Temperature and Ohmic Resistance of Gases. 349 



measure. If r be the resistance measured in ohms, R = rX 10 9 , 

 so that 



T = 



xlO 4 



What we are concerned with is the ratio of r to the period of 

 the currents ; if the latter be y^Q second, the ratio is l/100r, 

 so that if r be a good number of ohms — it must have exceeded 

 100 in the particular experiments — there is nothing to fear 

 from self-induction. It would seem to follow generally that 

 if the voltage be not too small, say not falling below 10 volts, 

 there should be no difficulty in obtaining sufficient effect from 

 a shunt-coil whose self-induction may be neglected. It may 

 be remarked that since the efficiency of the coil varies as w, 

 while L varies as n 2 , it will be advantageous to keep n (and r) 

 down so long as the self-induction of the whole shunt-circuit 

 is mainly that of the coil. 



If the main and the shunt-coils were wound closely together, 

 the disturbance due to mutual induction would be of the same 

 order of magnitude as that due to self-induction. If the 

 coils are separated, as is otherwise convenient, the influence 

 of mutual induction will be less, and may be neglected under 

 the conditions above defined. 



As to the effect of self-induction, if present, we know that 

 the lag <j) is given by 



tan</> = L/VR, (11) 



where p = 2irx frequency. The angle of lag of the main 

 current (0), which it is the object of the measurements to 

 determine, is then given by 



0=e + 4>, (12) 



6 being the phase-difference of the two currents as found 

 directly from the observations. 



XL VII. The Temperature and (Jhmic Resistance of Gases 

 during the Oscillatory Electric Discharge. By John 

 Trowbridge and Theodore Wm. Richards*. 



IN our papers f on " The Spectra of Argon and The Multiple 

 Spectra of Gases " we have emphasized the importance of 

 considering the electrical condition of the circuit in which is 

 placed the Plucker tube containing the gas under examination. 

 We have pointed anew to the fact that in general the continuous 

 discharge of an accumulator produces one spectrum, while 



* Communicated by the Authors, 

 f Phil. Mag-, vol. xliii. pp. 77, 135. 



Phil Mag. S. 5. Vol. 43. No. 264. May 1397. 2 E 



