1G4 The Ohio Journal of Science [Vol. XVIII, No. 5, 



Later in this paper we shall discuss the conditions under 

 which the practical case, Figure 2, may be said to conform to 

 the ideal case, Figure 3. For the moment we shall call them 

 identical. 



Abraham's expression for the potential difference, per 

 unit length of the wires (Figure 1) is 



27rX \ o * 

 T ) cos ZTT 7lt 



where A is a constant, k the capacity per unit length, X the 

 wave-length, 7 the phase change due to the end-capacity and n 

 the frequency. We consider the total energy on the receiver 

 that surges through the thermo-couple as made up of two parts, 

 that on the wires themselves and that on the condenser. Sup- 

 pose at a certain moment the condenser plates are charged to 

 a maximum value. Due to the distributed capacity of the wires 

 there is also at that moment a charge on them. A moment 

 later these charges discharge through the thermocouple thus 

 recharging the plates and wires with electricity of the opposite 

 sign. During the half period of the galvanometer, viz., 1.4 sec, 

 millions of vibrations surge through the thermocouple. The 

 galvanometer needle moves off until the loss of energy by heat 

 conduction and radiation from the thermocouple equals the 

 input of energy. The scale usually moves off in a very vigorous 

 fashion showing that the losses of energy are not appreciable 

 till near the end of the half period of the galvanometer. We 

 shall assume the rate of loss of heat energy by radiation from 

 the junction to be independent of the frequency of the tone 

 surging through it, and that Newton's law of cooling holds 

 with respect to the surroundings. 



In order to calculate the energy that surges through the 

 thermocouple we must get the root-mean-square value of the 

 potential as it is distributed both as to space and time. If we 



substitute — for t in the above expression we can say that 



the total energy on the wires is given by the expression 



n 



2 2 \4 27r/ 



u 



27ra;L , 

 cos^ I dx 



1 



