456 Dr. E. Goldstein on the Influence of the 



experiments next to be mentioned it was made equal to twice 

 the radius of curvature of the spherical kathode. 



If we now assume, as for example Crookes does in his well- 

 known memoirs, that from each point of a concave kathode 

 only one rectilinear ray radiates, and that along the normal to 

 the surface, it would follow that the phosphorescent image of 

 a concave kathode on a concave spherical wall, at a distance 

 of twice the radius of curvature of the kathode, would be iden- 

 tical in form and dimensions with the kathode itself, if the 

 radius of the vessel were equal to that of the kathode; it would 

 be coincident in form and nearly in dimensions with the ka- 

 thode itself if, as in my experiments, the radius of the vessel 

 were greater than that of the kathode, without the kathode 

 having any considerable aperture. There will be no essential 

 change in the character of the phenomena to be expected, if 

 we also take into account the feebler phosphorescence caused 

 by the rays * emitted by the elements of the kathode on its 

 edge in variously oblique directions up to the tangential di- 

 rection. But experiments show very different phenomena. 



1. Fig. 9 a represents a square of the actual size, ground into 

 a spherical surface of 40 millim. diameter; and fig. 96 repre- 

 sents the phosphorescent image, also of the actual size, formed 

 by this kathode in a highly exhausted glass vessel of 8 centim. 

 diameter ; we remark a star of light with four rays, the axes of 

 the rays being at right angles to the sides of the square ka- 

 thode. In the figure representing the luminous star, the edge 

 of the kathode is marked by black dots in order to indicate the 

 relative positions of kathode and image. At extreme exhaus- 

 tions there appear, less distinctly marked, four much shorter 

 rays coming from the centre of the image and corresponding 

 to the directions of the diagonals of the kathodef. 



An equilateral triangle having the same curvature (fig. 10) 

 produced a star with three rays, whose axes were at right 

 angles to the sides of the triangle. So also polygons of 5, 6, 

 7, and 8 sides gave stars, with a corresponding number of 

 rays, whose axes appeared to bisect the sides of the polygon 

 at right angles. 



The position of these figures with reference to the kathode 



* Bine neue Form dectrischer Abstossinu/, i. p. 11. 



t In the accompanying figures of portions of the surface of a sphere, 

 the arcs of great circles between the centre of the light-figure and the 

 separate points forming the bounding surface of the figures are approxi- 

 mately represented by the chords of these arcs, or in the smaller figures 

 by the corresponding aliquot parts of the>e chords. This corresponds 

 with the method of measurement employed, in which distances on the 

 spherical surface were determined by the direct distance between the 

 points of a pair of compasses applied to the surface. 



