416 Prof. E. Wiedemann on the Behaviour of Gases 



sponds to ordinary conditions in our discharge-tubes, then 

 a" = 25; and if, further, we bring together the constants in U, 

 we have, nearly, 



U=1-3A<T 245 !. 



If we take two tubes, of which the one is about 1 centim., 

 the other about 1 millim. wide, then for these, if A x and A 2 

 denote the initial temperatures, 



W = l'?>A 1 e- 2i5t y and U" = l-3A a e- a46x,00 «. 



A numerical calculation, neglecting the factor 1*3, shows 

 that in the middle of a tube of 1 centim. width, after yj^ 

 second the rise of temperature will have sunk about -^j, after 

 joqq second ^, and that, on the other hand, in a tube of 

 1 millim. diameter the same changes will have taken place 

 after the Yoioo an( ^ ^ ne TooVoo seC0G d. If we assume that 

 in the narrow tube the gas has attained a temperature of 

 1000°, a case easily realized, then (again neglecting 1*3) after 

 the lapse of the times t the temperatures 6 (which, it is true, 

 give only a measure of the order of magnitude of those actu- 

 ally present) would be 



*=io- 6 lO" 5 io- 4 io- 3 



0=980 815 133 1-4 xlO- 6 . 



If, therefore, there are 1000 discharges in the second, the gas 

 is after each almost in its original condition ; if there are 

 100,000, this is not the case. 



These considerations hold good for the case of a capillary 

 tube, where, in fact, a considerable rise in temperature accom- 

 panies the luminosity. As yet no afterglow has been recog- 

 nized with certainty following the separate discharges. Also 

 in wider tubes experiment shows us that, contrary to theory, 

 no afterglow occurs — a fact to which we will return later. 



The above discussion can of course only furnish a measure 

 of the order of the magnitudes in question. An exact discus- 

 sion is as yet not possible, the constants not being certainly 

 determined. Similar methods would hold good if we desired 

 further to take into consideration the radiation of the gas. 



The experiments of my father, of Rontgen, myself, and 

 others have shown that with a uniform supply of electricity a 

 perfectly definite potential is necessary to discharge — that, 

 further, the electricity passes in separate discharges which are 

 almost instantaneous, and which do not appear lengthened in 

 the rotating mirror. With a galvanic battery the electricity 

 used in each discharge is rapidly supplied again ; and it is a 



