Mr. J. F. W. Herschel on the aberrations of 
an insensible change in the value of f, especially since the 
greatest value of c very little exceeds 
Opticians usually regard only the co-efficients p,p’, &c. 
which represent the dispersive powers ; and the first of our 
equations (r), which assigns a relation among the powers of 
the lenses of a very simple nature, has in general been the 
only one resorted to to insure the achromaticity of the sys- 
tem. It has long however been a subject of complaint, that 
however perfectly the foci of a double object-glass be adjusted 
to unite the extreme rays of the spectrum, a more or less 
considerable quantity of uncorrected colour remains, which 
cannot be destroyed by such adjustment. This is obviously 
owing to the non-proportionality of the quantities of p , q, r, in 
different media, which renders it impossible to satisfy more 
than the first of the equations (/'), or to what is termed the 
irrationality of the coloured spaces, in the spectra ; and the 
attention of the optical philosopher has for some time past 
been turned to the discovery of media, in which either this 
defect of proportionality shall be imperceptible, or else so 
considerable, as to admit a more perfect correction by the use 
of three lenses of different media, so adjusted as to satisfy 
two of the equations. As the co-efficients q, r, &c> furnish 
equations exactly similar to those afforded by p , it would not 
be amiss, were they designated in future by the epithet of 
dispersive powers of the 2d, 3d, and superior orders, and w'ere 
each medium regarded as having its own peculiar system of 
dispersive powers of all orders to infinity according to the 
values of p, q, r, &c. It is almost superfluous to remark on 
the very interesting field of experimental enquiry which this 
view lays open, in which however, little progress can be ex- 
