AN AUTOCOLLIMATING MOUNTING FOR A CONCAVE GRATING. BY HORACE CLARK RICHARDS. (Read April 20, 1912.) "For most spectroscopic problems Rowland's concave grating is an almost ideal aid," says W. Voigt in a recent article.1 Its focal property enables us to dispense with lenses or mirrors, and so avoid. the accompanying aberration, absorption and scattering of the light, and when once it is adjusted it is in focus for all orders of spectra. The usual form of mounting, however, is perhaps not quite so ideal. A large, perfectly dark room is required, the apparatus is heavy and cumbersome, or else lacking in rigidity, and what is still more important in some kinds of work, the position and direction of the emergent light change with each change of wave-length. Moreover it is not readily adapted to astronomical purposes. The theory of the Rowland mounting is well known. If the source is placed at any point of the circumference of a circle constructed on the radius of the grating as a diameter, in the plane perpendicular to the ruling, the spectra will all be brought to a focus at points on the same circle. Of these spectra Rowland selected that which was at the center of curvature of the grating as giving a normal spectrum of constant scale. The necessary conditions were insured by placing the slit at the angle of a rectangular track, along the two arms of which moved the grating and the camera or eyepiece, the two rigidly connected by a rod of the proper length (Fig. 1). It is easily seen that while the source is fixed, the image is displaced in passing through the spectrum. To avoid this objection, Lewis2 interchanged the slit and camera, and Abney3 fixed the position of the grating and camera and 'W. Voigt, Phys. Zeits., 13, 217 (1912). 3 'E. P. Lewis, Astrophys. Jour., 2, 1 (1895). W. de W. Abney, Phil. Trans., 177, II., 457 (1886). mounted the slit on an arm pivoted at the center of the line joining them (Fig. 2). These methods however require the source of light to be movable, which is usually undesirable and in some cases impracticable. Wadsworth suggested several arrangements to overcome the difficulty, using auxiliary mirrors and more or less complicated mechanism, but these involve additional adjustments and loss of light. It may be added that the grating has also been used FIG. I. S with parallel light in astronomical work, but the aberration is much greater than with Rowland's mounting." The method here discussed is briefly that of autocollimation. That part of the light is used which after being diffracted is returned toward the slit. If therefore the slit is on Rowland's circle, the spectrum will be formed on the same circle and one point of it will coincide with the slit (Fig. 3). The ingoing and outcoming beams may be separated when necessary by the usual reflecting prism, or by slightly tilting the grating. Thus a double slit may be F. L. O. Wadsworth, Astrophys. Jour., 2, 370 (1895). used, the light being sent through one slit and returned through the other. The wave-length of the light which is returned through the slit is given by the formula. where e is the distance between consecutive rulings, the angle made by the light with the grating-normal, and m the order of the spectrum. It follows that at a given angle the order is twice that which is produced at the center of curvature. FIG. 2. The principle of autocollimation has been often used with prism spectroscopes since it was first suggested by Duboscq" and Littrow." It was first used with a plane grating by Liveing and Dewar, and is employed in many recent grating spectroscopes. It has however, as far as I know, not been used with the concave grating, although one of the chief objections to this form of mounting-the reflec 6 See H. Kayser, "Handbuch der Spectroscopie," I., 511. 'O. v. Littrow, Wien. Ber., 47, II., 26 (1863). G. D. Liveing and J. Dewar, Cambridge Proc., 4, 336 (1883). tion from the inner surface of the collimating objective-would be done away with. Perhaps the reason lies partly in the fact that the focal length changes in passing through the spectra, so that not only the inclination of the grating but also its distance from the slit must be altered, and in addition the focal plane is inclined to the direction of the light by an angle which varies with the setting. Thus in Fig. 3 the normals to the grating and to the spectrum make O Ꮗ FIG. 3. the same angle with the light, and the distance GS between grating and slit is p cos p, where p is the radius of the grating. As the inclination of the grating is altered, that of the spectrum must be altered by an equal amount, and the distance GS properly changed." 9 Since writing the above my attention has been called to an article by A. Eagle (Astrophys. Jour., 31, 120, 1910) describing an autocollimating mounting for a concave grating. The mounting has the disadvantages mentioned, namely that the distance of the grating and inclination of the camera must be separately adjusted for each angle of incidence; disadvantages which it is sought to overcome in the mounting described in this paper. The advantages of the autocollimating mounting are discussed at length by Mr. Eagle with conclusions similar to those given here. These adjustments however may be automatically made in the following manner. As in Rowland's mounting, let the slit be fixed. at S (Fig. 3) and the grating be capable of sliding along the line GS and also of rotating about a vertical axis passing through its center. Now if two equal horizontal arms of length p/2 be pivoted at G and S respectively and hinged together at their other ends at O, and the arm OG be attached to the grating holder so as to be parallel to the grating-normal, the grating will keep the proper inclination as it slides along GS, for G and S are constrained to remain on the Rowland circle. This is in fact exactly equivalent to one half of a Rowland mounting. Moreover, if the camera is mounted to rotate about a vertical axis through S, and the arm OS is similarly attached normally to the photographic plate, the plate, if bent as usual into the arc of the proper circle, will continue to fit this circle throughout its motion and the spectrum will be in focus on all parts. In practice the arms OG and OS would be excessively long and inconvenient, and would tend to bend the vertical axes at G and S. They could of course be balanced by a pair of similar arms on the other side, but the apparatus would then be still more cumbersome. The same effect may however be attained by a series of links of the "lazy-tongs" pattern, the total length when open being equal to the radius of the grating (Fig. 4). The first and last link on one side will correspond in direction to the arms OG and OS, and these are fixed normal to the grating and plate respectively. It is obvious that as either side may be used, all of the grating spectra become available. A wooden model of the apparatus has been constructed for use with a six-foot grating, which exhibits the proposed arrangement and which in spite of its crudity renders excellent service. A more efficient mount is in process of construction. Sliding along a horizontal track is a block carrying a vertical pin on which as an axis turn the ends of the link motion and the platform for the grating. This latter may be clamped in any position to either of the adjacent link bars. At one end of the track is a fixed block with a similar vertical axis. This axis carries the other end of the linkage, a |