370 
Prof. E. Goldstein on 
rays which form continuations of the shortest radii of the 
polygon, while in the case of odd-sided polygons the rays 
appear to form continuations of the longest radii. It will 
be seen that this arrangement is consistent with the suppo- 
sition that the rays originate from the opposite sides. If the 
polygons have unequal angles, then in the case of odd-sided 
figures the pencils may appear at points other than the 
angular points, and in the case of even-sided figures at 
points other than the middle points of the sides, but always 
in a manner consistent with the supposition that they start 
from the opposite sides. 
The rays of these star-shaped figures possess all the 
properties which may be observed in connexion with true 
canal rays. 
If the double cathode consists of two congruent rectangles, 
then a luminous pattern is produced like that shown in fig. 4, 
Fis. 4. 
which corresponds to a certain pressure of the gas. There 
arise in the space between the cathodes, from their longer 
sides, two wide rosy luminous bands, whose initially almost 
parallel boundaries converge more and more with decreasing 
pressure of the gas. From the smaller sides there arise two 
thin pencils of much feebler luminosity, not represented in 
the figure. The appearance of the two w r ide bands does not 
change appreciably if the shorter sides of the plates be 
connected by plane walls, the cathode then forming a hollow 
parallelepiped. 
If the line of sight be parallel to the long sides of the 
cathode, the pencils appear in the form of feebly divergent 
bands, which proceed from the entire width of the space 
