igO . PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 



standing any number of previous refractions by glasses, &c. have the same final 

 velocity that would have been acquired on its passing immediately out of air into 

 that medium. This being the case, it appears, that though the intervention of 

 an object-glass may shorten the focal distance of such a telescope, yet it will not 

 displace the image nor alter the rule of inferring the final velocity of the rays in 

 the dense medium from the aberration given ; at least when this is supposed to 

 be the same with Dr. Bradley's. 



But further, if the aberration of such a telescope should differ from the Brad- 

 leyan one, and give, for example, the angle omb, fig. 15, still the ray po, 

 which falls on o the vertex, must be considered as an incident ray, which, after 

 refraction, passes along the axis. By prop, a therefore, the velocity of the ray, 

 whatever this may be after refraction, must be to that velocity by which it would 

 have moved relatively in the axis, so inclined to its path, previous to the refrac- 

 tion, inversely as the sines of incidence and refraction. Now this being duly 

 considered, it will be found that the velocity within the medium, corresponding 

 to this supposed aberration, or the absolute velocity within the medium, must 

 be to the velocity within the medium corresponding to the Bradleyan aberration, 

 inversely as the tangents of these two angles : for let v and v express the veloci- 

 ties before and after refraction corresponding to the Bradleyan angle, and x and 

 x the velocities before and after corresponding to the supposed uncommon angle, 

 x being the actual velocity after refraction ; then, because by prop, a the ante- 

 cedent is to the consequent, in both cases, in the same ratio, viz. as the sine of 

 refraction to the sine of incidence, it will be v : v :: x : x, and therefore v : x :: 

 v : x. But from the nature of the aberration v must be to x (this supposititious 

 velocity before incidence) inversely as the tangents of the angles of the two aber- 

 rations. This therefore must be the ratio of v to x. But v is given, as before 

 shown ; therefore x the velocity within the medium corresponding to the sup- 

 posed observed aberration is also given, and by the same rule as was found for- 

 merly in the case of the first telescope. 



What has been at present advanced is unconnected with any hypothetical 

 notions concerning the rays or the cause of refraction. Light has been con- 

 sidered only as something which moves uniformly from one place to another, 

 and which is always refracted according to a known law. The first of these pro- 

 perties has been put beyond all doubt by the observations of Dr. Bradley and 

 Mr. Molyneux ; and it has been long known that the last is quite agreeable to 

 experience. 



It has indeed always been taken for granted, that the velocity of the ray 

 whicn passes through the centre of convexity, represents the common velocity 

 of all the contemporary light of the converging pencil. This may perhaps be 

 reckoned a circumstance of which we have no proof. But it must be considered, 



