236 Prof. A. Schuster on Electric Inertia and 



If the flow is periodic so that a, b, c are proportional to e ipf , 

 where i stands for V — 1, we obtain by dividing out the time 

 factor 



V"a=^ L -r-a. 



1 H- KfAip 



This equation shows that the inertia will affect the mag- 

 netic induction and consequently the lines of flow only when 

 tcfip becomes an appreciable fraction. But fi itself we have 

 found small in liquids and solids, while k is never greater than 

 10 -3 . Hence K/np cannot produce appreciable effects until p 

 becomes of the order of magnitude which holds for luminous 

 radiations. But that case will require separate treatment as 

 our equations are not correct for rapid variations of the 

 currents. 



In the numerical example given in § 8, /n was found to be 

 equal to 5*4 x 10 6 for a current-density of 1*5 x 10 -4 . The 

 product Kjju in the case considered will be independent of the 

 density. The fall of potential in the experiment was 5 volts 

 per cm., so that the conductance was *3 X 10~ 12 , and the cross- 

 section being 2 the product k/j, becomes *8 X 10~ 6 . This 

 product would be considerably larger at lower pressures, and 

 when the frequency is of the order of magnitude of ley den- 

 jar discharges it is very likely that the term depending on 

 the inertia of convection is very appreciable. Some of the 

 facts brought to light in J. J. Thomson's work on luminous 

 discharges produced by induction in tubes without electrodes 

 seem to point in that direction. When tcfip becomes large 

 compared to unity, the equation reduces to 



so that, for instance, 



- x/i? 

 a = e m- x cos^j 



would represent a possible disturbance. 



10. The effects of inertia may become very appreciable in 

 the case of luminous vibrations, to which our equations do 

 not apply, as the term depending on the specific inductive 

 capacity has been left out of account. In forming the more 

 complete equations a difficulty presents itself which is due to 

 the fact that the displacement currents may also to some 

 extent have inertia or what is equivalent to inertia. The 

 apparent masses will not be in general the same as those 

 involved in the conduction currents, though in the case of 



