232 Mr. Barlow on the rules and principles for 
in the Phil. Trans, for 1821, to which I shall refer more at 
length in a subsequent page. These, I believe, constitute 
every attempt that has been made in this country to bring 
the strict laws of optics, applicable to these cases, within the 
reach of numerical calculation.* 
More numerous attempts have been made by foreign 
mathematicians ; but as far as my knowledge of them extends, 
they have in no instance been attended with the success that 
might have been expected from the deservedly high reputa¬ 
tion of their authors. 
I have spoken above principally of the methods of deter¬ 
mining the radii of curvature of the lenses ; but in order to 
enter upon this calculation, certain data are necessary, which 
require previous experiments and tedious numerical compu¬ 
tations ; so that upon the whole, to take two specimens of 
glass of unknown indices and dispersions, to form an object 
glass of them, free from colour and spherical aberration, 
requires very formidable calculations, involving in them, 
according to the best methods yet employed, certain princi¬ 
ples and operations which we ought hardly to expect practical 
opticians to be masters of. At all events, every simplifica¬ 
tion that can be thrown into experiments and calculations of 
this kind must be desirable; and, I am greatly in hopes it 
will be found that I have, in the following pages, contributed 
* since this Paper was written, Mr. Herschel has also published in the Ency¬ 
clopaedia Metropolitana, under the article Light, a still more extended investiga¬ 
tion relative to this and other optical subjects; to which article it will likewise be 
necessary for me to refer as we proceed; and if, after all, any reference should be 
omitted which ought to be made, it must be attributed to this Paper having been 
written before the publication of the former. 
