263 
Mr. Barlow on the rules and principles for 
Approximate method of computing the curves for an achromatic 
object-glass. 
25. On refering to the formula (14,) for finding the value 
of p, it will be seen that the first term which expresses the 
aberration due to the aberration at the first surface, is very 
inconsiderable with respect to the other term, and that the 
former may be omitted in all common cases without produc¬ 
ing any sensible error. This omission serves to contract the 
operation very considerably, while by a simple inspection of 
the table (art. 13.) it will be seen that its several columns 
are so nearly the same, that any mean one may be adopted 
instead of the whole : availing ourselves of this circumstance, 
every rule and principle for constructing an object-glass may 
be comprised in the following short synopsis, and the result 
may be used with every degree of confidence in all ordinary 
cases; although in large telescopes, and in cases where the 
index and dispersions are very extraordinary, it will be 
necessary to employ the exact formula already illustrated. 
According to the approximation here alluded to the rules for 
the computation may be stated as follows. 
