348 Mr. Barlow on the rules and principles for 
The latter r"\ being concave or convex accordingly as q' is 
positive or negative. 
It is to be observed, however, that if in these results r' 
should be less than r", or if it should exceed it too much, so 
as to leave the contact surfaces too wide, a new supposition 
of the value of q' must be made till the required approxima¬ 
tion, stated in our fourth condition (art. 6.) is obtained. 
12. It fortunately happens that the most laborious part of 
the above operation, viz. the solution of the equation from 
which the value of q in the plate lens is obtained, is readily 
reduced to a tabulated form, whereby this calculation is alto¬ 
gether avoided. This is done in the following short table, in 
which all the more practicable values of q are given for the 
several indices a = *500, a — *510, a *520, and a = -530 ; 
and it will be seen that so little change takes place in the 
value of q, for these changes of indices, that the number 
answering to any value of a between these limits may be 
readily found by simple proportion. 
In this Table p represents the amount of aberration as 
determined by equation (14), and in the adjacent column is 
given the corresponding value of q : as to the method of 
using the table it will be readily comprehended from an 
example. 
