terrestrial objects; and I think that the only real advantage to be gained by the use of this material is from its transparency. I am not sure how far this advantage in the present state of glass manufacture will be actually realized. Rock-crystal is undoubtedly a most beautifully transparent substance, but so is the best modern glass; and when employing alternately the old and actually greenish, though I must say well-made, object-glass, and the new one compounded with rock-crystal on objects varying in distance from half-a-mile to ten and fifteen miles, I was unable to say that one showed more illumination than the other. It is true that in an erecting eye-piece there are four lenses, in this case all of glass, so that altogether the improvement is only one-sixth instead of fivesixths (because the flint-glass must always remain in the objectglass), of that due to the actual difference in transparency between crown-glass and quartz; but I own that I expected more. At the same time I do think that a small land telescope, say of 1 inch object-glass, like my own, with all the lenses in the eye-piece of quartz, would be perhaps an expensive but certainly a very perfect instrument1. Since I read this paper, Prof. Stokes has kindly drawn my attention to the complete table of the spectrum for quartz given by Rudberg in Poggendorf, 1828, vol. XIV. (and also in Miller's Mineralogy), as well as to a paper of his own on a kindred subject in the Proceedings of the R. S., 1877. If we combine Fraunhofer and Rudberg's results for the three substances we are discussing, viz. flint-glass, crown-glass and quartz, and compare them with those given by Brewster, we find that while the first two experts make the dispersive powers '068, 039, 032, the latter makes them 052 (about), 033, 026, from which it is clear that the dispersive ratios between the first and second and the first and third are about the same, whichever authority we follow; but that the radii of the surfaces of the lenses will be considerably affected by the use of quartz, e.g. if crown-glass is used, in a compound lens of 10 inches focal length, the focal length of the flint lens ought to be about 7·63 inches, and that of the crown-glass lens 4.33 inches; while the lens compounded with quartz will require a focal length of 10-8 inches for the flint-lens, and 5.2 inches for the lens actually cut from quartz the radii of the surfaces being correspondingly modified according to the table. I have also obtained a copy of M. Cauchoix's patent, dated Paris, July 7, 1828. In it he simply says that rock-crystal being 1 Herschel (New Edinb. Phil. Mag. vi. p. 367), stating the dispersive ratio of flint- and crown-glass to be 0.567, gives a table and rules for estimating the proper focal lengths of the crown and flint lenses for an achromatic object-glass of an assumed focal length of 10 inches. Fraunhofer's dispersive ratio is about 577 for the same substances. of a higher refractive index, and less dispersive than crown-glass, the substitution of the one for the other diminishes the focal length of the compound lens "when the curves of the flint lens are diminished,” i.e. when the radii are increased. This seems correct, allowing that it is prudent to diminish the focal length at all. He then proceeds by claiming as original a design to substitute for flint-glass a liquid oil enclosed in glass, which is obviously only a form of Prof. Barlow's invention, which I believe has been found impracticable. Thirdly, he proposes to use rock-crystal in eyepieces; we may say, an obvious inference from his first invention. It is clear from this short abstract of his Patent, that whatever his own method of working may have been, M. Cauchoix was offering to the public an ingenious invention rather than a scientific novelty. For the convenience of my readers I have reprinted Fraunhofer's and Rudberg's Indices for the three substances we have been considering. The dispersive powers I have given above; or they may easily be obtained by the formula = Мо - Мо where μ, Prof. Stokes informs me, may be safely taken between D and E, about one-third of the distance from D. SP. G. μΒ. MC. μD. μG. μH. 1-62775 1.62968 1.63504 1.64202 1.64826 1.66029 1.67106 μΕ. με. (2) On an altazimuth constructed from the designs of the late Rev. Dr W. Pearson. By A. FREEMAN, M.A. This instrument is described in Dr Pearson's Practical Astronomy, vol. II. pp. 464-468, and is figured in perspective on Plate XXIII. of that work. It is a portable instrument, inasmuch as it can be taken to pieces and packed in a box 311⁄2 inches long, 161 broad and 7 deep. It was specially designed by the late Rev. Dr Wm. Pearson, then Rector of South Kilworth, Leicestershire, and Treasurer of the Royal Astronomical Society, and was made in 1820 by Fayrer, one of Troughton's workmen. The telescope has an object-glass by Tulley with a clear aperture of 265 inches and a focal length of 43-4 inches: it is fitted with a direct and also with a diagonal eye-piece, and is excellent as regards defining power. The telescope is mounted so as to be capable of reversion in altitude and azimuth, the plane of the attached circle remaining vertical during the process. The axis of motion of the vertical circle can be adjusted and retained horizontal, when the axis of motion in azimuth has been adjusted to a vertical position: these adjustments are effected by means of the levels, one of which is fixed in the plane of the vertical circle, the other hangs on the axis of that circle, the extremity of this axis remote from the circle being adjustible by opposing screws to perpendicularity with the vertical axis of the instrument. The motion in azimuth results from the revolution of a hollow cone, about two feet long, about an upright axis having cylindrical bearings, and fitted securely to the tripod base. The chief peculiarity of the instrument is the bracket attached to the revolving cone and supported by a prop. This bracket and the horizontal solid axis which it bears form a counterpoise to the vertical circle and the telescope. The vertical circle is supplied with a three branch alidade which revolves about the horizontal axis to which this circle is rigidly fixed by strong radial bars. Each branch of the alidade bears a vernier read by a microscope applied successively to each. The reading of the verniers may also be effected after clamping the alidade to the circle by bringing each in succession opposite to a micro-telescope fitted to the frame of the instrument. The three branches of the alidade are moreover connected by a circular rim at right angles to the plane of the circle, and this rim can be clamped to the revolving cone of the azimuthal motion. The vertical circle can be clamped either to the revolving cone, or to the alidade. The telescope is capable of adjustment so that its line of collimation may be parallel, or may make a small fixed angle with the axis of the revolving cone, by means of a microscope fixed to that cone and viewing on its cross wires a small dot on a slightly adjustible piece of platinum borne by a short arm projecting from the tube of the telescope. This instrument, after the death of the designer, passed into the hands of a country gentleman, who sold it to the Rev. N. S. Godfrey, Vicar of St Bartholomew, Southsea, from whom I purchased it about Easter 1881. With the sanction of the Museums Syndicate I have added it by gift to the Plumian Professor's collection of apparatus, having found it to be a very useful example of a well graduated and adjustible altazimuth telescope, or zenith instrument. The vertical circle is graduated to every 5' of arc and is read by three verniers to every 5", its radins is about 8 inches. The horizontal circle is graduated to every 10' of arc and is read by two verniers to every 10", its radius is about 6 inches. I have determined the errors of excentricity of both alidades in magnitude and direction, as also the angles between their arms by discussion of the readings of each circle in three or more positions, representing each reading in the form given in Chauvenet's Astronomy, vol. II. § 27. 33 These errors are small. The magnitudes of the errors of excentricity are 8"-487 for the vertical circle, and 14"046 for the horizontal circle, estimated in arcs of the respective graduated circles, equivalent respectively to 100 and 100 of an inch. It is unnecessary to state the direction of the error, since if all the verniers be read, the means of the readings in two different positions of the instrument determine without error the angles through which the circles have been turned from the one position to the other. The value of a scale-division of the striding-level is 1"12, that of a scale-division of the attached-level is 2" 54. In the focus of the object-glass is a frame containing one horizontal and five vertical threads. The intervals of the vertical threads were determined by collimating each in succession on the image of the fixed cross-wires of an opposed auxiliary telescope, noting for each coincidence the readings of one of the verniers of the horizontal circle of the instrument. The intervals being small, it was unnecessary to read both verniers. In succession from the apparent left of the field of view, i.e. from the side nearest the revolving cone of the instrument, the intervals were 6′ 40′′, 5′ 40′′, 6′ 30′′, 6′ 30′′. These threads therefore have been very improperly placed by the opticians (Troughton and Simms) whom I employed for that purpose. The original threads were removed by Mr Godfrey. Inequality of intervals might however usefully remove doubts as the position of the instrument when it was employed, whether to the right or to the left of its axis. The magnifying powers of the eye-pieces are only moderate. The illumination of the field of view is capable of improve ment. A cylindrical zinc cover has recently been made, in two parts fitting each other, so as to protect the instrument from weather, when adjusted on a stone base provided for it on the isolated wall of the Plumian Professor's Observatory. May 15, 1882. Mr F. M. BALFOUR, PRESIDENT, IN THE CHAIR. The President announced that the adjudicators for the Hopkins Prize for the period 1871-73 had awarded the prize to Lord Rayleigh for his various important papers connected with the Theory of Vibrations, and particularly for his paper on the Theory of Resonance. The following communications were made to the Society: (1) On the measurements of a bead of platinum, by the late Professor W. H. Miller. By Professor W. J. LEWIS. [Introduction. Some time ago Mrs Miller entrusted to me the following work of the late Professor Miller, with a statement that he was at work on it at the period when his health finally broke down. The actual measurements were, I believe, all made during the autumn of 1874, and I remember Prof. Miller showing me the arrangement of the goniometers when I came to study with him in September of that year. There is no note of the exact manner in which the upper goniometer was fixed and adjusted. If the method be again resorted to, the neatest way of arranging the goniometers would be to clamp to the horizontal |