292 Messrs. Balfour Stewart and Tait on the Heating [Dec. 6, 



ill a uniform magnetic field. To find its electrical state at a given in- 

 stant. At the given instant let the axes of y, z coincide with a, 5, c ; 

 then using the notation in the paper on the Electromagnetic field *, 



P Q R electromotive force, a /3 y magnetic intensity, vi/ electric tension, 

 ju = coefficient of magnetic induction=l for everything but iron, ^, r 

 electric currents, resistance of cubic unit of volume. 



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



Solving, we get 



_l^(o ci^a b-fj _^ ax (py \ ^ 



; 1 ^ ox r ^^P]/ \ ri 



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

 duced in unit of volume in unit of time is + 2" whole heat 

 produced in the ellipsoid in unit of time is 



— abc^ \ -T + vi ? \ • 



15 p \ (f +c'^ b''-\-c~ \ 



If c is small compared with «, it becomes 



If the axis is horizontal, 



a^ + /3^=ff sin^0 + V% 

 where H=horizoutal 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, w=27r?z, 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^=0-0375x 10" 



TT 



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



. 9 ^ 



p is the same for metrical and for British measure. 



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

 .*. a" + /3^= 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 for c^. 



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

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



Phil. Trans. 1865, p. 459. 



