through Exhausted Tubes without Electrodes. 459 



the average value of which is 



XT 2 



lbcr J 



As this is proportional to the conductivity, the best conductors 

 will absorb the most energy. 



The other case which we shall consider is that in which na 

 is very large. This applies to the metal tubes and rods. 



In this case, 



J (mr) = 



Thus 



v 27rur 

 ^nrq— —ne~ ^ a ~ r "> [ a \ V* 



approximately. 



Then taking the real part of the expression for q, 



4.7rq=— < - > [otcospt—p&mpt). 

 The rate of heat-production is again 



C a 



1 crq^wrdr ; 

 the mean value of which is 



a* C a ^TTfip -(«-,) V^ 



>tJo 



10 



« V^ 



<fr 



s/pfitr, 



and is thus proportional to the square root of yw»<r. Hence for 

 iron and copper cylinders of the same dimensions it would be 

 about 70 times as large in the iron as in the copper, assuming 

 that the iron retains its magnetic properties under these very 

 rapidly alternating forces. The result explains the effect of 

 the iron in stopping the discharge. As I am not aware that 

 any magnetic properties of iron under such rapidly alternating 

 forces have been observed, I was anxious to make quite sure 

 that the difference between iron and brass was not due solely 



