e theory
is analogous. His instrument was called the _eriometer_ (see
"Chromatics," vol. iii. of supp. to _Ency. Brit._, 1817).

7. _Influence of Aberration. Optical Power of Instruments._--Our
investigations and estimates of resolving power have thus far proceeded
upon the supposition that there are no optical imperfections, whether of
the nature of a regular aberration or dependent upon irregularities of
material and workmanship. In practice there will always be a certain
aberration or error of phase, which we may also regard as the deviation
of the actual wave-surface from its intended position. In general, we
may say that aberration is unimportant when it nowhere (or at any rate
over a relatively small area only) exceeds a small fraction of the
wave-length ([lamda]). Thus in estimating the intensity at a focal point,
where, in the absence of aberration, all the secondary waves would have
exactly the same phase, we see that an aberration nowhere exceeding
1/4[lambda] can have but little effect.

The only case in which the influence of small aberration upon the
entire image has been calculated (_Phil. Mag._, 1879) is that of a
rectangular aperture, traversed by a cylindrical wave with aberration
equal to cx^3. The aberration is here unsymmetrical, the wave being in
advance of its proper place in one half of the aperture, but behind in
the other half. No terms in x or x^2 need be considered. The first
would correspond to a general turning of the beam; and the second
would imply imperfect focusing of the central parts. The effect of
aberration may be considered in two ways. We may suppose the aperture
(a) constant, and inquire into the operation of an increasing
aberration; or we may take a given value of c (i.e. a given
wave-surface) and examine the effect of a varying aperture. The
results in the second case show that an increase of aperture up to
that corresponding to an extreme aberration of half a period has no
ill effect upon the central band (S 3), but it increases unduly the
intensity of one of the neighbouring lateral bands; and the practical
conclusion is that the best results will be obtained from an aperture
giving an extreme aberration of from a quarter to half a period, and
that with an increased aperture aberration is not so much a direct
cause of deterioration as an obstacle to the attainment of that
improved definition which should accompany the increase of