474 PHILOSOPHICAL TRANSACTIONS. [ANNO 1784. 



by a certain force impelling it towards the refracting medium, an hypothesis 

 which perfectly accounts for all the appearances. On this hypothesis, the 

 velocity of light in any medium, in whatever direction it falls on it, will always 

 bear a given ratio to the velocity it had before it fell on it, and the sines of in- 

 cidence and refraction will, in consequence of this, bear the same ratio to each 

 other with these velocities inversely. Thus, according to this hypothesis, if the 

 sines of the angles of incidence and refraction, when light passes out of air into 

 glass, are in the ratio of 31 to 20, the velocity of light in the glass must be to 

 its velocity in air in the same proportion of 3 1 to 20. But because the areas, 

 representing the forces generating these velocities, are 1 as the squares of the ve- 

 locities, art. 5 and 6, these areas must be to each other as 961 to 400. And if 

 400 represent the area which corresponds to the force producing the original ve- 

 locity of light, 56l, the difference between 961 and 400, must represent the 

 area corresponding to the additional force, by which the light was accelerated at 

 the surface of the glass. 



31. In art. 19 we supposed, by way of example, the velocity of the light of 

 some particular star to be diminished in the ratio of 19 to 20, and it was there 

 observed, that the area representing the remaining force which would be neces- 

 sary to generate the velocity 19, was therefore properly represented by |-g-£ parts 

 of the area, that should represent the force that would be necessary to generate 

 the whole velocity of light, when undiminished. If then we add 56 1, the area 

 representing the force by which the light is accelerated at the surface of the 

 glass, to 36l, the area representing the force which would have generated the 

 diminished velocity of the star's light, the square root of 922, their sum, will 

 represent the velocity of the light with the diminished velocity, after it has en- 

 tered the glass. And the square root of 922 being 30.364, the sines of inci- 

 dence and refraction of such light, out of air into glass, will consequently be as 

 30.364 to 19, or what is equal to it, as 31. 96 to 20 instead of 31 to 20, the 

 ratio of the sines of incidence and refraction, when the light enters the glass 

 with its velocity undiminished. 



32. Hence a prism, with a small refracting angle, might perhaps be found to 

 be no very inconvenient instrument for this purpose : for by such a prism, 

 whose refracting angle was of l', for instance, the light with its velocity undimi- 

 nished would be turned out of its way 33", and with the diminished velocity 35 ;/ .88 

 nearly, the difference between which being almost I 11 53'", would be the quan- 

 tity by which the light, whose velocity was diminished, would be turned out of 

 its way more than that whose velocity was undiminished. 



33. Let us now be supposed to make use of such a prism to look, at two stars, 

 under the same circumstances as the two stars in the example above-mentioned, 

 the central one of which should be large enough to diminish the velocity of its 



