24:6 Mr. J. H. Jeans on the 



the graph calculated from theory is therefore of interest, and 

 it is at once obvious that there are considerable differences 

 between the two curves. 



In particular the theoretical graph is convex to the axis of 

 x at every point, while the experimental graph shows con- 

 cavity over two regions of the axis. 



Now when a graph for y is drawn from measurements 

 actually taken from a tube through which a discharge is 

 passing, a comparison of the graph so obtained with the 

 glowing tube shows that the discharge is accompanied by 

 luminosity at those parts of the tube at wbich the graph is 

 concave to the axis, and at no others. There are also, as 

 Thomson points out (I. c. ante, p. 267), theoretical reasons 

 which lead us to suppose that luminosity is accompanied by 

 concavity of the graph. 



Thus the graph at which Thomson arrives, being convex at 

 every point, precludes the possibility of luminosity in any 

 part of the tube ; it shows the distribution of electric force 

 in a non-luminous discharge. 



Further, it is well-known that under suitable conditions 

 the gas in a discharge-tube presents a striated appearance, 

 light and dark bands occurring alternately and at regular 

 intervals, except in the neighbourhood of the electrodes. 

 Thomson has obtained a discharge through a tube fifty feet 

 in length, and observed that the whole tube, with the exception 

 of a few inches near the cathode, was filled with these 

 striatums. 



It appears therefore as if the true system of electrical 

 equations, account being taken of the. volume equations only, 

 without reference to the boundary conditions, ought to lead 

 to an infinite system of striations ; in fact, the graph for y 

 should be a regular succession of waves, and y itself a periodic 

 function of w. 



It must be borne in mind that Thomson's graph is only one 

 out of an infinite series of curves, all of which are represented 

 by the same differential equations, and this leads us to con- 

 sider firstly, whether any other member of this family of 

 curves bears any resemblance to Graham's experimental 

 curve ; and, secondly, whether any member can consist of a 

 series of regular waves, and so correspond to a periodic 

 solution. 



Now r it will appear in the course of the present paper that 

 there is considerable probability that both of these questions 

 must be answered in the negative. If this is so, it follows 

 that the complete explanation cannot be implicity contained 

 in Thomson's differential equation; in order to arrive at it, 



