VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. ]87 



equable lateral motion of the telescope, df and ef will be as the times of the 

 points d and e arriving at f : therefore, in the last case, the intersection of the 

 cross wires, supposed at e, will meet the image at f, and accordingly the star 

 will be seen in the axis. 



From what has been said it will appear, that if df, fig. 14, be taken to ef, 

 as the sine of incidence to the sine of refraction peculiar to the medium which 

 fills the telescope ; then, from the property of the focus, we shall have this pro- 

 portion, viz. bf : fm :: df : ef. Hence the line emo, passing through m, must 

 be parallel to db ; but db, as before, denotes the position of Dr. Bradley's teles- 

 cope, when the aberration of the star is at its maximum, and emo, parallel to 

 it, denotes the position of the water telescope, at the same time, on the suppo- 

 sition that the velocity of the rays without and within are as ef to df, or in- 

 versely as the sines of incidence and refraction peculiar to water. Here then we 

 discover what must be the law of variation as to the velocity of the rays, pro- 

 vided that the aberration given by such a telescope shall come out the same with 

 that found by Dr. Bradley. It is the very same which follows from the New- 

 tonian principles : for from the manner of observing, the angle of aberration is 

 always determined by the position of the telescope necessary for having the image 

 formed somewhere in the axis. 



But supposing that in the course of observing with such a telescope, the 

 aberration should come out different from what has already been ascertained by 

 Dr. Bradley, it may next be inquired how, from the difference given, the ve- 

 locity of light within the telescope is to be deduced. (Fig. 15,) Imagine then 

 such a telescope actually to give fmd as the greatest angle of aberration, and let 

 this be supposed greater than that of Dr. Bradley's, which, for example, let be 

 fme. From what has been already said, the velocity of light corresponding to 

 this last mentioned angle, is deducible from the known refraction of the medium 

 which fills the telescope ; and, by construction, the velocity corresponding to 

 fmd, the angle given, must be to the former, inversely as the tangents of these 

 angles. From this consideration we have the following analogy, for finding the 

 velocity corresponding to whatever difference there may be observed between the 

 two aberrations at present alluded to. The rule in all cases must be ; " as the 

 tangent of the observed angle is to the tangent of the Bradleyan angle, so is the 

 velocity of light deducible from the hypothesis of the observed angle being the 

 same with that of Dr. Bradley, to the velocity sought." It has already been 

 shown, how the former of these velocities can be universally ascertained, from 

 the known refraction of the medium which is taken to fill the telescope, and 

 therefore the last term of the above proportion, which is the velocity sought, is 

 thereby given. 



In a telescope of this kind will not have escaped notice, that the ray bf, 



b b '2 



