258 Mr. A. S. Percival : Method of 



readiness with which it is adapted to the case of external 

 forces. We have only to put as the imposed condition the 

 constancy — not of the kinetic energy as above throughout, 

 but — of the total energy (Cp. Jeans, Phil. Mag. v. p. 617, 

 1903). Of course the acceleration must not be of such 

 magnitude as to mask the random character of the molecular 

 motion (Cp. Watson, ' Kinetic Theory of Gases,' p. 35) . The 

 second argument, however, is perhaps not so incontrovertible 

 but that it may be indebted to the others for some corrobo- 

 ration. The three arguments are mutually complementary. 



XXVI. Method of Tracing Caustic Curves. 

 By A. S. Percival, M.A., M.B. Camb* 



A CAUSTIC CURVE is the locus of all the primary 

 focal lines formed by the intersection of two contiguous 

 reflected or refracted rays. 



Many mathematicians have devoted their energies to the 

 problem of discovering the general equation of a Caustic 

 Curve, but without success as far as I know except in a 

 few special cases. The method usually given in the books 

 is first to find an expression for the refracted wave-front, 

 which is a Cartesian oval, and then to find the evolute of this 

 curve. This is a most tedious and laborious proceeding, but 

 in this paper I submit a simple method which will enable 

 one to trace the Caustic due, to either reflexion or refraction 

 at a single spherical surface with ease, expedition, and 

 accuracy. As corresponding points can be marked off after 

 refraction at another surface, the Caustic formed by a lens 

 can be plotted out in a reasonable time. 



Now different lenses show differently shaped Caustics, 

 and it will be found that the general rules for the size and 

 position of the Least Circle of Aberration are by no means 

 true when a lens is used with its full aperture. 



Refractio?i at a Single Spherical Surface. 



Let S be the source of light ; consider the ray SP making 

 an angle 6 with the axis SCA, incident at P and refracted 

 as PR. Let RP produced meet the axis at T. Prom C 

 drop the perpendiculars CM and CN on the incident and 

 refracted rays respectively. 



* Communicated by Professor J. W. Nicholson, F.R.S. 



