Mr. Moseley on Caustics. 263 



posited near transition rocks : the chalk of Maestricht, at the 

 loot of the Ardennes ; that of Saintonge, not far from the gra- 

 nites of La Vendee ; and that of Valognes, near the old rocks 

 of the Cotentin. The absence in the latter country of the fer- 

 ruginous sand [sable ferrugineux), the still uncertain place of 

 the greensand {sable vert), and of every rock which might 

 exclusively represent the upper chalk; the mixture of the fos- 

 sils of the two chalks, and the isolated geographical situation 

 of this little basin, — are circumstances sufficiently powerful to 

 afford colour for this supposition. H. T. D. B. 



XLI V. On Caustics. By Mr. H. Moseley, A.B. St. John's 



College, Cambridge. * 



'pHE term Caustic is throughout the following paper to be 

 understood as applying itself to the locus of the ultimate 

 mtersections of consecutive rays of light after their reflexion 

 or refraction at a curvilinear surface. 



On Caustics by Rejiexion. 

 To determine the caustic formed by rays incident from a 

 given pomt S on a given reflecting curve;' let us imagine an 

 ellipse, havmg its focus in S, to be so described through any 

 point P of the reflecting curve, as to have a contact^ the 

 second order with the curve in that point,~conditions which 

 It may evidently be made to satisfy, since it involves five 

 arbitrary constants m its equation, of which two may be made 

 to hx the position of its focus, and the remaining three wiU 

 give It the contact required. 



Now, since the curvature of the osculating ellipse and that 

 ot the given curve are the same in their point of contact, ravs 

 uicident at that point will be similarly reflected by the two 

 curves. But m the ellipse, rays incident from S will be re- 

 flected so as to intersect in (the further focus) H. The in- 

 tersection of rays reflected by the given curve will, therefore 

 also be in H. And the question reduces itself to the deter- 

 mination ot the curve described by the focus H of that oscu- 

 lating ellipse; whose focus S is in the radiating point. 



Let «/3 be the axes of the ellipse thus taken at the point P- 

 V a perpendicular to the common tangent of the two curves 

 at that point, from 8; r the length of the incident ray, SP- 

 g that portion of the reflected ray which is intercepted between 

 the reflecting curve and the caustic, or HP. 



• Communicated by the Author. 



Then 



