﻿The Hon. J. W. Strutt on Double Refraction. 527 



rection bisect respectively the two supplemental dihedral angles 

 made by planes passing through the wave-normal and thetwo optic 

 axes, remains the same as before ; but the positions of the optic 

 axes themselves, as determined by the principal indices of refrac- 

 tion, are somewhat different; the difference, however, is but 

 small if the differences between « 2 , 6 2 , c 2 are a good deal smaller 

 than the quantities themselves. Each principal section of the 

 wave-surface, instead of being a circle and an ellipse, is a circle 

 and an oval, to which an ellipse is a near approximation. The 

 difference between the inclinations of the optic axes and be- 

 tween the amounts of extraordinary refraction in the principal 

 planes, on the two theories, though small, are quite sensible 

 in observation, but only on condition that the observations are 

 made with great precision. We see from this example of what 

 great advantage for the advancement of theory observations of 

 this character may be." 

 And again : — 



"The curious and unexpected phenomenon of conical refraction 

 has justly been regarded as one of the most striking proofs of 

 the general correctness of the conclusions resulting from the 

 theory of Fresnel. But I wish to point out that the pheno- 

 menon is not competent to decide between several theories lead- 

 ing to Fresnel' s construction as a near approximation We 



see, therefore, that the limitation of the number of tangent 

 planes to the wave-surface which can be drawn in a given direc- 

 tion on one side of the centre to two, or at the most three, is 

 intimately bound up with the number of dimensions of space ; 

 so that the existence of the phenomenon of internal conical re- 

 fraction is no proof of the truth of the particular form of wave- 

 surface assigned by Fresnel rather than that to which some 

 other theory would conduct. Were the law of wave-velocity ex- 

 pressed, for example, by the construction already mentioned 

 having reference to the ellipsoid (12), the wave-surface (in this 

 case a surface of the 16th degree) would still have plane curves 

 of contact with the tangent-plane, which in this case also, as in 

 the wave-surface of Fresnel, are, as I find, circles, though that 

 they should be circles could not have been foreseen. 



" The existence of external conical refraction depends upon the 

 existence of a conical point in the wave-surface, by which the inte- 

 rior sheet passes to the exterior. The existence of a conical point 

 is not, like that of a plane curve of contact, a necessary property 

 of a wave- surface. Still it will readily be conceived that if FresnePs 

 wave-surface be, as it undoubtedly is, at least a near approxima- 

 tion to the true wave-surface, and if the latter have, moreover, 

 plane curves of contact with the tangent plane, the mode by 

 which the exterior sheet passes within one of these plane curves 



