acted on by the magnet were scrupulously withdrawn. 25 grains of this pure ore being subjected to analysis, I obtained the following constituents : If we exclude the unknown salt, which I have called white matter, we see that the ore is a compound of 2 atoms green oxide of chrome 1 atom peroxide of iron 1 atom alumina 10 5 The very slight excess of iron and alumina, together with the trace of silica, were probably derived from some small green particles (obviously the gangue of the ore), which I could detect with a glass in the portion of the picked ore that had not been pounded. It is more than likely that one or two of them had got mixed with the pounded ore. From the analysis of the Shetland ore, in the table, it seems to follow, that it contains no admixture of octahedral iron ore; for in it alone the green oxide of chromium, and the per oxide of iron, bear to each other the ratio of 2 to 1. All the other specimens subjected to analysis have been contaminated with iron ore. APPENDIX. Since the preceding paper was drawn up, I have found that when green oxide of chromium is precipitated by a fixed alkaline carbonate, we cannot free it from the fixed alkali by washing. This probably occasioned the want of success which attended some of the experiments related in the second section of the paper. XV. Rules and principles for determining the dispersive ratio of glass; and for computing the radii of curvature for achromatic object-glasses, submitted to the test of experiment. By PETER BARLOW, Esq. F. R. S. Mem. Imp. Ac. Petrop. &c. Read May 3, 1827. 1. Ir is very remarkable, since the achromatic telescope is altogether of English origin, that in no one of our separate optical treatises are to be found specific rules for its construction, fitted for the use of practical opticians. Some essays of this kind have indeed been attempted; the first of which is found in MARTIN'S "New Elements of Optics," published in 1751; but the principle there adopted is erroneous, and of course the deductions, although possessing a great appearance of simplicity, are wholly useless. Under the article Telescope, in the Encyclopædia Britannica, is another essay of this kind, which is correct in principle, but far from possessing the degree of simplicity which is desirable for practical purposes. Under the like article in Rees's Cyclopædia is a treatise on the same subject, which may be considered wholly practical; it is founded however upon MARTIN's method, but corrected by an empyrical multiplier, which answers remarkably well in many instances, but is erroneous in all extraordinary cases. Lastly, an elaborate and highly scientific investigation relative to these constructions was published by Mr. Herschel, in the Phil. Trans. for 1821, to which I shall refer more at length in a subsequent page. These, I believe, constitute every attempt that has been made in this country to bring the strict laws of optics, applicable to these cases, within the reach of numerical calculation.* More numerous attempts have been made by foreign mathematicians; but as far as my knowledge of them extends, they have in no instance been attended with the success that might have been expected from the deservedly high reputation of their authors. I have spoken above principally of the methods of determining the radii of curvature of the lenses; but in order to enter upon this calculation, certain data are necessary, which require previous experiments and tedious numerical computations; so that upon the whole, to take two specimens of glass of unknown indices and dispersions, to form an object glass of them, free from colour and spherical aberration, requires very formidable calculations, involving in them, according to the best methods yet employed, certain principles and operations which we ought hardly to expect practical opticians to be masters of. At all events, every simplification that can be thrown into experiments and calculations of this kind must be desirable; and, I am greatly in hopes it will be found that I have, in the following pages, contributed * Since this Paper was written, Mr. HERSCHEL has also published in the Encyclopædia Metropolitana, under the article LIGHT, a still more extended investigation relative to this and other optical subjects; to which article it will likewise be necessary for me to refer as we proceed; and if, after all, any reference should be omitted which ought to be made, it must be attributed to this Paper having been written before the publication of the former. a little towards this object. Probably, also, the immediate comparison of the computed results, with experiments on a large scale, will add a value to this Paper, which it might not otherwise have been thought to possess, and for which I am indebted to Messrs. W. and T. GILBERT, who very liberally engaged to submit to the test of experiments any theoretical deductions I might be led to in an investigation of these subjects. On the determination of the index of refraction. 2. The following method of determining the index of refraction, by means of a lens, is not given as new; it has, on the contrary, been long practised; but as it forms the foundation of the method for determining the dispersive ratio, and will occupy but a few lines, I shall be excused for introducing it into this Paper. It is simply this :-since by knowing the radii of curvature of a lens, and its index of refraction, we may compute the focal length; so conversely, by knowing the radii and measuring the focal length, we may compute the index of refraction. The method which we employed for measuring the focal length of a lens, was as follows: a tube about 2 inches in diameter, and which exactly measured 10 inches from the back of the lens to its other extremity, was fitted with a draw tube of the same length, graduated to inches and tenths, and which, by means of a vernier, might be read to the hundredth of an inch. This was fitted with a positive eye-piece, which was adjustable to bring the cross wires exactly into its focus, and the graduations above-named commenced from this MDCCCXXVII. Hh |