different foci, but each zone has a
definite focus.

E. Irregular diffraction fringes point to bad annealing of the glass.
This may be checked by an examination of the lens in polarised light.

F. If the disc appear blurred and coloured, however the focus be
adjusted, incomplete correction for chromatic aberration is inferred.
If in addition the colouring is unsymmetrical (in an extreme case the
star disc is drawn out to a coloured band), want of centering is to be
inferred. This will also show itself by the interference fringes
having the characteristics described in C.

(2) The following steps may be taken in applying a remedy:

A. The adjusting screws of the cell mounting the object glass may
be worked until the best result is attained; this requires great
care and patience. Any errors left over are to be attributed to
other causes than the want of collinearity of the axes of object
glass and eyepiece.

B. Astigmatism is detected by rotating the object glass or object
glass cell. If the oval fringes still persist and the longer axis
follows the lens, astigmatism may be inferred. Similarly, by rotating
one lens on the other, astigmatism, or want of centering (quite a
different thing) may be localised to the lens.

C. The presence of flexure may be confirmed by altering the position
of the points of support with respect to the eyepiece, the lens
maintaining its original position. The addition of more points of
support will in general reduce the ill effects. How to get rid of
them I do not know; they are only serious with large lenses.

D. Spherical aberration may be located by using stops and zonal
screens, and observing the effect on the image. Sir H. Grubb
determines whether any point on the lens requires to be raised or
lowered, by touching the glass at that point with a warm hand or
cooling it by ether. The effects so produced are the differential
results of the change of figure and of refractive index. By observing
the effect of the heating or cooling of any part, the operator will
know whether to raise or lower that part, provided that by a suitable
preliminary experiment he has determined the relation between the
effect produced by the change of figure, and that due to the
temperature variation of the refractive index. In general it is
sufficient to consider the change of shape only and neglect the change
in refractive power.

E. Marked astigmatism has never been noticed by me, but