for Optical Purposes. 205 
still so nearly normal as to have its error neglected for most 
purposes. 
It is also to be noted that this theorem of the normal spectrum 
applies also to the flat grating used with telescopes, and to 
either reflecting or transmitting gratings ; but in these cases 
only a small portion of the spectrum can be used, as no lens 
can be made perfectly achromatic. And so, as the distance of 
the micrometer has constantly to be changed when one passes 
along the spectrum, its constant does not remain constant but 
varies in an irregular manner. But it would be possible to 
fix the grating, one objective, and the camera rigidly on a 
bar, and then focus by moving the slit or then other objective. 
In this case the spectrum would be normal, but would pro- 
bably be in focus for only a small length only, and the adjust- 
ment of the focus would not be automatic. 
Another important property of the concave grating is that 
all the superimposed spectra are in focus at the same point, 
and so by micrometric measurements the relative wave-lengths 
are readily determined. Hence, knowing the absolute wave- 
length of one line, the whole spectrum can be measured. 
Prof. Peirce has determined the absolute wave-length of one 
line with great care; and I am now measuring the coinci- 
dences. This method is greatly more accurate than any 
hitherto known, as by mere eye-inspection the relative wave- 
length can often be judged to one part in twenty thousand, 
and with a micrometer to 1 in 1,000,000. Again, in dealing 
with the invisible portion of the spectrum, the focus can be 
obtained by examining the superimposed spectrum. Capt. 
Abney, by using a concave mirror in the place of telescopes, 
has been enabled to use this method for obtaining the focus 
in photographing the ultra-red rays of the spectrum. 
But nothing can exceed the beauty and simplicity of the 
concave grating when mounted on a movable bar such as I 
have described and illustrated in fig. 1. Having selected the 
grating which we wish to use, we mount it in its plate-holder 
and put the proper collimating eyepiece in place. We then 
carefully adjust the focus by altering the length of p until 
the cross-hairs are at the exact centre of curvature of the 
grating. On moving the bar the whole series of spectra are 
then in exact focus, and the value of a division of the micro- 
meter is a known quantity for that particular grating. The 
wooden way, A C, on which the carriage moves is gradu- 
ated to equal divisions representing wave-lengths, since the 
wave-length is proportional to the distance A C. We can 
thus set the instrument to any particular wave-length we 
may wish to study, or even determine the wave-length to 
