J86 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 



ray gbf passes into the medium without being refracted by it, and bmf would be 

 considered as the axis of the telescope. 



Now let the spherical refracting surface with its wires, or the unusual telescope, 

 be carried laterally with the motion of the earth towards a. Conceive gbf to be 

 a line not partaking of this lateral motion, which at any particular moment 

 passes through m, the centre of convexity. Along this line suppose one of 

 many rays to pass from a star situated in the pole of the ecliptic. Then will all 

 the contemporary light of this pencil of parallel rays be made to converge, so as 

 to meet in a focus somewhere in the unrefracted ray bf. Let f therefore be the 

 point in absolute space where the image of the star is so formed. Let the paral- 

 lel motion of the telescope, whose refracting spherical surface is abc, be in the 

 direction of hf, and take fd to fb as the lateral velocity of the telescope to the 

 velocity of light in air, and join bd : then it is manifest that bd will be the po- 

 sition of a telescope such as Dr. Bradley's, when the image of the star is formed 

 in the axis bd, and that ibg, or its equal fbd, will be the angle of greatest 

 aberration. 



Also, the velocity of the rays, as they proceed to the focus f, after refraction 

 at the surface abc, being supposed the same as in air, it is evident, that the line 

 dml drawn through d and the centre of convexity m, must give the position of 

 the axis of this kind of telescope, when the image of the star is formed there : 

 for, by the hypothesis, the image is formed at f in absolute space ; and since bf 

 is supposed to be to fd, as the velocity of light within the medium, to the 

 lateral velocity of the telescope, the point d of the axis dl will arrive at f, when 

 the rays arrive there to form the image. And the observer not knowing, or at 

 present not taking account of, the lateral motion of the telescope, will suppose, 

 that the line lmd, joining the image of the star and the centre of convexity m, 

 is the true direction of the star ; just as before he concluded, that fmbg would 

 be the direction of the star when the lateral motion of the telescope was sup- 

 posed to be nothing. Hence it is evident, that the intersection of the cross 

 wires, used in observing, must now be placed at d ; or else, if those be still used 

 that were before supposed to be at f, the refracting surface abc, with the line 

 or axis bf, must revolve about the centre m, till the vertex b comes to l, and 

 the cross wires f to d. 



In like manner, if the velocity of the rays were increased after refraction at 

 the spherical surface in any ratio, as that of df to ef, the refraction continuing 

 the same, then emo, drawn through the centre of convexity, would now give 

 the position of the axis of the telescope necessary for receiving the image 

 formed at f. For the space described by the rays in passing downwards to the 

 focus, in this case and the former being equal, the times of their converging at 

 f will be reciprocally as the velocities, or as ef to df. But, on account of the 



