ON FARADAY'S LINES OF FORCE. 229 



J 7 



whence cot < = - ^ *>, I = *** /.sing. 



To understand the meaning of these expressions let us take a particular case. 



Let the axis of the revolving shell be vertical, and let the revolution be 

 from north to west. Let / be the total intensity of the terrestrial magnetism, 

 and let the dip be 0, then /cos 6 is the horizontal component in the direction 

 of magnetic north. 



The result of the rotation is to produce currents in the shell about an 



T 



axis inclined at a small angle = tan" 1 -y w to the south of magnetic west, and 



the external effect of these currents is the same as that of a magnet whose 

 moment is 



% -j __ Ta If I cos 0. 



V2Wf-j.1V 



The moment of the couple due to terrestrial magnetism tending to stop the 

 rotation is 



jn , a 



JtT cos" 0, 



and the loss of work due to this in unit of time is 



247T& Tt 



cos' 0. 



This loss of work is made up by an evolution of heat in the substance of 

 the shell, as is proved by a recent experiment of M. Foucault (see Comptes 

 Rendus, XLI. p. 450). 



