Shape of the Kathode in Geissler's Tubes. 461 



kathode with varying distance of wall : and the figure pro- 

 duced by a particular kathode h corresponds to a greater dis- 

 tance of wall from the kathode used to compare with, the 

 greater the curvature of the kathode k is. 



This result might indeed have been regarded as a priori 

 probable. We might indeed expect to obtain simultaneously 

 like figures from different kathodes (similar in their original 

 plane condition) by making the distance of the wall equal to 

 np, npi, np 2 , &c. for different radii of curvature p, p 1} p 2 , &c. 

 — that is, the distance of the wall in each case the same mul- 

 tiple or submultiple of the radius of curvature — as, for example, 

 by placing each kathode at a distance from the wall equal to 

 twice its radius of curvature. 



But experiment shows also that in this case the phases are 

 different; and the increased curvature acts in the same way 

 as, cceteris paribus, the increase of the distance of the wall or 

 an increase of the density of gas. This influence goes so far 

 that, with kathodes which are much curved, it has not been 

 found possible by exhausting the gas to produce those forms 

 of the series of figures which, with electrodes of less curvature, 

 correspond to the lowest degrees of the scale of density. Thus, 

 for example, with the four-armed cross fig. 11a, of a radius 

 of curvature of 12^ millim. instead of 20 millim., and with a 

 distance of wall 2p, we find it impossible by exhausting to 

 reach the phase of the dark cross fig. 115. The figure 

 obtained immediately before the cessation of the current at 

 the greatest exhaustion is the figure with curved points, 

 fig. 12 c. 



6. If we leave the general form of the kathode and its cur- 

 vature unaltered, but increase the aperture of the kathode, 

 this increase acts also as an increase of the distance of the wall 

 would do. 



If, for example, we replace a square of 12 millim. in the 

 side which has been bent to form a spherical surface of 40 mil- 

 lim. diameter by a square of similar curvature, but with sides 

 30 millim. long, then at the extreme exhaustion we do not 

 advance further than fig. 15 c?, whilst the small square gives 

 us figures up to 15^. 



We obtain similar results with the more complicated forms 

 of kathodes — for example, the four-armed cross made up of 

 rectangles, fig. 11 a. If the length of the cross be increased 

 from 20 to 25 millim. without altering the width of the arms, 

 then at the greatest exhaustion at which the current will pass, 

 the dark cross is just visible ; but it cannot be obtained with 

 arms of any considerable breadth. 



If the cross is increased to 40 millim. the dark cross is no 



