VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 18Q 



the same manner it may be shown, that at any other time the particle will be 

 found in the intersection : therefore, from the time of its direction being 

 changed at e, it must pass relatively along the moving line as before. By a 

 small alteration in the construction it may be shown, that if the absolute path 

 had been so changed at b as to have augmented the angle fbd, still the particle 

 would have moved relatively along db, provided its velocity after had been to its 

 velocity before, as the sine of fbd the first angle, to the sine of the increased 

 angle. 



To apply therefore this proposition to the present investigation, let db be 

 conceived as the axis of a telescope perpendicular to the spherical surface of a 

 refracting medium which accompanies it in its lateral motion, sb the absolute 

 path of a particle of light which had passed relatively along db produced, till its 

 arrival at b, and br its absolute path within the medium of the telescope. Then 

 it is evident that fbd, or its equal cbs, will be universally the angle of incidence, 

 and rbd the angle of refraction. Hence, by prop. A, that ray of the parallel 

 pencil which is refracted at o, the vertex of the spherical surface in fig. 14, must 

 still pass relatively along the axis, provided the velocity within the telescope be to 

 its former in air, as the sine of incidence to the sine of refraction. But the 

 image of the star being produced by the meeting of all the contemporary light, 

 will consequently be found in the axis, which, by hypothesis, deviates frum (he 

 true place of the star by the same quantity as Dr. Bradley's angle ; so that in this 

 way of considering the matter, the same thing results which was formerly shown 

 in regard to a telescope so constructed. 



By prop, a it is also manifest, that whatever number of refractions that ray 

 which falls on the extremity of the axis suffers, in pervading object-glasses of 

 any figure, or even dense media beyond the object-glass, if bounded by trans- 

 parent planes to which the axis produced is perpendicular, yet if the velocities 

 and refractions so correspond, still the ray in question will pass relatively along 

 the axis till it meet the rest at the focus : for here the refracted ray in the first 

 medium becomes the incident ray in relation to its path in the 2d, and this in its 

 turn becomes an incident ray in relation to its path in the 3d medium, &c. and 

 therefore, by the prop, a, can never deviate from the moving axis, whatever be 

 the refractive density of the media, or however these are disposed in the order of 

 succession. And since, by Sir Isaac Newton's theorem, the ratio of the sine of 

 incidence to the sine of refraction, in the passage of a ray out of one medium 

 into another, is compounded of the ratio which the former has to the latter, in 

 the passage of that ray out of the first medium into any third, and of the ratio 

 of the former to the latter in the passage of the same ray out of the 3d medium 

 into the 2d, &c. it follows, that if the velocities be related to the degree of re- 

 fraction as before-mentioned, the ray in the last dense medium will, notvuth- 



