252 DISCHARGE OF ELECTRICITY. 



let us consider the work done in a secondary circuit whose resistance is 

 R, whose coefficient of self-induction is L, and which has a coefficient 

 of mutual induction, M, with the primary circuit. If the frequency of 

 the current circulating in tlie primary is p, we can easily prove thatthe 

 rate of absorption of work by the secondary is proi^ortional to 



R M2 jj2 



Thus the work given to the secondary viinislies when 11 = and when 

 R^ infinity, and has a, nutxiiuum value when R = L^>. Thus the con- 

 dition that the secondary should absorb a considerable amount of work 

 is that the resistance should not differ much from a value depending 

 on the shape of the circuit and the frequency of the current in the 

 primary. No appreciable amount of work is consumed w hen the resist- 

 ance is very much greater or very much less than this value. 1 tested 

 this result by placing inside B a coil of copper wire. When the ends 

 were free, so that no current could pass through it, it produced no 

 efit'ect upon the bulb in A; when the ends were joined so that there 

 was only a very small resistance in the circuit, the effect Avas, if any- 

 thing, to increase the brightness of the discharge in A. When how- 

 ever the ends were connected through a carbon resistance which could 

 be adjusted at will, the discharge in A became very distinctly duller 

 when there was a very considerable resistance in the circuit. This 

 experiment confirms the conclusion that to absorb energy the resist- 

 ance must lie within certain limits, and be neither too large nor too 

 small. 



We can now see the cause of the differences observed when the sub- 

 stances mentioned above were put into B. The brass rod and tube 

 did not dim the discharge in A, because their resistance was too low; 

 the weak solution of electrolyte, because the resistance was too great; 

 while the resistances of the crucible and the strong solution of ele(;- 

 trolyte which obliterated the discharge from A were near the value for 

 which the absorption of energy by the system was a maxinuim. 



The case of iron is very interesting because it shows that even under 

 these very rapidly alternating forces, iron still retains its magnetic 

 properties. A striking illustration of the difference l)etween iron and 

 other metals is shown when we take an iron rod and place it in B, the 

 discharge in A immediately stops; if we now slip a brass tube over the 

 iron rod tlie discluirge in A is at once restored. If on the other hand 

 we use a brass rod and an iron tube, when the rod is put in B without 

 the tube the discharge in A is bright; if we slij) the iron tube over the 

 rod, the discharge stops. 



To compare the amount of heat produced in the brass and iron sec- 

 ondaries [calculations are introduced by which the author estimates 

 that] for iron and copper cylinders of the same dimensions it would be 

 about seventy times as large in the iron as in the copper, assuming 



