542 



Mr. A. Schuster. 



could not be altered more than in the ratio of one to two, and it is 

 not possible to tell, therefore, how far the above will express the 

 results for a greater change in the current density. The constancy 

 of k depends on the fact which I have verified within these limits of 

 currents, that the potentials at different points of the negative glow all 

 rise and fall in the same ratio when the current is altered, the kathode 

 being at zero potential. 



From the characteristic equation for the potential, which in our 

 case reduces to 



d*Y , 2 



= ~ W/,J 



in which v stands for the velocity of light, we may now deduce p, or 

 the volume- density of electricity near the kathode. 



The law which I have given above suggests at once that p is a linear 

 function of Y or its differential coefficients, for it implies that if Y is 

 any solution of the characteristic equation, XV must also be a solution. 

 The question will be discussed in the complete account of these ex- 

 periments, and it is not necessary to enter into it here. From equa- 

 tion (1) we derive 



4th; 2 /> = /c 2 Y e-** (2.), 



which shows that the kathode is covered with an atmosphere of positively 

 charged particles diminishing outwards in volume-density . 



The law of variation of density is the same as that found in the 

 atmosphere near the earth's surface ; but the mathematical conditions 

 are very different. The gravitational force near the earth is sensibly 

 constant, while the electrical forces near the kathode vary as much 

 as the density. 



If the curve which connects Y and x is plotted, its curvature, and 

 therefore the electrification, can be traced through the dark space 

 and into the negative glow, but inside the glow it rapidly diminishes. 

 The formula for p does not lay claim to more than an approximate 

 expression of the facts, which may, however, in default of more 

 accurate knowledge help us to form some idea of the distribution of' 

 volume- density. Even though (1) may hold with considerable 

 accuracy, (2) may not give correct results for those parts of the glow 

 which are close up to the electrode ; for the curve representing Y 

 near the origin is a very steep line, slightly curved. A small change 

 in the curvature will make a considerable change in p, without 

 affecting the main curve to an appreciable extent. It seems prob- 

 able, however, that the electrification continues to increase up to 

 the electrode itself, and that the formula will express the main 

 features of the distribution. When the lines of flow are radial the 

 law of distribution of volume-density is less simple, but the general 

 result is the same. 



