+Diffraction Grating.+--The best method of measuring the wave-lengths of heat and light is by means of the "Diffraction Grating." This consists essentially of a large number of fine parallel equidistant slits placed very close to one another. For the measurement of the wave-lengths of light and of the shorter heat waves, it is usually produced by ruling a large number of very fine close equidistant lines on a piece of glass or on a polished mirror by means of a diamond point. The ruled lines are opaque on the glass and do not reflect on the mirror, and consequently the spaces in between act as slits. {73} +Rowland's Gratings.+--The ruling of these gratings is a very difficult and tedious business, but the difficulties have been surmounted in a very remarkable manner by Rowland, so that the gratings ruled on his machine have become standard instruments throughout the world. He succeeded in ruling gratings 6 inches in diameter with 14,000 lines to the inch, truly a remarkable performance when we remember that if the diamond point develops the slightest chip in the process, the whole grating is spoilt. [Illustration: FIG. 25.] The action of the grating can be made clear by means of Fig. 25. Let A, B, C, D represent the {74} equidistant slits in a grating, and let the straight lines to the left of the grating represent at any instant the crests of some simple plane waves coming up to the grating. The small fractions of the original waves emerging from the slits A, B, C, D will spread out from the slits so that the crests of the small wavelets may at any instant be represented by a series of concentric circles, starting from each slit as centre. The series of crests from each slit are represented in the figure. Now notice that a line PQ parallel to the original waves lies on one of the crests from each slit, and therefore the wavelets will make up a plane wave parallel to the original wave. This may therefore be brought to a focus by means of a convex lens just as if the grating were removed, except that the intensity of the wave is less. But a line, LM, also lies on a series of crests, the crest from A being one wave-length behind that from B, the one from B a wave-length behind that from C, and so on. The wavelets will therefore form a plane wave LM, which will move in the direction perpendicular to itself (_i.e._ the direction DK) and may be brought to a focus in that direction by means of a lens. Draw CH and DK perpendicular to LM, and draw CE perpendicular to DK, _i.e._ parallel to LM. The difference between CH and DK is evidently one wave-length, _i.e._ DE is one wave-length. If [Greek: alpha] is the angle between the direction of PQ and LM, DE is evidently equal to CD sin [Greek: alpha] and therefore one wave-length=CD sin [Greek: alpha]. From the ruling of the grating we know the value {75} of CD, and therefore by measuring [Greek: alpha] we can calculate the wave-length.