200 PHILOSOPHICAL TRANSACTIONS. [ANNO 179?. 



perhaps beyond what is necessary ; but its great importance to the whole theory I 

 hope will plead my excuse. 



Let us now suppose that a homogeneal beam passes through the spheres of 

 flexion : it will follow that no divergence can take place from the bending power of 

 the body ; so that we have only to estimate the effect produced by the reflexion, and 

 to inquire whether the different reflexibilities of the rays can cause the images to 

 vary their sizes according as they are formed by different rays. In fig. 7, let ab be 

 the body, cd the limit of its sphere of reflexion, and ip a beam of homogeneal rays, 

 as red, incident at p and reflected to e, forming there the image Rr. It is evident 

 that the greater reflexibility of the rays ip can only alter the position of the centre of 

 Rr, making it nearer the perpendicular than the centre of an image formed by any 

 other rays would be. But the greater length of Rr shows that a greater quantity of 

 rays is reflected, or that the same quantity is spread over a greater space, and that 

 in the following way. Let ifH be a beam of violet-making rays entering abcd, and 

 reflected so as to form the image rv. The force exerted by ab decreasing according 

 to some law (of which we are as yet ignorant) as the distance increases, is not suf- 

 ficient to turn the rays back till they have come a certain length within abcd. But 

 for the same reason it turns back all that it does reflect before they come nearer than 

 a certain distance ; between these 1 limits therefore the rays are turned back. But 

 the limits are not the same to all the rays ; some begin to be turned at a greater 

 distance from the body than others, and consequently are reflected to a greater dis- 

 tance from the middle ray of the incident beam. Thus if ifH be changed to a red- 

 making beam, it begins to be turned back at f. and the rays farthest from ab are 

 reflected to r instead of to v, where they fell when ipfi was violet- making ; not but 

 that the same quantity of rays is reflected, the only difference is, that the most re- 

 flexible are reflected farthest from the body by their greater reflexibility, and farthest 

 from each other by this other property. Exactly the same happens in the case of 

 refraction, mutatis mutandis ; but there seems to be a slight variation in the man- 

 ner in which the different rays are disposed into images of different sizes by flexion. 

 In this case also the bending body's action reaches farther when exerted on some 

 rays than when exerted on others : but then, the direction of the rays not passing 

 through the body, those which are farthest off and at too great a distance to be 

 bent, never coming nearer, are not bent at all ; and consequently as the least 

 flexible rays are in this predicament at the smallest distance, and the most flexible 

 not till the distance is greater, the images formed out of the former must be less 

 than those formed out of the latter. This difference in the way in which the phe 

 nomenon appears, does not argue the smallest difference in the cause : it only fol- 

 lows from the different position of the rays, with respect to the acting body, in the 

 2 cases. I infer then from the whole, that different sorts of rays come within the 

 spheres of flexion, reflexion, and refraction, at different distances, and that the actions 

 of bodies extend farthest when exerted on the most flexible. It may perhaps be 



