136 Mr Larmor, On the Laws of the [Jan. 26, 



Every beam in a homogeneous medium therefore converges to 

 two ray-caustic surfaces which are the two sheets of the surface 

 of centres of curvature of the wave-fronts. Each of these surfaces 

 is physically made up of a series of parallel bright and dark sheets, 

 of which the first is much the brightest, whose distances and 

 relative intensities always retain the same proportions. These 

 distances are at any point proportional to the cube root of the 

 radius of curvature of the normal section of the caustic surface 

 containing the ray which touches it at that point. 



5. It is easy enough to obtain actual examples of this general 

 proposition. On looking at a bright lamp, sufficiently distant 

 to be treated as a luminous point, through a plate of glass covered 

 with fine rain-drops, the caustic surfaces after refraction through 

 the drops are produced within the eye itself, and their sections by 

 the plane of the retina appear as bright curves projected into the 

 field of vision. These curves are each accompanied by the other 

 parallel diffraction bands, which separate and become more marked 

 as the curves recede asymptotically, while they assume a dif- 

 ferent character near the cusps which are a feature of all sections 

 of caustic surfaces. Near these cusps in the cross-section of the 

 caustic surface two different pencils of light come into inter- 

 ference. 



These phenomena are quite different from the ordinary cases 

 of entoptic diffraction, in which when the eye is put out of focus 

 by a lens, and a bright sky is viewed through a pinhole, the 

 pencil of light coming through the pinhole projects on the 

 retina shadows of the muscae volitantes floating in the aqueous 

 humour, and these are accompanied by the ordinary bands at the 

 boundaries of shadows. This case of an obstacle is the exact 

 complement of that of a similar hole in a screen as regards the 

 position of the bands ; so that when the obstacle is small, the 

 diffraction bands round the shadow form exact circles, irrespective 

 of its shape, which is the ordinary visual appearance. 



The cusped caustic bands are easily seen when a distant street- 

 lamp is viewed through a spectacle lens with minute rain-drops 

 deposited on it. 



The diffraction problem which has here been discussed includes 

 diffraction at a focal line, with an unlimited beam. In practical 

 questions such as those relating to spectroscopes and the Her- 

 schelian telescope, the exact focussing would however introduce 

 the nature of the aperture into the discussion, and the limits of 

 the integral would enter. 



6. In the case of a cylindrical beam the bands near the caustic 

 have been counted up to 30 or more by W. H. Miller, and the 

 divergence of the more remote ones is too great to allow an 



