If monochromatic light be viewed with such an instrument a series of bright lines — sharp maxima — each an image of the slit will be seen distributed on each side of the central image. The image nearest the central one is said to be of the °first order,)) the next of the "second order,)) etc. The properties of these images and of diffraction spectra, in general, are most briefly described by the following three equa tions, which follow directly from the wave the ory of light (a+ b) (sin i + sin 0)--tts a . . . (Eq. A).
Here a + b is the distance between corre sponding points on two consecutive rulings —the so-called grating constant. The angle of incidence is denoted by i; the angle of diffrac tion by 0; the order of the spectrum by m and the wave-length by A. This equation tells us exactly in what position, 0, we must set the view-telescope in order to observe a line of any given wave-length. Conversely it enables us to compute the wave-length when once we know the grating constant and the directions of the incident and diffracted rays.
b) 2 . p(ah) ' (Eq. B).
2 Here I is the intensity of the spectrum of a monchromatic source of wave-length a in any given direction, produced by a grating which has n lines ruled upon it at a uniform distance, a + b, apart.
I' is the intensity which a single aperture would give in the same direction. The "given direction)) is here defined by fe whose value is 27r .
t + sin e) the symbols having the same- meaning as in Eq. A.
It is important here to observe that Eq. A. merely defines the direction in which I of Eq. B reaches its principal maxima.
Lord Rayleigh has shown that the resolving power of a grating, R, is defined by the follow ing simple expression: R = = mN . (Eq. C) where N is the total number of rulings on the grating and m is the order of spectrum em ployed.
All of the best gratings of the world up to the present time have been ruled on Rowland's dividing engines at Johns Hopkins University. After Rowland's death, in 1901, his two ruling engines were not again used until Dr. J. A. Anderson took up this work in 1910. Most of these gratings are ruled with from 5,000 to 20,000 lines per inch; some of them have a ruled surface six inches in width, thus giving a re solving power of no less than 400,000 in the fourth-order spectrum. Such a resolving power is far in excess of anything attainable with prisms of practicable size. Dr. J. A. Anderson,
and others, have recently devoted much atten tion to the problem of securing replicas, or reproductions, of the expensive Rowland grat ings. The attempts thus far are full of prom ise, and if they become wholly successful it will be possible for the physicist and astronomer to secure this fundamentally important part of his apparatus at a cost which will be com paratively only a nominal one.
Concave Grating Recent advances in spectroscopy are due in a very large degree to the invention of the concave grating by Rowland in 1883. The distinguishing feat ures of this instrument are that it requires no collimator and no view-telescope, and that it gives spectra which are normal throughout a large range. The ruling is upon a concave spherical mirror of speculum metal, the dis tance between the lines being equal when meas ured along a chord. It was with a spectograph of this type that Rowland and Higgs each pre pared his superb atlas of the solar spectrum. The same kind of grating was also employed by Kayser and Runge in their profound study of the spectra of the elements.
The Echelon Spectroscope.— Measured by resolving power, the Echelon, devised by Mi chelson in 1898, is still a more effective instru ment. This is essentially a grating with only a few rulings in which the form of the groove is under perfect control. This result is ob tained by using a pile of plane parallel plates of equal thickness, the edge of each plate being slightly displaced over that of its preceding neighbor. The high resolving power is ob tained by use of spectra of high orders, even as high as several thousand. The Echelon is especially adapted to the separation of the close components of a spectral line, as in the case of the Zeeman effect.
The Interferometer.— Another device for separating the close compound of what is or dinarily called a single spectral line is the interferometer, which is also largely due to Michelson. It is this invention which makes it possible to use the wave-length of the red cad mium ray as a standard of length instead of the international metre at Paris; for Michelson has shown that by the interferometer he can meas ure wave-lengths with an accuracy of one part in a million.