﻿Disk rotating in a Vacuum. 29 



it is 



^MR, 2 sin 2 </>. 



In this expression R sin (f> has a simple meaning; for it is 

 nothing more than the magnitude of the alternate rising and 

 sinking of the edge of the disk R, the value of which is 0*015 

 inch or 0*38 millim. By introducing this value the loss of 

 vis viva may also be written 



— MA 3 



This vis viva of motion changed into heat is first of all con- 

 sumed in raising the temperature of the disk, and is then im- 

 parted to the surrounding medium by radiation. Since after 

 some time both the velocity of the rotation and also the excess of 

 the temperature of the disk over that of the surrounding me- 

 dium became constant, the heat lost in a second by radiation 

 must be equivalent to vis viva transformed into heat during the 

 same time. The first may be calculated from Newton's law of 

 cooling, which, owing to the small amount of the heating, may 

 be unhesitatingly accepted. If the constant excess of the tem- 

 perature of the disk amounts to t degrees, the quantity of heat 

 radiated in a second from both surfaces of the disk is 



if the constant h denotes the heat which is radiated by the unit 

 of surface for an increase of 1 degree. I obtain the mechanical 

 work equivalent to this heat by multiplying by Q^, where g is 

 the accelerating force of gravity, and Q the height to which the 

 unit of mass can be raised by the unit of heat. The equivalent 

 in work of that heat is therefore 



ZirliRHQg. 



The work thus produced corresponds to the vis viva consumed 

 — that is, 



hmQg=^Mk 3 . 



The first idea suggested by an inspection of this formula is a 

 circumstance which apparently disagrees with observation. For 

 Stewart and Tait have observed that the heating of the disk is 

 inversely proportional to its thickness. From the above equation 

 we might be tempted to conclude that the heating t increases 

 proportionally to the mass M, and therefore also to the thickness 

 of the disk. We must, however, remember that the oscillation 

 must be the greater the less the thickness of the disk*. The os- 



* It is true that the above numbers do not accurately confirm this; but 

 they are only approximate measurements. 



