through Exhausted Tubes without Electrodes. 457 



Thus the work given to the secondary vanishes when R = 

 and when R== infinity, and has a maximum value when 

 R=Ljt?. Thus the condition 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 when the resis- 

 tance is very much greater or very much less than this value. 

 I 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 effect upon the bulb in A ; when the ends 

 were joined so that there was only a very small resistance in 

 the circuit, the effect was, if anything, to increase the bright- 

 ness of the discharge in A. When, however, 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 resistance 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 substances mentioned above were put into B. The brass 

 rod and tube did not dim the discharge in A, because their 

 resistance was too 1ow t ; the weak solution of electrolyte, 

 because the resistance was too great; while the resistances 

 of the crucible and the strong solution of electrolyte which 

 obliterated the discharge from A were near the value for 

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



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 between 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 

 the discharge 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 slip 

 the iron tube over the rod, the discharge stops. 



To compare the amount of heat produced in the brass and 

 iron secondaries, let us take the case of an infinite cylinder 

 exposed to an external magnetic force parallel to the axis 

 equal to H e^. 



If H is the magnetic force inside the cylinder at a distance 

 r from the axis, H satisfies the differential equation 



dr 2 r dr a dt ' 



