468 



Lord Rayleigh's Notes on some 



distances are the lines a, b y c, . . . . and whose common axis is 

 the line A B C P. In the standard case the lenses are sup- 

 posed to be concaves. Then if tt be the apparent distance, 



n ^ OA . AP OB . BP , OC . OP , OA . AB . BP 



<J7T= OP H I 7 1 h J 



a b c ao 



OA.AO.OP , OB. BO. OP OA.AB.BO.OP 



ac 



be 



abe 



The statement is for three lenses, but the law of formation 

 of the terms is general. If a, b, c are infinite, we fall back on 

 direct vision, and 07r = OP. If any of the lenses are convex, 

 the focal distances of such lenses must be looked upon as 

 negative. 



" § 262. Corol. 1. While the glasses are fixt, if the eye and 

 object be supposed to change places, the apparent distance, 

 magnitude, and situation of the object will be the same as 

 before. For the interval OP being the same, and being divided 

 by the same glasses into the same parts, will give the same 

 theorem for the apparent distance as before." This is a pro- 

 position of the utmost importance, from which follows without 

 much difficulty : — 



" § 263. Corol. 2. When an object PL is seen through any 

 number of glasses, the breadth of the principal pencil where it 

 falls on the eye at 0, is to its breadth at the object-glass C, as 

 the apparent distance of the object to its real distance from 

 the object-glass ; and consequently in Telescopes, as the true 

 magnitude of the object to the apparent." 



True magnitude here means apparent magnitude as seen 

 directly, and the theorem is identical with that enunciated 

 more than half a century later by Lagrange *. 



In the investigation of apparent brightness the extreme ray 

 PfsrK from the central point P of the image is considered 

 (fig.2):- 



Fig. 2. 



O A B C P 



" If K be not less than N, the area of the pupil will be 

 totally inlightened by the pencil which flows from P. Let 

 PUrNbe a ray of that pencil, cutting the object-glass C t 



* " Sur une loi generale d'Optique/' Memoires de VAcademie de Berlin, 

 1803. 



