262 Dr. L. Trenchard More on the Coincidence of 



cPy 

 according to whether -^ is negative or positive. Lumin- 

 escence may accordingly be expected whenever the graph is 

 concave to the axis, and darkness where it is convex *. 



In fig. 6 let u, v be the points of inflexion which are 

 known to exist in D/3 X , a'B. 



Then from ft' to u the curve is convex to the axis, and 

 therefore we expect darkness — the Crookes's dark space. 



From u to s the curve is concave, and therefore we expect 

 luminosity — the negative glow. 



Beyond s we expect alternations of light and darkness — 

 the striae— until we come to the neighbourhood of the anode, 

 and here the solution leads us to expect phenomena similar to 

 those occurring at the cathode. 



What happens in nature is that the appearances presented 

 at the anode vary greatly in different discharges, and, in 

 general, bear very little resemblance to those observed at the 

 cathode. This appears, at first, to be in opposition to our 

 theory, but I hope in the second part of this paper to show 

 that, so far from being in opposition to the theory, it becomes 

 a logical consequence of the theory as soon as we introduce 

 the supposition that the velocity of the negative ions is much 

 greater than that of the positive. 



XXI. On the Coincidence of Refracted Rays of Light in 

 Crystalline Media. By Louis Trenchard More, Ph.D., 

 Adjunct-Professor of Physics in the University of Nebraska^ . 



IT is very generally assumed in treatises on optics that rays 

 o£ light in doubly-refracting media break up into two 

 parts, unless the light traverses a path coinciding with an 

 opiic axis of the crystal, or unless the path coincides with the 

 major or minor axis of the elliptic section of the wave-sarface. 

 In the former case, both the velocities and the directions of the 

 ravs coincide ; in the latter, although the velocities are 

 different, the paths are the same. That these are but two 

 special cases of an infinite number in which the paths of the 

 ordinary and extraordinary rays coincide was first shown by 

 Dr. D. B. Brace \. The reason that this phenomenon has 

 hitherto escaped experimenters is probably because, under 

 these conditions, the angle of refraction of the rays is, in 

 general, either so large that it is greater than the critical 



* J. J. Thomson, Phil. Mag. xlvii. p. 267 (1899). 

 t Communicated by the Author. Read in part to the American 

 Mathematical Society, August 1699. 

 \ Wied. Ann. Bd. xxvi. p. 576. 



