for nearly forty years a favourite subject of study with the late Mr. Harcourt. Having commenced in 1834 some experiments on vitrifaction, with the object stated in the title of this notice, he was encouraged by a recommendation, which is printed in the 4th volume of the Transactions of the British Association, to pursue the subject further. A report on a gas-furnace, the construction of which formed a preliminary inquiry, in which was expended the pecuniary grant made by the Association for this research in 1836, is printed in the Report of the Association for 1844, but the results of the actual experiments on glass have never yet been published. My own connexion with these researches commenced at the Meeting of the British Association at Cambridge in 1862, when Mr. Harcourt placed in my hands some prisms formed of the glasses which he had prepared, to enable me to determine their character as to fluorescence, which was of interest from the circumstance that the composition of the glasses was known. I was led indirectly to observe the fixed lines of the spectra formed by means of them; and as I used sunlight, which he had not found it convenient to employ, I was enabled to see further into the red and violet than he had done, which was favourable to a more accurate measure of the dispersive powers. This inquiry, being in furtherance of the original object of the experiments, seemed far more important than that as to fluorescence, and caused Mr. Harcourt to resume his experiments with the liveliest interest, an interest which he kept up to the last. Indeed it was only a few days before his death that his last experiment was made. To show the extent of the research, I may mention that as many as 166 masses of glass were formed and cut into prisms, each mass doubtless in many cases involving several preliminary experiments, besides disks and masses for other purposes. Perhaps I may be permitted here to refer to what I said to this Section on a former occasion as to the advantage of working in concert. I may certainly say for myself, and I think it will not be deemed at all derogatory to the memory of my esteemed friend and fellow-labourer if I say of him, that I do not think that either of us working singly could have obtained the results we arrived at by working together. It is well known how difficult it is, especially on a small scale, to prepare homogeneous glass. Of the first group of prisms, 28 in number, 10 only were sufficiently good to show a few of the principal dark lines of the solar spectrum; the rest had to be examined by the bright lines in artificial sources of light. These prisms appeared to have been cut at random by the optician from the mass of glass supplied to him. Theory and observation alike showed that striæ interfere comparatively little with an accurate determination of refractive indices when they lie in planes perpendicular to the edge of the prism. Accordingly the prisms used in the rest of the research were formed from the glass mass that came out of the crucible by cutting two planes, passing through the same horizontal line a little below the surface, and inclined 2230 right and left of the vertical, and by polishing the enclosed wedge of 45°. In the central portion of the mass the stria have a tendency to arrange themselves in nearly vertical lines, from the operation of currents of convection; and by cutting in the manner described, the most favourable direction of the striae is secured for a good part of the prism. This attention to the direction of cutting, combined no doubt with increased experience in the manufacture of glass, was attended with such good results that now it was quite the exception for a prism not to show the more conspicuous dark lines. On account of the inconvenience of working with silicates, arising from the difficulty of fusion and the pasty character of the fused glasses, Mr. Harcourt's experiments were chiefly carried on with phosphates, combined in many cases with fluorides, and sometimes with borates, tungstates, molybdates, or titanates. The glasses formed involved the elements potassium, sodium, lithium, barium, strontium, calcium, glucinum, magnesium, aluminium, manganese, zinc, cadmium, tin, lead, thallium, bismuth, antimony, arsenic, tungsten, molybdenum, titanium, vanadium, nickel, chromium, uranium, phosphorus, fluorine, boron, sulphur. A very interesting subject of inquiry presented itself collaterally with the original object, namely, to inquire whether glasses could be found which would * Report of the British Association for 1862, Trans. of Sect. p. 1. achromatize each other so as to exhibit no secondary spectrum, or a single glass which would achromatize in that manner a combination of crown and flint. This inquiry presented considerable difficulties. The dispersion of a medium is small compared with its refraction; and if the dispersive power be regarded as a small quantity of the first order, the irrationality between two media must be regarded as depending on small quantities of the second order. If striæ and imperfections of the kind present an obstacle to a very accurate determination of dispersive power, it will readily be understood that the errors of observation which they occasion go far to swallow up the small quantities on the observation of which the determination of irrationality depends. Accordingly, little success attended the attempts to draw conclusions as to irrationality from the direct observation of refractive indices; but by a particular method of compensation, in which the experimental prism was achromatized by prism built up of slender prisms of crown and flint, I was enabled to draw trustworthy conclusions as to the character in this respect of those prisms which were sufficiently good to show a few of the principal dark lines of the solar spectrum. Theoretically any three different kinds of glass may be made to form a combination achromatic as to secondary as well as primary colour, but practically the character of dispersion is usually connected with its amount, in such a manner that the determinant of the system of three simple equations which must be satisfied is very small, and the curvatures of the three lenses required to form an achromatic combination are very great. For a long time little hope of a practical solution of the problem seemed to present itself, in consequence of the general prevalence of the approximate law referred to above. A prism containing molybdic acid was the first to give fair hopes of success. Mr. Harcourt warmly entered into this subject, and prosecuted his experiments with unwearied zeal. The earlier molybdic glasses prepared were many of them rather deeply coloured, and most of them of a perishable nature. At last, after numerous experiments, molybdic glasses were obtained pretty free from colour and permanent. Titanium had not yet been tried, and about this time a glass containing titanic acid was prepared and cut into a prism. Titanic acid proved to be equal or superior to molybdic in its power of extending the blue end of the spectrum more than corresponds to the dispersive power of the glass; while in every other respect (freedom from colour, permanence of the glass, greater abundance of the element) it had a decided advantage; and a great variety of titanic glasses were prepared, cut into prisms, and measured. One of these led to the suspicion that boracic acid had an opposite effect, to test which Mr. Harcourt formed some simple borates of lead, with varying proportions of boracic acid. These fully bore out the expectation; the terborate for instance, which in dispersive power nearly agrees with flint glass, agrees on the other hand, in the relative extension of the blue and red ends of the spectrum, with a combination of about one part, by volume, of flint glass with two of crown. By combining a negative or concave lens of terborate of lead with positive lenses of crown and flint, or else a positive lens of titanic glass with negative lenses of crown and flint, or even with a negative of very low flint and a positive of crown, achromatic triple combinations free from secondary colour may be formed without encountering (at least in the case of the titanic glass) formidable curvatures; and by substituting at the same time a titanic glass for crown, and a borate of lead for flint, the curvatures may be a little further reduced. There is no advantage in using three different kinds of glass rather than two to form a fully achromatic combination, except that the latter course might require the two kinds of glass to be made expressly, whereas with three we may employ for two the crown and flint of commerce. Enough titanium might, however, be introduced into a glass to render it capable of being perfectly achromatized by Chance's "light flint." In a triple objective the middle lens may be made to fit both the others, and be cemented. Terborate of lead, which is somewhat liable to tarnish, might thus be protected by being placed in the middle. Even if two kinds only of glass are used, it is desirable to divide the convex lens into two, for the sake of diminishing the curvatures. On calculating the curvatures so as to destroy spherical as well as chromatic aberration, and at the same time to make the adjacent surfaces fit, very suitable forms were obtained with the data furnished by Mr. Harcourt's glasses. After encountering great difficulties from striæ, Mr. Harcourt at last succeeded in preparing disks of terborate of lead and of a titanic glass which are fairly homogeneous, and with which it is intended to attempt the construction of an actual objective which shall give images free from secondary colour, or nearly so. This notice has extended to a greater length than I had intended, but it still gives only a meagre account of a research extending over so many years. It is my intention to draw up a full account for presentation to the scientific world in some other form. I have already said that the grant made to Mr. Harcourt for these researches in 1836 has long since been expended, as was stated in his Report of 1844; but it was his wish, in recognition of that grant, that the first mention of the results he obtained should be made to the British Association; and I doubt not that the members will receive with satisfaction this mark of consideration, which they will connect with the memory of one to whom the Association as a body is so deeply indebted. On one Cause of Transparency. By G. JOHNSTONE STONEY, M.A., F.R.S. The motion of the æther which constitutes light is known to be subject to four restrictions:-First, it is periodic; secondly, it is transversal; thirdly, it is (at all events temporarily) polarized; and, fourthly, its periodic time lies between the limits which correspond to the extent of the visible spectrum. By temporary polarization is meant the persistence of the same kind of wave over a long series of waves before waves of another kind succeed, that persistence which the phenomena of diffraction have made known to us*. And the many respects in which radiant heat and light have been found to be identical enable us to say that the first three of the foregoing restrictions apply to radiant heat. We also know (see Philosophical Magazine' for April and for July 1871) that the lines in the spectra of gases arise from periodic motions in the molecules of the gas, each such motion giving rise to one or more lines corresponding to terms of an harmonic series. And we know that under certain conditions these lines dilate and run into one another, so as in many cases to produce regions of continuous absorption. All these phenomena may safely be attributed to periodic motions in the molecules of the gas, the dilatation of the lines being due to perturbations which affect the periodic times. After the periodic time has been disturbed (probably on the occasion of the collisions between molecules) it seems to settle down gradually towards its normal amount, thus imparting breadth to the corresponding spectral lines. The question now naturally presents itself What results from motions in the molecules which are not periodic, or which are in any other way unfitted to produce radiant heat? And here the phenomena of acoustics come to our aid. When a bell is struck, more or less regularly, periodic motions are both produced. The more regularly periodic motions produce the tone of the bell which is heard at a distance, while the less regular motions, though they are often very intense, produce a clang heard only in the vicinity of the bell; in other words, the energy is expended in the neighbourhood of the bell. Similarly, if the molecules of a body are engaged in irregular motions, such motions, though they may occasion a violent agitation of the others, are mechanically incapable of producing such an undulation as constitutes radiant heat. The disturbance is necessarily local; in other words, as much energy is restored by the moving æther to the molecules as is imparted by the motion of the molecules to the æther. This absence of radiation is one of the properties of a transparent body; and the other thermal (or optical) properties of transparent bodies may be presumed to depend also on these partially irregular motions. Thus Fizeau has proved by experiment that a flow of water of about Rays of common light have been found to interfere, of which one was retarded 15 millims., or about 30,000 wave-lengths, behind the other, showing what a long series of nearly similar waves usually succeed one another in unpolarized light before waves of another type come in. seven metres per second produced a very sensible effect on the velocity with which light was propagated in the direction of the motion; in other words, when the molecular motions had a preponderance in one direction, this was found to alter the refractive index in that direction. This shows that the molecular motions do affect the refractive index; and it is perhaps not too much to presume that the phenomena of the irrationality of the spectra produced by prisms of different materials of double refraction and polarization in crystals of other than the cubical system, and of circular polarization in solids and liquids, will be found to result from modifications of the irregular motions either of or within the molecules. Other facts appear to confirm this presumption: where from the form of a crystal we have reason to suppose that the irregular molecular motions are not symmetrically distributed in different directions, there we uniformly find the phenomena of double refraction; and in those solids where they are symmetrically disposed the refraction becomes double if they are exposed to strain, i. e. as soon as an unsymmetrical distribution of the molecular motions is artificially induced. On the whole we appear justified in drawing the probable inference that all the phenomena of transparency are intimately associated with the molecular motions which want that kind of regularity which would fit them to be the source of luminous undulations. What is certain is, first, that certain periodic molecular motions do produce the phenomena of opacity in gases; and secondly, that irregular molecular motions are incapable of producing the effect of opacity, since they cannot radiate. By irregular motions, where the phrase occurs in this communication, are to be understood motions which are not approximately periodic, or which from any other cause cannot set up in the æther such an undulation as that which constitutes radiant heat. On the advantage of referring the positions of Lines in the Spectrum to a Scale of Wave-numbers. By G. JOHNSTONE STONEY, M.Á., F.R.S. At the last Meeting of the British Association Mr. Stoney made a communication, from which it seemed to appear that each periodic motion in the molecules of a gas will in general (.e. unless the motion be a simple pendulous one, or else mechanically small) give rise to several lines in the spectrum of the gas, and that the lines which thus result from one motion have periods that are harmonics of the periodic time of the parent motion. Since that time he has been engaged, in conjunction with Dr. Emerson Reynolds, of Dublin, in testing this theory; and in this inquiry it has been found convenient to refer the positions of all lines in the spectrum to a scale of reciprocals of the wave-lengths. This scale has the great convenience, for the purposes of the investigation, that a system of lines with periodic times that are harmonics of one periodic time are equidistant upon it; and it has the further convenience, which recommends it for general use, that it resembles the spectrum as seen in the spectroscope much more closely than the scale of direct wave-lengths used by Ångström in his classic map. 2 The position marked 2000 upon this scale occurs about the middle of the spectrum, and corresponds to Angström's wave-length 5000. The numbers which Angström uses are tenth-metres, i. e. the lengths obtained by dividing the metre into 100 parts; and from this it follows that each number on the new scale signifies the number of light-waves in a millimetre: thus 2000 upon a map drawn to this scale marks the position of the ray whose wave-length is of a millimetre. The new scale may therefore be appropriately called a scale of wavenumbers. If, then, k be the wave-number of a fundamental motion in the æther, its wave-length will be th of a millimetre, and its harmonics will have the wavek 1 1 lengths &c.; in other words, they occupy the positions 2k, 3k, &c. upon 2k' 3k' the new map. Hence it is easy to see that a system of lines which are equally spaced along the map at intervals of k divisions are harmonics of a fundamental motion whose wave-number is k, whose wave-length is th of a millimetre, and T whose periodic time is where is the periodic time of an undulation in the 石 æther consisting of waves one millimetre long. If we use Foucault's determination of the velocity of light, viz. 298,000,000 metres per second, the value of this constant is r = 3.3557 twelfth-seconds, meaning by a twelfth-second a second of time divided by 1012, which, in other words, is the millionth part of the millionth of a second of time. Thus the proposed numbers give the same information as a list of direct wavelengths, and in a more commodious form for theoretical purposes; while at the same time the map of the spectrum drawn to this scale is to be preferred for use in the laboratory, because it represents the spectrum formed by a prism with comparatively little distortion. This will be apparent from the following Table of the wave-numbers of the principal lines of the solar spectrum:— On the Wave-lengths of the Spectra of the Hydrocarbons. The author stated that in 1856 he had communicated to the Royal Society of Edinburgh a paper, published in vol. xxi. of their Transactions, entitled "On the Prismatic Spectra of the Flames of Compounds of Carbon and Hydrogen." In his observations on these substances he made use of an arrangement (employed by him still earlier in 1847) identical with that which, since the publication of Kirchhoff and Bunsen's researches in Spectrum-analysis, is familiarly known as a "Spectroscope," namely, an observing telescope, a prism, and a collimator, receiving the light to be examined through a narrow slit at its principal focus. The observations published in 1856 consist of carefully observed minimum deviations of fourteen dark lines of the sun spectrum, and of twelve bright lines of the hydrocarbon spectra, which bright lines were found to be identical in fifteen different hydrocarbons examined. No absolute coincidences between the lines in the solar and terrestrial spectra were observed, except that, long before discovered by Fraunhofer, between the double sun-line D and the double yellow line of ordinary flames, now, wherever it may be seen, referred to sodium. The yellow line was generally present in the hydrocarbon spectra; but, from a careful quantitative experiment, it was ascertained that the 2,500,000th part of a troy grain of sodium rendered its presence in a flame sensible: and the conclusion was then distinctly stated, it is believed for the first time, that whenever or whereever the double yellow line appears it is due to the presence of minute traces of sodium. In this state the observations of 1856 had remained until lately, when the author was requested by his friend Professor Piazzi Smyth to compute the wave-lengths of some of the hydrocarbon lines. As no exact coincidence existed between these and the lines of the solar spectrum, it was necessary to have recourse to some process of interpolation; and that which suggested itself to the author was founded upon Lagrange's well-known Interpolation theorem. In order to verify as far as possible the results, the computation of the wave-lengths of the hydrocarbon lines was repeated by interpolating between different groups of sun lines; and the discrepancies between the numbers so obtained in no case extended beyond the place of units in Ångström's scale of wave-lengths, where unity expresses the ten millionth part of a millimetre. The subject was brought before the Association in order |