262 Prof. J. A. Fleming on the Poulsen Arc as a 



of the arc current and the supply voltage. For instance, in 

 one case the potential difference of the arc electrodes was 

 found to be 320 volts and the arc current 8'4 amperes, whilst 

 in two separate measurements with the wattmeter the power 

 taken up was found to be 2632 and 2674 watts. The product 

 of amperes and volts is 2688, and hence the power factor by 

 these measurements is 0*98 or 0*99, or practically unity. 



If the current through the arc can be kept sufficiently 

 constant, which is rather difficult, the power radiated may be 

 also measured by the wattmeter. For suppose that we have 

 a direct-coupled antenna joined at some point to the con- 

 denser circuit, we may then take wattmeter readings with 

 and without the attached antenna, and the difference will be 

 the power radiated. 



In the case of the long helix above mentioned, the power 

 given to the arc when the helix was attached to the condenser 

 circuit was 2674 watts, as measured by the wattmeter, and 

 with the helix removed it was 2632 watts, the arc current 

 remaining constant at 8*4 amperes. Hence in this case it 

 appears that the radiation and power consumption due to the 

 attachment of the helix is 42 w^atts. The measurements, 

 however, cannot be made very accurately in the case of small 

 power radiation. 



In the case of a direct-coupled antenna which is emitting 

 a wave-length corresponding to its fundamental oscillation, 

 the radiation can be approximately calculated from a formula 

 given by Hertz. Hertz shows that in the case of a dumbbell 

 oscillator having an electric moment 0, the energy E 

 radiated per period is given by the expression 



E = o 3 ergs per period, 



where X is the wave-length of the radiation. 



If C is the capacity of one-half of the oscillator with 

 respect to the other, and Y is the maximum potential differ- 

 ence of the parts during an oscillation, and I the effective 

 length, then Q = CYZ. 



If I is the maximum value of the current in the oscillator 

 during a period, then 



I = 2t™CV and Q 2 = I 2 Z 2 /4tt 2 >i 2 , 



where n is the frequency. 

 Accordingly, 



w 4tt 2 I 2 Z 2 . , 



E = "aXv" ergs per penod - 



