80 



SCIENCE 



[Vol. LVI, No. 1438 



frequency change, indicating that the method 

 is sufficiently sensitive to afford a means of 

 detecting such small changes of capacity as 

 are caused by introducing a gas as the dielectric 

 instead of vacuum. 



The method is particularly applicable to the 

 determination of the dielectric constants of 

 gases as it will be seen from the following that 

 only the difference between the constant and 

 unity is measured. 



Siuce the authors started the above investiga- 

 tion L. M. Hull of the Bureau of Standards 

 has described* the use of the hot-cathode Braun 

 tube to determine frequency ratios. 



Two oscillating circuits are made to deflect 

 a cathode beam in two directions at right 

 angles to each other. The combined deflections 

 produce one of the well-known Lissajous' fig- 

 ures. If the hvo circuits are of exactly the 

 same frequency, say 500,000 cycles, the result- 

 ing figure will in general be an ellipse. A 

 change of capacity sufficient to cause a fre- 

 quency change of 5 cycles per second will cause 

 the ellipse to revolve 5 times per second. The 

 change of frequency, if small, may thus be 

 counted directly. The frequency of the master 

 circuit must be kept constant during the time 

 of observation. This can be done. 



Let Cj be a portion of the capacity in the 

 one oscillating circuit and let it be so arranged 

 that the dielectric may be either vacuum or a 

 gas of dielectric constant K. 



Then 



1 

 F = 



where F is the frequency and C is the capacity 

 of the remainder of the circuit, distributed 

 capacity included. If the introduction of a gas 

 in the condenser C^ causes a change / in the 

 frequency due to additional capacity AC, we 

 shall have 



1 

 F ^f = — 



Eliminating L and solving for AC 

 f{2F — f)iC + C^) 



AC = 



(F—fr- 



Neglecting / as small compared with F 

 2f(C + C^) 



Since 



AC = 



r 



AC = C^(K— 1) 



2f(C + C^) 



1 = 



C F 



It is readily seen that the largest error is in 

 the determination of the initial capacities. The 

 preceding equation also indicates that only the 

 excess of the dielectric constant over unity is 

 measured. Should it be found possible to sur- 

 round the entire capacity wifli the gas the above 

 equation reduces to 



F 

 and the method would then be one of quite 

 remarkable accuracy. 



If the capacity be kept constant and the 

 inductance varied, the first two equations may 

 be written 



1 



^■K^LC 



F—f: 



t^L 



* Proe. Inst. Eadio Engr., 9, p. 130. 



2^Y(Z,-f Ai)C 

 where C is the entire capacity of the circuit. 

 Eliminating C we have 



2fL 

 F 



If the master circuit can be kept constant 

 for 60 seconds, and such has already been ac- 

 complished, a change of inductance of the order 

 of 1 part in 10' can be detected. 



The aljility to detect so small a change in an 

 inductance makes it now possible to use the 

 inductance as the basis of an ether-drift experi- 

 ment similar to that of Trouton and Noble.^ 

 Even though the experiment be doomed to null 

 effect it is nevertheless necessary that it be 

 carried out. 



The above method may also be applied to 

 the determination of the magnetic penneabili- 

 ties of gases. 



H. G. Tasker 

 L. T. Jones 

 Department or Physics, 

 University of California 



^Proc. Eoy. Soc, 72 (1903), p. 132. 



