246 The Mathematical Electricians of the 



the induced magnetization I with the magnetizing force H he 

 had given in a form equivalent to 



( I x = aH x + b'ffy + c"ff z , 

 I y = a"H x + bH y + c'H Z) 

 I z = a'H r + b"H y + cH z . 



Thomson now* showed that the nine coefficients a, b' ', c" . . ., 

 introduced by Poisson, are not independent of each other. For 

 a sphere composed of the magnecrystalline substance, if placed 

 in a uniform field of force, would be acted on by a couple : and 

 the work done by this couple when the sphere, supposed of 

 unit volume, performs a complete revolution round the axis of x 

 may be easily shown to be 7rH(l - H^j IP) (- &" + c). But this 

 work must be zero, since the system is restored to its primitive 

 condition ; and hence ~b" and c must be equal. Similarly e" = a, 

 and a" = b f . By change of axes three more coefficients may be 

 removed, so that the equations may be brought to the form 



777" T TT T TT 



JC ~ Kl/Z x , Iy = K-lJily, 1 Z = Ka/Zz, 



where KI, K Z , K 3 may be called the principal magnetic suscepti- 

 bilities. 



In the same year (1851) Thomson investigated the energy 

 which, as was evident from Faraday's work on self-induction, 

 must be stored in connexion with every electric current. He 

 showed that, in his own words, f " the value of a current in a 

 closed conductor, left without electromotive force, is the 

 quantity of work that would be got by letting all the infinitely 

 small currents into which it may be divided along the lines of 

 motion of the electricity come together from an infinite distance, 

 and make it up. Each of these ' infinitely small currents ' is of 

 course in a circuit which is generally of finite length ; it is the 

 section of each partial conductor and the strength of the current 

 in it that must be infinitely small." 



* Phil. Mag. (4) i (1851), p. 177: Papers on Electrostatics and Magnetism, 

 p. 471. 



t Papers on Electrostatics and Magnetism, p. 446. 



