230 Royal Society: — Messrs. Balfour Stewart and Tait on 



20. It was suggested to the authors by Professor Stokes and by Mr. 

 Grove, that the effect might be due to vibrations of the disk, the 

 energy of which, owing to the viscosity of the disk for such vibra- 

 tions, might ultimately become converted into heat ; and it is neces- 

 sary to examine this question. 



(1) The thickest aluminium disk was found to be out of truth not. 

 more than '015 inch on each side. Hence, the thickness of this disk 

 being -05 inch, when turned with moderate rapidity, its apparent 

 thickness should be 



•015 + -05 + -015 = -08; 



and experiment showed that when turned very fast, its apparent 

 thickness was no greater. The greatest possible range of vibrations 

 o Ithe disk at its circumference could not, therefore, be more than 

 •015 inch on either side of the position of rest. 



Again, it was ascertained by means of the note given by this disk, 

 that it vibrates about 250 times per second. 



Let us suppose the whole mass to have the same range of ex- 

 cursion (this will of course increase the result), the equation of 

 vibration (not allowing for loss by viscosity) is 



4?= a 01 5 cos nlj 

 and also time of vibration 



_2tt_ 1 

 n 250* 

 Hence 



^=500x3-14 = 1570, say, 



dx in * in * 



»*• 3r= — '015 X 1570 sin nt, .*. greatest velocity =23'55, 



or say 2 feet per second. 



Hence the energy of this motion in foot pounds, 



i> 2 

 =weight of disk in pounds X — 



2g 



= weight of disk in pounds through y 1 ^- 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 constantly (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 -J-J of a foot. Reducing this to its heat-equi- 

 valent, 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. 



