522 Mr. J. H. Jeans o?i the 



this equation will, at any specified point o£ the discharge, 

 remain unaltered if we suppose that q has the same value at 

 every point of the discharge as it has at the point in question. 

 Using this value for g, we can draw a diagram similar to 

 fig. 1 (Part I. p. 251), and at the point in this diagram 

 corresponding to that point of the discharge which we are 



considering, the value of -^ will have the same sign as has 



the value of j- for a point moving with the shading at this 

 point. d y 



But q varies from point to point of the discharge, and as q 

 varies the vertex of the parabola in fig. 1 will move up and 

 down the axis of symmetry, while the parabola will always 

 pass through the two points A and B. The vertex can never 

 pass to infinity along this axis, since q can never actually 

 vanish* (equation 10, Part I.), and the vertex can never 

 pass on to the axis y = 0, since q can never become infinite. 



Hence the points at which -j-~ vanishes will no longer (as in 



§ 5) lie on a single parabola, but they will all lie within a 

 certain region which is bounded by two parabolas, both of 

 which pass through the two points A, B,' and are concave to 

 the line joining them. From this it follows that there must 

 be curves of the four types shown in fig. 2, which will satisfy 

 the differential equation, and therefore there must be two 

 curves similar to those shown in fig. 5, which will satisfy the 

 differential equation together with the boundary conditions. 



Under the present conditions it would be useless to attempt 

 to discover under what circumstances these two forms of 

 solution will be the only possible forms. In what follows it 

 will be assumed that we are dealing with a solution of the 

 type which is represented by the discontinuous line in fig. 5. 



§ 13. Reference has already been made to the variety 

 which is observed in the appearance of the discharge near to 

 the anode. The theory has been found to be capable of 

 accounting for the phenomena observed near the cathode, 

 and also for the striated column in the middle of the tube, 

 but it has not, so far, accounted for the apparent difference 

 in the behaviour of the two electrodes. The considerations 

 put forward in the next two sections are meant to suggest a 

 way in which this difference may arise, although no attempt 



* For instance, if we regard dissociation as the result of collision, we 

 must remember that all velocities are possible at every point. Hence 

 however small the chances of dissociation may be, the " expectation " of 

 the number of dissociations (and therefore the value of q) will never 

 absolutely vanish. 



