Page:Optics.djvu/96

 This is positive, if $m⁄∆−1⁄∆′$ be less than $=m⁄∆−1⁄m∆−m−1⁄mr$, and negative when $=(m−1⁄m)1⁄∆−m−1⁄mr$ is above that value; when $=m^{2}−1⁄m∆−m−1⁄mr$, there is no aberration. See p. 54. Note.

When $=m−1⁄m(m+1⁄∆−1⁄r)$ is negative, or the surface convex, the aberration is always positive.

99. We will now pass on to the aberration in a lens, (Fig. 96.)

We may consider this as consisting of two parts: As to the first, we may consider the ratio of the variations as the same with that of the differentials of $∆$ and $(m+1)r$.
 * 1) The variation in the second focal distance arising from the aberration in the first ($A∆ [sic]$).
 * 2) The additional aberration in the refraction at the second surface ($∆=(m+1)r$).

Then since the first aberration is $r$,

For the second part we must alter our formula by putting