and the Achromatism of Microscopes. 235 
The preliminary investigation for the variation of the power 
of a lens suggested a mode of treating of the achromatic 
object-glass, which is, I think, as simple as any that has yet 
appeared. And a Jaw which I have assumed for the dispersive 
power of one medium in terms of that of another, reduces at 
once to mathematical investigation every thing relating to the 
irrationality of dispersion. Some speculations on achromatic 
object-glasses I have, therefore, given in the beginning. 
I have been induced to press this subject on the notice of 
the Society from a conviction of its importance, and a know- 
ledge of the little attention usually paid to it. In the date of 
its invention, the achromatic eye-piece is prior to the object- 
glass: in its application it is even more general; in its theory it 
is, I think, more interesting: and in the principles of that theory 
it is not more difficult. Yet while the object-glass continues to 
receive the attention of scientific men, the theory of the eye- 
piece in the space of 40 years has received no improvement: 
in the elementary works on Optics, the object-glass is described 
at length, but the eye-piece is entirely omitted. If it should 
appear that in this paper I have rendered the theory more 
generally accessible to the inquiring mathematician, or more 
easily adapted to the purposes of the practical optician, I trust 
that it will have the approbation of this Society. 
(1) In the following articles, we shall use the letter x to 
express the index of refraction for rays of some one colour, 
which we shall call mean rays, passing out of glass or any other 
refracting medium into air; and shal] denote the index of re- 
fraction for rays of any other colour by x+én. The letter 3 pre- 
fixed to any quantity dependent on z will be employed to denote 
the alteration produced in that quantity by changing n to n +n. 
(2) As we shall make great use of the expression for the 
variation of the power of a lens, we will investigate it here. Let 
Vol. If. Pare IL. Hu 
