3^ PHILOSOPHICAL TKANSACTIONS, [aNNO J740. 



side, and as much convex on the other ; according to the method propounded 

 by Sir Isaac Newton, in his most excellent book, of Optics. 



It may be imagined perhaps, at first view, that, if our reasoning is just, the 

 errors of refracting telescopes, occasioned by the different refrangibility of 

 light, may be corrected by a like artifice : but the aberration of the rays from 

 the principal focus is there so great, and bears so considerable a proportion to 

 the focal length of the telescope, that the error cannot be rectified by the in- 

 terposition of any lens, until the rays are, by a contrary refraction, collected 

 again at an infinite distance, which renders this expedient quite useless: how- 

 ever, there is no need to despair of accomplishing even this, by other methods : 

 and, by the way, we may observe, if it were worth while to seek a remedy for 

 the errors occasioned by the spherical figure of the object-glass only, in diop- 

 trical telescopes ; that might be obtained by the proper application of a suitable 

 lens, between the focus and the vertex of the object-glass ; which is much 

 more easy and practicable, than the grinding of glasses to hyperbolical or ellip- 

 tical figures. 



For a further illustration of the foregoing, it may be proper to exhibit the 

 several parts and proportions of a telescope in numbers, computed according to 

 the theorems already delivered ; and in practice we judge it will be most con- 

 venient, that the radii of the spheres, to which the concave and convex sides 

 of the speculum are ground, be nearly in the ratio of 6 to 5 ; as in the follow- 

 ing example ; where, in fig. 4, 



ABCDEF represents the great speculum of glass, ground concave on one side, 

 and convex on the other; quicksilvered over the convex side, and of an equal 

 thickness all round its circumference. 



The radius of concavity = a = 48 inches. 



The radius of convexity = e = 40 inches. 



Then putting n, the sine of incidence := 100; w?, the sign of refraction of 

 the least refrangible rays, out of glass into air, =154; and f*, the sine of re- 

 fraction of the most refrangible rays, = 1 56 ; as Sir Isaac Newton found them 

 by experiments; we shall have, 



PB, the focal length of the speculum with regard to the most refrangible 

 rays ^ J 8.2926 -f, which will be somewhat increased by the thickness of the 

 glass, when that is considerable. 



pa, the greatest aberration of the rays, occasioned by their different degrees 

 of refrangibility, = .05594 -|-, which quantity, in practice, should be a very 

 little augmented, rather than otherwise; therefore we put it here = .056 = t. 



The radius of the concave surface of the lens, turned towards the speculum, 

 viz. of GHi, = V =: 2.8 inches. 



