compound lenses and object-glasses. 227 
(and I have consulted many) ; nor, of course, lias any part 
of their attention been directed to obviate, experimentally, a 
source of indistinctness they could not perceive to exist. 
Clairaut in the Memoirs of the Academy for 1757 has 
computed the radii of a double object-glass from the con- 
dition of their touching throughout the whole extent of their 
interior surfaces; a very desirable thing in practice, and 
the curvatures which result are very convenient. Clairaut 
however has employed in his computations, indices of re- 
fraction (1.600 and 1.55) higher, especially the latter, than 
what are now easily met with ; and when the average values, 
such as are likely to occur most frequently, are employed, 
the construction becomes imaginary for the more dispersive 
kinds of glass ; and within the limits for which it is real, the 
radii change so rapidly as to render it difficult to interpolate 
between their calculated values ; so that to the artist who is 
no algebraist this construction loses much of its real ad- 
vantage. 
There remains a condition unaccountably overlooked (so 
far as my reading has extended) and which the nature of 
the formulae of aberration, as given in the following pages, 
almost forces on our attention ; I mean, the destruction of 
the aberration not only for parallel rays, or when the tele- 
scope is directed to celestial objects, but also for rays di- 
verging from a point at any finite distance. The perfection 
of the telescope, when directed to land objects, seems to 
require this ; and though, in astronomical telescopes, it may 
appear uncalled for, the construction possesses other advan- 
tages of so high an order as to recommend it even there : 
these are, 1st. the very moderate curvatures required for the 
mdcccxxi. G g 
