26l 
determining the dispersive ratio of glass ^ &c. 
bute the difficulty which we certainly found in submitting 
Mr. Herschel’s numbers to practice. Nothing can be desired 
more accurate nor more elegant than the principles and the 
analysis on which it is founded, nor any thing more simple 
than the ultimate result; but it happens, that except the most 
rigid agreement has place between the computed radii and 
the radii employed, the discrepance has a very considerable 
effect upon the correction of the object-glass. 
The rule which I have endeavoured to explain in the pre¬ 
ceding pages is, I believe, equally correct, but it possesses 
none of the elegance of investigation which distinguishes the 
other. To compensate for this, however, it has an extensive 
range of application, and will enable us in all cases to select 
those particular radii which will produce the required cor¬ 
rection with the least liability to error, and with the closest 
contact surfaces. We may also, by rejecting the latter con¬ 
dition, match any flint whatsoever with its proper plate; 
which is I believe a great practical convenience. 
The above are only a few out of a great number of expe¬ 
riments, but I have selected them so that they embrace all 
the varieties which can ever occur; viz. with the flint double 
concave when q is positive; with the flint plano-concave when 
q is infinite ; and with it concavo-convex when q is negative. 
So that I hope no one who has any knowledge of the meaning 
of an algebraical formula, can be at any loss in submitting 
the rules I have endeavoured to illustrate to a practical 
application. 
