376 Radiation produced by slowly moving Cathode Hays. 



communicated by the corpuscles to the molecules o£ the gas, 

 the luminosity would be small near the cathode (hence the dark 

 space), would reach a maximum (at the luminous boundary of 

 the dark space), and then diminish through the negative 

 glow. The darkness near the cathode would be exaggerated 

 i£ the pressure around the cathode were less than that in the 

 rest of the tube. I think there is some evidence that this is 

 the case, and hope to return to this point on a future occasion. 

 Fall of Potential, near the Anode. — When we have a uniform 

 positive column, the electric force along it is constant, and 

 hence there are as many positive as negative ions in this 

 region; hence the number of positive ions which cross the 

 tube, going from anode towards cathode in unit time, is 



h . 

 k x -\-k 2 

 The ions which cross a section at P have to be produced 

 between P and the anode. Now, if these ions are produced 

 by the action of the moving corpuscles, the number of ions 

 produced in unit time is 



J 



~f(Xe\)d X 



where the integration extends over the space between the 

 anode and P, hence 



J 



" U f(Xe\)d.v<^ 



Now nu is not greater than i, hence 



f£/(X*) 



te<fc 



k\ ~t~ k 2 



Suppose, for example, /(X<?\) = AX^X, where A is a con- 

 stant, then the equation becomes 



where V is the difference of potential between the anode and 

 P. Hence we see that there must be a finite difference of 

 potential between the anode and the nearest point where the 

 electric force in the positive column is constant. Such a fail of 

 potential at the anode has been observed by Skinner; and 

 we hope to return to the comparison of the results of this 

 theory with the results of Skinner's experiments, as well 

 as the explanation in a similar way of the fall of potential 

 at the cathode, in a future paper, 



