the Heating of a Disk by rapid Rotation in vacuo. 227 



Where H=horizontal magnetic force, and V = vertical magnetic force, 

 and = angle between the axis of rotation and the magnetic meridian, 

 a=radius and c half the thickness, h)=27rn, where n denotes the 

 revolutions per second; ju= 1 ; p is the resistance of unit length and 

 unit section. 



Now, the resistance of 1 metre long and 1 millimetre diameter 



= -^10 G =0*0375xl0 7 



32 



for aluminium in metrical units by Matthiessen, or ——-5- 



9 3 

 p is the same for metrical and for British measure. 



At Kew horizontal force=3*81, dip 68°' 10 ; 0=90° in the experi- 

 ments, .•. a 2 + /3 2 = 104*8 British measure. 



The revolving body is not an ellipsoid but a cylinder, equally thick 



15 

 throughout ; to correct for this we shall put -5- <? for c 8 . 



We get for the energy converted into heat by electrical action per 

 second 12*91 in grain-foot-second measure. 



Now 772g= energy required to raise 1 grain of water 1° Fahr. 



The disk = — th — x '22 grain of water, .*. energy corresponding to 1° 



16 



or rise of temperature per second 



32*2 

 = 772 X^g-X 15400, 



12*91 



12*91 



Fahr. or about 



1540X15400"" 23716000 

 2 ™ degree in 30 seconds. 



degn 



1 



This is when the heat is uniformly distributed through the thick- 

 ness of the disk, which it will be in less than thirty seconds. If 

 there were no conduction, the rise of temperature at the surface would 

 be about twice the value found above. 



(2) It would appear from the above formula that the heating effect 

 due to this cause should increase with the thickness of the disk. 



The following experiments show that, on the contrary, the heating 

 effect, as regards temperature, diminishes as the thickness of the disk 

 increases. 



s 







No. of ob* 

 servations 

 in each set. 



1 



No. of turns 

 of handle 

 at full 

 speed. 



Heat indi- 

 cation, in 

 Fahr. 



Tension of 1 

 air, in 

 inches. 





XIII. 

 XX 



3 

 3 



30 

 30 



20 

 21 



0-8 

 1-7 



0-4 

 0-4 



Aluminium disk -^ inch thick. 

 Aluminium disk ^ inch thick. 



(3) The heat indication afforded by an ebonite disk is against the 



Q2 



