2 36 
Mr. Barlow on the rules and principles for 
achromatism in an object glass, it is requisite that the focal 
lengths of the two lenses be to each other in the ratio of their 
dispersive powers ; that is, the ratio of the dispersive power 
of the flint being to that of the plate as 1 : d, the focal length 
of the flint must be to that of the plate also as 1 id, the two 
lenses being in contact. 
If therefore we have two lenses, viz. a concave flint, and a 
convex plate, in which the focal length of the latter bears a 
greater ratio to that of the former than 1 to d, we must open 
the two lenses from each other till the required ratio is ob- 
tained, when the object will be colourless, and therefore 
conversely, when the image is colourless, we shall be sure 
that the ratio of the focal lengths will be that also of the 
dispersive powers. 
To illustrate this a little more particularly, let /, /' be the 
focal lengths of the plate and flint lens, and let 8 be the 
distance of the lenses when the image is colourless. Then, 
first, it is obvious, that the effect will be the same as if we had 
a plate lens in contact with the flint, which had for its focal 
length/- — /but the actual quantity of its dispersion that due 
to the whole focal length/; that is, the same as a plate lens 
of focal length/ — 8 , and whose dispersive power =jzz} • 
And since in this state the image is colourless, it follows 
that 
/' =/— s ::1 : fzr d - 
And therefore d, which is the quantity sought, is found from 
the equation 
d = M (2 ). 
The lenses we employed were about 2^- inches in diameter. 
