corresponds to the dispersive power; while on the other hand terborate of lead, which in dispersive power nearly agrees with flint glass, lies decidedly nearer to crown than to flint in point of irrationality. By the use of such glasses it would be possible to destroy the secondary dispersion in an object-glass. Terborate of lead is slightly yellow, is too soft to be easily worked to a correct form, and is rather liable to tarnish, though the last defect does not much signify when the terborate is used for the middle lens of a triple, of which the adjacent surfaces fit each other and are cemented. The most promising combination, however, appeared to be a titanic glass in lieu of crown, achromatized by a light flint. In consequence of the elevation of dispersive power produced by the introduction of titanic acid, the curvature would be rather severe if the objective were constructed of only two lenses; but by making the objective a triple, the convex lens being replaced by two convex lenses placed first and third, the curvatures to be encountered would be no greater than in an ordinary double. ON THE IMPROVEMENT OF THE SPECTROSCOPE. BY THOMAS GRUBB, F.R.S. Note appended by Prof. STOKES. [From the Proceedings of the Royal Society, XXII, April 30, 1874, p. 309.] IF a ray of light be refracted in any manner through any number of prisms arranged as in a spectroscope, undergoing, it may be, any number of intermediate reflections at surfaces parallel to the common direction of the edges of the prisms-or, more generally, if a ray be thus refracted or reflected at the surfaces of any number of media bounded by cylindrical surfaces in the most general sense (including, of course, plane as a particular case), the generating lines of which are parallel, and for brevity's sake will be supposed vertical, and if a be the altitude of the ray in air, a', a'', . . ., its altitudes in the media of which the refractive indices are μ', μ”,......., then (1) The successive altitudes will be determined by the equations just as if the ray passed through a set of parallel plates. (2) The course of the horizontal projection of the ray will be the same as would be that of an actual ray passing through a set μ'cos a' μ" cos a" of media of refractive indices instead of μ, μ",.... As a <a, the fictitious index is greater than the actual, and therefore the deviation of the projection is increased by obliquity. These two propositions, belonging to common optics, place the justice of Mr Grubb's conclusions in a clear light*. [* Namely, that the curvature of the lines, when the slit is straight, is a function of (in fact proportional to) the dispersion. For developments, cf. Lord Rayleigh, Phil. Mag. vIII, 1879, Scientific Papers, 1, p. 542, and Larmor, Proc. Camb. Phil. Soc. vII, 1890, p. 85.] ON THE CONSTRUCTION OF A PERFECTLY ACHROMATIC TELESCOPE. [From the Report of the British Association for the Advancement Ar the Meeting of the Association at Edinburgh in 1871, it was stated that it was in contemplation actually to construct a telescope, by means of disks of glass prepared by the late Mr Vernon Harcourt, which should be achromatic as to secondary as well as primary dispersion. This intention was subsequently carried out, and the telescope, which was constructed by Mr Howard Grubb, was now exhibited to the Section. The original intention was to construct the objective of a phosphatic glass containing a suitable percentage of titanic acid, achromatized by a glass of terborate of lead*. As the curvature of the convex lens would be rather severe if the whole convex power were thrown into a single lens, it was intended to use two lenses of this glass, one in front and one behind, with the concave terborate of lead placed between them. It was found that, provided not more than about of the convex power were thrown behind, the adjacent surfaces might be made to fit, consistently with the condition of destroying the spherical as well as the chromatic aberration. This would render it possible to cement the glasses, and thereby protect the terborate, which was rather liable to tarnish. At the time of Mr Harcourt's death, two disks of the titanic. glass had been prepared, which it was hoped would be good enough for employment, as also two disks of terborate. These were placed in Mr Grubb's hands. On polishing, one of the titanic disks was found to be too badly striated to be employed; the other was pretty fair. As it would have required a rather * The percentage of titanic acid was so chosen that there should be no irrationality of dispersion between the titanic glass and the terborate. THE CONSTRUCTION OF A PERFECTLY ACHROMATIC TELESCOPE. 357 6 severe curvature of the first surface, and an unusual convexity of the last, to throw the whole convex power into the first lens, using a mere shell of crown glass behind to protect the terborate, Prof. Stokes thought it more prudent to throw about of the whole convex power into the third or crown-glass lens, though at the sacrifice of an absolute destruction of secondary dispersion, which by this change from the original design might be expected to be just barely perceptible. Of the terborate disks, the less striated happened to be slightly muddy, from some accident in the preparation; but as this signified less than the striæ, Mr Grubb deemed it better to employ this disk. The telescope exhibited to the Meeting was of about 2 inches aperture and 21 inches focal length, and was provided with an objective of the ordinary kind, by which the other could be replaced, for contrasting the performance. When the telescope was turned on to a chimney seen against the sky or other suitable object, and half the object-glass covered by a screen with its edge parallel to the edges of the object, in the case of the ordinary objective vivid green and purple were seen about the two edges, whereas with the Harcourt objective there was barely any perceptible colour. It was not, of course, to be expected that the performance of the telescope should be good, on account of the difficulty of preparing glass free from striæ, but it was quite sufficient to show the possibility of destroying the secondary colour, which was the object of the construction. ON THE OPTICAL PROPERTIES OF A TITANO-SILICIC GLASS. [From the Report of the British Association for the Advancement of Science, Bristol, 1875.] AT the Meeting of the Association at Edinburgh in 1871, Professor Stokes gave a preliminary account of a long series of researches in which the late Mr Vernon Harcourt had been engaged on the optical properties of glasses of a great variety of composition, and in which, since 1862, Professor Stokes had cooperated with him*. One object of the research was to obtain, if possible, two glasses which should achromatize each other without leaving a secondary spectrum, or a glass which should form with two others a triple combination, an objective composed of which should be free from defects of irrationality, without requiring undue curvature in the individual lenses. Among phosphatic glasses, the series in which Mr Harcourt's experiments were for the most part carried on, the best solution of this problem was offered by glasses in which a portion of the phosphoric was replaced by titanic acid. It was found, in fact, that the substitution of titanic for phosphoric acid, while raising, it is true, the dispersive power, at the same time produces a separation of the colours at the blue as compared with that at the red end of the spectrum, which ordinarily belongs only to glasses of a much higher dispersive power. A telescope made of disks of glass prepared by Mr Harcourt was, after his death, constructed for Mrs Harcourt by Mr Howard Grubb, and was exhibited to the Mathematical Section at the late Meeting in Belfast. This telescope, which is briefly described in the 'Report't, was found fully to answer the expectations that had been formed of it as to destruction of secondary dispersion. Several considerations seemed to make it probable that the substitution of titanic acid for a portion of the silica in an ordinary crown glass would have an effect similar to what had * Report for 1871. Transactions of the Sections, p. 38 [supra, p. 339]. |