ine there would
be no difficulty in applying a remedy by making [sigma] slightly
variable towards the edges. Or, retaining [sigma] constant, we might
attain compensation by so polishing the surface as to bring the
circumference slightly forward in comparison with the position it
would occupy upon a true sphere.

It may be remarked that these calculations apply to the rays in the
primary plane only. The image is greatly affected with astigmatism;
but this is of little consequence, if [gamma] in (8) be small enough.
Curvature of the primary focal line having a very injurious effect
upon definition, it may be inferred from the excellent performance of
these gratings that [gamma] is in fact small. Its value does not
appear to have been calculated. The other coefficients in (8) vanish
in virtue of the symmetry.

The mechanical arrangements for maintaining the focus are of great
simplicity. The grating at A and the eye-piece at O are rigidly
attached to a bar AO, whose ends rest on carriages, moving on rails
OQ, AQ at right angles to each other. A tie between the middle point
of the rod OA and Q can be used if thought desirable.

The absence of chromatic aberration gives a great advantage in the
comparison of overlapping spectra, which Rowland has turned to
excellent account in his determinations of the relative wave-lengths of
lines in the solar spectrum (_Phil. Mag._, 1887).

For absolute determinations of wave-lengths plane gratings are used.
It is found (Bell, _Phil. Mag._, 1887) that the angular measurements
present less difficulty than the comparison of the grating interval
with the standard metre. There is also some uncertainty as to the
actual temperature of the grating when in use. In order to minimize
the heating action of the light, it might be submitted to a
preliminary prismatic analysis before it reaches the slit of the
spectrometer, after the manner of Helmholtz.

In spite of the many improvements introduced by Rowland and of the care
with which his observations were made, recent workers have come to the
conclusion that errors of unexpected amount have crept into his
measurements of wave-lengths, and there is even a disposition to discard
the grating altogether for fundamental work in favour of the so-called
"interference methods," as developed by A. A. Michelson, and by C. Fabry
and J. B. Perot. The grating would in any case retain its utility fo