Mr maxwell, ON FARADAY'S LINES OF FORCE. 88 



We must therefore have the following equations, since the state of the shell is the same at 

 every instant, 



T 



L sin - 2 i* cos = /, sin + toS/ sin (b 



T 



— 2/' sin ^ "= w(Ji sin - 2i* cos <f>), 



whence 



247rA; 

 T 

 24,irk 



^o^<P= - -^TZi «' -f = i ^^ .-^1 sin Q- 



V.f-^ 



ID 



2iTrk 



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 6, then 

 J cos 9 is the horizontal component in the direction of magnetic north. 



The result of the rotation is to produce currents in the shell about an axis inclined at a 



T 



small angle = tan"' ^ -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 



1 Tw 



^B?I cos 9. 



2 v'247rA;]'+ Tu^ 

 "The moment of the couple due to terrestrial magnetism tending to stop the rotation is 



■mPcos^9, 



2 247rAl^ + rV 

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



247rA Tw^ 



R'rcos^9. 



2 24^ + T'w* 



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 Comptea Bendus, xli. p. 450). 



11—2 



