VOL. L.] PHILOSOPHICAL TRANSACTIONS. ^y I 



the white flint or crystal. He therefore ground a wedge of white flint of about 

 25°, and another of crown of about 29°, which refracted nearly alike; but their 

 divergency of the colours was very different. He then ground several others of 

 crown to different angles, till he got one which was equal, with respect to the 

 divergency of the light, to that in the white flint; for when they were put toge- 

 ther, so as to refract in contrary directions, the refracted light was entirely free 

 from colour. Then measuring the refractions of each wedge, he found that of 

 the white glass to be to that of the crown nearly as 2 to 3 ; and this proportion 

 would hold very nearly in all small angles. Therefore any two wedges made in 

 this proportion, and applied together, so as to refract in a contrary direction, 

 would refract the light without any difference of refrangibility. 



To make therefore two spherical glasses, that shall refract the light in con- 

 trary directions, it is easy to understand, that one must be concave, and the 

 other convex ; and as the rays are to converge to a real focus, the excess of re- 

 fraction must evidently be in the convex ; and as the convex is to refract most, it 

 appears from the experiment, that it must be made with crown glass, and the 

 Concave with white flint glass. And further, as the refractions of spherical glasses 

 are in an inverse ratio of their focal distances, it follows, that the focal distances 

 of the two glasses should be inversely as the ratios of the refractions of the 

 wedges: for being thus proportioned, every ray of light that passes through this 

 combined glass, at whatever distance it may pass from its axe, will constantly be 

 refracted, by the difference between two contrary refractions, in the proportion 

 required, and therefore the different refrangibility of the light will be entirely 

 removed. 



Having thus got rid of the principal cause of the imperfection of refracting 

 telescopes, there seemed to be nothing more to do, but to go to work on this 

 principle ; but he had not made many attempts, before he found that the removal 

 of one impediment, had introduced another equally detrimental (the same as he 

 had before found in two glasses with water between them): for the two glasses, 

 that were to be combined together, were the segments of very deep spheres; and 

 therefore the aberrations from the spherical surfaces became very considerable, 

 and greatly disturbed the distinctness of the image. Though this appeared at 

 first a very great difficulty, yet he was not long without hopes of a remedy: for 

 considering that the surfaces of spherical glasses admit of great variations, though 

 the focal distance be limited, and that by these variations their aberrations may 

 be made more or less, almost at pleasure; he plainly saw the possibility of making 

 the aberrations of any two glasses equal ; and as in this case the refractions of 

 the two glasses were contrary to each other, their aberrations, being equal, would 

 entirely vanish. And thus at last he obtained a perfect theory for making object 

 glasses, to the apertures of which he could scarcely conceive any limits; for if 



