in the proportion of 3 to 2, than that of the thick 

 disk. On the supposition that the heat generated is due to vibration, if 

 we call the heat generated during 30 seconds in the thick disk =1, then 

 that generated during the same time in the thin disk ought to be 



where the first factor is on account of difference of time of vibration, the 

 second on account of difference of range, the third on account of difference 

 of mass, and the fourth on account of difference of viscosity. 



But the heating effect (as far as quantity of heat is concerned) produced 

 in the thin disk is as nearly as possible the same as that produced in the 

 thick disk. 



This fact is therefore against the hj^pothesis that the heating effect is 

 due to vibration. 



(3) In order to estimate the effect (if any) of want of truth in the disk, 

 the thick aluminium disk was purposely put out of truth about 3| times 



