368 Mr. 0. Heaviside on Electromagnetic Waves, and the 



At distance r from the centre of the sphere, within it, at 

 time t after starting h, we have 



T?— hv ^ cos sr— (sr) ~ l sin sr e pt (9A&\ 



= ^Trktf p(d/dp){(sa)~ l smsa cos sa' 



subject to the determinantal equation, over whose roots the 

 summation extends, p being now algebraic. Effecting the 

 differentiation indicated, we obtain 



E = _ ife. $ cos *r-(*r)- 1 ^n * ^ _ _ / 247) 



4^^ cos sa v y 



The corresponding solution for the radial component of the 

 magnetic force, say H r , is 



/o7 /i\ ^7 /»<* cos 5 ^ — (s/0 -1 sin sr . , . ON 



H r =(P cos 0)— 4/i cos 2 22^ eP • • (248) 



s r cos sa 



At the centre of the sphere, let H be the intensity of the 

 actual magnetic force. It is, by (248), 



H =fMl + 2 2(cos 5 a)- 1 e^}. . . (249) 



Thus the magnetic force arrives at the centre of the sphere 

 in identically the same manner as current arrives at the 

 distant end of an Atlantic cable according to the electro- 

 static theory, when a steady impressed force is applied at the 

 beginning, with terminal short-circuits. In the case of the 

 cable the first time-constant is 



where Bi is the total resistance and SZ the total permittance. 

 It is not greatly different from 1 second, so that, by (245), 

 the sphere should be about a foot in radius to imitate, at its 

 centre, the arrival curve of the cable. 



To be precise we should not speak of magnetizing the 

 sphere, because (ignoring the minute diamagnetism) it does 

 not become magnetized. The principle, however, is the 

 same. We set up the flux magnetic induction. But the 

 magnetic terminology is defective. Perhaps it would be not 

 objected to if we say we inductize* the sphere, whether we 

 magnetize it or not. This is, at any rate, better than ex- 

 tending the meaning of the word magnetize, which is already 

 precise in the mathematical theory, though of uncertain 

 application in practice, from the variable behaviour of iron. 



* Accent the first syllable, like magnetize. Practical men sometimes 

 speak of energizing a core, &c. But energize is too general ; by using 

 inductize we specify what flux is set up. 



