March, 1918] A Lecher System — Experimental 155 



It seems very likely that the question of damping can be 

 handled thus simply for the cases here considered. Blake 

 and Sheard have shown that we are dealing here, when the 

 coupling is loose (.r=ll cm. is a very loose coupling), with the 

 free vibrations strictly and since our system is a strictly non- 

 radiant system the damping must be very small. It is perhaps 

 an open question whether the logarithmic decrement thus 

 measured was the decrement of the receiver merely or of the 

 total oscillating system. Likely the former, however, since 

 the oscillator and the distance y was purposely changed so as 

 to have the energy at the receiver the maximum possible for 

 each tone, with a given constant input of energy at the oscillator 

 spark-gap. 



YI. Relation Between Tone-Intensity and Edge-on 



Distance. 



Thus the energy at the receiver is distributed among the 

 various tones as follows, the figures being read off directly 

 from the curves of Figure 6: fundamental 172, third 106, fifth 

 37.7, seventh 11.3, ninth 3.8, eleventh 1.8. Expressed in per 

 cent, the figures run 100%, 61.63%, 21.92%, 6.57%, 2.21%, 

 1.05%. With the more complete data given in this paper we 

 have thus been able to determine quantitatively the influence 

 of the edge-on distance between plates upon the tone-intensity. 

 Blake and Sheard were able to give a qualitative answer only. 



If we plot the optimum distance between plates, t/s, against 

 the frequency- number, ^ve get Curve III of Figure 9. With 

 an average error of less than 1 per cent, and a maximum error 

 of 1.7 per cent, this curve gives the empirical relation 



\ ~s~ loge 7/s = Constant. 



We are not prepared at present to state whether such a 

 relation has an}^ important significance. Calculating the 

 distances t/s required to fit the formula we get the following 

 values: 36.8, 15.5, 11.1, 9.15, 8.00, 7.25. In the curves of 

 Figure 6 the short lines parallel to the y axis cutting across the 

 curves are shown at these points. Manifestly, within the 

 limits of error, they cut at the top of each maximum. 



