282 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the supply current was 0.55 ampere, and there were four turns on the 

 primary helix. The secondary wave length was 100 meters and the 

 curves 1-5 give the values of h in amperes for the designated number 

 of turns on the secondary coil, as the resistance in the secondary 

 circuit was varied from to 16 ohms. On the same diagram appears 

 the voltage across the gap for the several conditions. 



These, and some of the curves shortly to be considered, are plotted 

 for, or in terms of, turns of secondary helix, the primary helix remain- 

 ing unchanged. With the apparatus used the mutual inductance 

 between the two circuits is not exactly proportional to the number of 

 secondary turns on account of a slight variation in the position of the 

 coils, but nearly enough so, so that the number of secondary turns can 

 be considered as proportional to the mutual inductance between the 

 primary and secondary circuits. 



The resistance used in the secondary circuit was an oil-cooled man- 

 ganin wire resistance, wound non-inductively, and with a wire of such 

 a diameter that the high frequency resistance is considered to be prac- 

 tically the same as the ordinary resistance. 



It is clear, on examination oiF the current curves of Figure 8, that if 

 a large current in a circuit of small resistance is desired, the mutual 

 inductance should be small. If, on the other hand, there is a consider- 

 able radiation of power from the secondary circuit, or if the circuit con- 

 tains a large resistance, it is necessary that the mutual inductance be 

 large. 



The reason for this necessary change in mutual inductance to suit 

 the various conditions is to be sought in the reaction of the secondary 

 current on the primary circuit. It is probable that the coupling 

 should be as close as possible consistent with a certain reaction, above 

 which the primary conditions, such as phase, etc., would be affected to 

 the extent of causing the power to decrease. Suppose then it be as- 

 sumed that the permissible reaction on the primary is constant, and 

 that the current in the secondary is proportional to M, the coefficient 

 of mutual inductance. Then it follows that the reaction voltage, Ei, 

 in the primary is 



El = const, oc 3II2. 



M 



But I2 ^ — if the wave length and primary current are constant. 

 R2 



Therefore 



^1 oc ^- = const., or M"^ a R^. 



