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



From these experiments it may be taken for granted that the heat 

 indication given by an ebonite disk is, like that from an aluminium 

 disk, independent both of the density and chemical constitution of 

 the residual gas. It is also highly probable that the unknown cause 

 of the heating effect is the same for both disks. 



18. To return now to the aluminium disk, it may be shown that 

 the heating of this disk is not caused by revolution under the earth's 

 magnetic force ; for (1) the following calculation, kindly furnished by 

 Professor Maxwell, shows that the heating effect due to this cause 

 would, for the aluminium disk -^j of an inch in thickness, amount, 

 under the circumstances of rotation, only to innhnr °^ a degree Fahr., 

 whereas the observed effect is more than half a degree. 



An ellipsoid, semiaxes a, b, c, revolves about the axis c with velo- 

 city u), in a uniform magnetic field. To find its electrical state at 

 a given instant. At the given instant let the axes of x, y, z coin- 

 cide with a, b, c, then using the notation in the paper on the Elec- 

 tromagnetic field *, 



PQR electromotive force, a j3 y magnetic intensity, xb electric ten- 

 sion, ju = coefficient of magnetic induction = 1 for everything but iron, 

 p, q, r electric currents, p — resistance of cubic unit of volume. 

 The condition of the currents being confined to the ellipsoid, is 



Solving, we get 





b 2 (3 iiu> ( ax ^ $y \ , 



juw a a uu) 



?= 7 



This is the complete solution. The heat (measured as energy) 

 produced in unit of volume in unit of time is pip^ + q^ + r'). The 

 whole heat produced in the ellipsoid in unit of time is 



be* J °V , ggl . 



U 2 -j-c 2 + £ 2 + c 2 j 



t 2 f ,.2„2 £2 7,2 



15 p 



If » b, this IS ~ £ -£~ (a 2 + /3 2 ). 



If c is small compared with a, it becomes 



|| £<A»V(« 2 +/3 2 ). 



If the axis is horizontal, 



« 2 + /3 2 =H 2 sin 2 + V 2 , 



* Phil. Trans. 1865, p. 459. 



