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triangle, the base of which is the exact length of the scale. Taking 8 inches, for example, as that length, the three sides of the triangle will be 8 inches. Now, it is possible to enlarge the base three, four, five, or any number of times, by extending the sides of the triangle in the same ratio; so that if it be desirable to enlarge the scale four times, a triangle is formed having its base four times longer, viz. equal to 32 inches; and dividing this new base into 100 parts, it is evident that each division will be four times larger than it could have been on the original base. Now, describing an arc, the chord of which is the base of the triangle, and attaching to the summit a thin metallic wire, the other end of which can slide on the arc, it is evident that each division of the magnified scale which may be covered by the wire will correspond exactly with an equal division of the original scale, so that, after having brought the metallic wire on the division of the increased scale indicating the size of the required image, and the wire being fixed on the index, it will be brought exactly on any division of the unity of measure, however small it may be. The author has described another plan to obtain the same result, and, perhaps, more effectively it consists in fixing the negative on a rack exactly the length of the scale, which, acting on a pinion adapted to a sufficiently large wheel containing the requisite divisions, will produce an entire revolution of the wheel; and an index being fixed on the table, will indicate on the wheel the exact amount of the course effected by the negative on the scale; and by turning the wheel to the division required, this will bring the negative with the greatest accuracy to the distance corresponding with the division. This system of focusing all camera-lenses might be very advantageous in photographic operations, and would be less subject to errors than the usual way of focusing on the ground glass.

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Relation entre les Phénomènes de la Polarisation Rotatoire, et les Formes Hémiedres ou Hemimorphes des Cristaux à un ou à deux Axes Optiques, Par A. DES CLOIZEAUX.

Tout le monde sait que la découverte de la polarisation de la lumière a rendu possible l'institution de nombreuses recherches, inabordables à tout autre mode d'observation, sur la constitution moléculaire des corps solides et liquides. Je n'entreprendrai pas ici de passer en revue les faits intéressants et les lois remarquables dont on doit la connaissance aux travaux des Malus, des Fresnel, des Herschel,. des Arago, des Brewster, des Biot, &c. Je m'occuperai seulement de la polarisation rotatoire et des relations que ce phénomène peut avoir avec la structure physique des corps cristallisés. Depuis que la science a été dotée des microscopes polarisants d'Amici et de Nörrenberg, on a pu étendre les observations optiques à un grand nombre de substances trop peu transparentes ou de trop petites dimensions pour se prêter à l'emploi des instruments généralement usités jusque dans ces dernières années. Le quartz est resté pendant très longtemps le seul corps solide dans lequel on eut constaté l'existence du pouvoir rotatoire, et Sir John Herschel a le premier fait remarquer qu'il paraissait y avoir une relation constante entre le sens de la rotation des cristaux et le sens suivant lequel s'enroule la spirale formée par plusieurs des faces connues sous les noms de faces plagièdres et par la face rhombe, lorsque l'axe principal des cristaux est placé verticalement devant l'observateur. Ce rapprochement a conduit à regarder le phénomène de la polarisation rotatoire comme dû à un arrangement particulier des molécules physiques qui se manifesterait quelquefois par des formes cristallines présentant l'hémiédrie dite plagièdre ou tournante. On sait que le caractère de cette hémiédrie est la non-superposition des solides symétriques résultant de la réunion des faces plagièdres situées à droite et à gauche d'une même face prismatique du quartz. L'observation prouve d'ailleurs qu'elle peut s'allier avec l'hémiédrie qui fournit pour la face rhombe deux solides inverses mais superposables. Il est en effet probable que c'est une structure de ce genre qui donne aux cristaux dextrogyres et aux cristaux lévogyres la propriété d'imprimer à la lumière polarisée des modifications de sens contraire; car on n'a jamais observé de phénomènes rotatoires dans les cristaux d'apatite, de Schéelite, d'érythroglucine, &c., sur lesquels on ne connaît jusqu'à présent que des formes hémièdres superposables. Malheureusement la dissymétrie intérieure n'est pas toujours accusée par des signes extérieurs, et l'observation seule indique si un corps cristallisé possède ou ne possède

pas la polarisation rotatoire. Ainsi, un grand nombre de cristaux de quartz ne portent aucune face plagièdre; le chlorate de soude, dans les cristaux duquel M. Marbach a découvert le pouvoir rotatoire, s'obtient tantôt en cubes parfaits, tantôt en tétraèdres simples ou en tétraèdres modifiés par les faces d'un dodécaèdre pentagonal qui occupent relativement à celles du tétraèdre deux positions inverses l'une de l'autre en rapport avec le sens de la rotation; le cinabre rhomboédrique et le sulfate de strychnine quadratique, qui, d'après mes observations, impriment aussi au plan de polarisation une déviation égale, pour le premier à 16 fois et pour le second à la moitié de celle que produit le quartz, n'ont offert jusqu'ici aucune trace d'hémiédrie ; cependant j'ai trouvé dans le cinabre des cristaux dextrogyres, des cristaux lévogyres, et des cristaux complexes où l'emploi de la lumière polarisée convergente manifeste les spirales d'Airy absolument comme dans le quartz. La cause qui donne naissance à la polarisation rotatoire dans les cristaux paraît donc indépendante de celle qui produit les formes hémiédriques; seulement, comme l'a fait voir M. Marbach, la production de ces formes peut être favorisée artificiellement en faisant varier les conditions dans lesquelles s'opère la cristallisation. Il est donc probable que les cristaux de quartz à faces plagièdres n'ont pas pris naissance dans les mêmes circonstances que ceux où les faces plagièdres manquent; tous les cristaux de cinabre connus jusqu'à ce jour ont dû au contraire se former sous l'influence de phénomènes géologiques semblables.

Depuis que M. Biot a découvert la déviation imprimée au plan de polarisation par certains liquides et certaines dissolutions, on s'est souvent demandé si les dissolutions actives susceptibles de cristalliser produisaient nécessairement des cristaux doués du pouvoir rotatoire. La plus grande partie des substances actives en dissolution cristallisant sous des formes qui possèdent deux axes optiques, la question est longtemps restée sans réponse expérimentale. Mais les travaux de M. Marbach et les miens, en révélant l'existence des trois seuls cas réalisables dans les cristaux dépourvus de la double réfraction ou dans les cristaux à un seul axe optique, semblent prouver que les deux genres de phénomènes sont indépendants l'un de l'autre. En effet, 1°, le chlorate de soude, inactif en dissolution dans l'eau, jouit du pouvoir rotatoire lorsqu'il est en cristaux; le quartz fondu ou à l'état de silice soluble et le quartz cristallisé présentent les mêmes différences.

2°. Le sulfate de strychnine quadratique à 13 équivalents d'eau, en dissolution comme en cristaux, dévie à gauche le plan de polarisation, seulement le pouvoir rotatoire des cristaux est environ 30 fois plus grand que celui de la dissolution.

3°. Le camphre ordinaire des laurinées, actif en dissolution et à l'état fondu, donne par sublimation des cristaux appartenant au système hexagonal, dans lesquels on ne peut constater aucune déviation du plan de polarisation, même sous une épaisseur de plusieurs millimètres.

Les cristaux à deux axes optiques, dont la dissolution possède le pouvoir rotatoire, sont assez nombreux; on a donc pu les soumettre à des expériences variées. D'après les recherches de M. Pasteur, l'existence du pouvoir rotatoire dans une dissolution serait le plus souvent (à l'exception des sulfamylates) accompagnée par l'hémiédrie non superposable ou l'hémimorphie d'une ou de deux des formes simples que présentent les cristaux dissous. Cette hémiédrie se montre d'ailleurs quelquefois sur les cristaux formés naturellement au sein d'une dissolution dans l'eau pure, d'autres fois elle doit être provoquée, soit en faisant varier la nature du dissolvant, soit en blessant les cristaux et les replaçant dans leur eau-mère*. S'il existe, comme pour l'acide tartrique, les tartrates et quelques autres substances d'origine organique, deux dissolutions, l'une lévogyre et l'autre dextrogyre, les formes hémièdres ou hémimorphes correspondantes produisent ordinairement (le sel de seignette potassique paraît seul faire exception) deux solides symétriques mais non superposables. La réciproque n'est pas vraie dans tous les cas, puisque le sulfate de magnésie et le formiate de strontiane, dont les cristaux offrent l'hémiédrie non superposable, fournissent des dissolutions inactives. Les causes qui produisent les formes cristallines hémièdres paraissent donc agir d'une manière plus générale que celle à laquelle est dû le pouvoir rotatoire moléculaire.

* Ann. de Chimie et de Physique, tom. xxxviii. et xlix.

On the Cohesion of Gases, and its relations to Carnot's Function and to recent Experiments on the Thermal effects of Elastic Fluids in Motion. By JAMES CROLL, Glasgow.

From the fact that those gases which are most easily liquefied by compression are those which are found to deviate most from the law of Mariotte, we are led to the conclusion that their deviations from this law are due to the mutual attraction of their particles. Deviations from Mariotte's law after the manner of carbonic acid follow as necessary consequences from cohesion. Other phenomena are also explainable on the same principle; such, for instance, as why the coefficient of expansion is greatest for the gases which deviate most from Mariotte's law-why the coefficient of expansion increases with the density in gases which deviate from this law-why, when equal weights are employed to compress different gases under the same conditions, the greatest amount of work is performed on the gas which deviates most-why, in the expansion of gases by heat, least work is performed by heating the gases which present the greatest deviation.

The influence of Cohesion in relation to the Experiments of Prof. W. Thomson and Dr. Joule on the Thermal effects of Elastic Fluids in Motion.

In these experiments, air, carbonic acid, or hydrogen, under very high pressure, was made to expand by forcing itself through a porous plug, and it was found that the temperature of the gas after expansion was somewhat less than before it; in other terms, the heat of friction was found to fall short of compensating the cold of expansion. The expenditure of elastic force experienced by the gas, in forcing itself through the porous plug, tends in the first instance to lower its temperature; but as this force is spent in friction, the heat produced from friction ought exactly to compensate the cold of expansion. This is only the case, however, when all the force of expansion has been spent in friction; if a portion of this force be consumed in producing some other effect than heat, then the heat of friction will not compensate the cold produced by the waste of force in expansion, and a cooling effect will be the result. Now it is perfectly evident that if the atoms of a gas when compressed attract each other, the force of expansion cannot be all converted into heat, a portion of it must be consumed in overcoming attraction, hence the heat of friction will fall short of compensating the cold of expansion by an amount equal to the equivalent of the work against attraction.

It is generally understood that in certain cases a heating instead of a cooling effect may take place. How this may occur is not so apparent. Prof. W. Thomson states, that when the temperature of air rises above a certain height, the heat of friction will exceed the cold of expansion, because P'V', the work which a pound of air must do in expanding through the plug, is rather less than PV, which is the work done on it in pushing it through the spiral up to the plug. It is by no means obvious how this can result in a heating effect. That which produces the cold of expansion is the expenditure of the elastic force in expanding through the plug; but as this force is not consumed on external work, but entirely spent in friction on the particles of the air itself, the force which it loses on the one hand is entirely restored to it on the other. But more force cannot be restored than was lost; for the force restored is just what was lost.

The only way whereby it is possible to account for a heating effect, is by supposing that a gas which exhibits the heating effect possesses a certain amount of elasticity independent of heat, and that the expenditure of this force in the production of heat by friction, is an expenditure of elastic force, but not an expenditure of heat—a conclusion which is very improbable.

The Influence of Cohesion in relation to Carnot's Function.

The following was suggested by Dr. Joule, in a letter to Prof. W. Thomson in 1848, as the true expression of Carnot's function,

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J denoting Joule's equivalent, E the coefficient of expansion*, and t the tempera* In this formula Carnot's function is equal to the mechanical equivalent of the thermal

ture in Centigrade degrees, measured from the temperature of melting ice. Prof. W. Thomson has been led, from calculations based upon Regnault's observations on the pressure and latent heat of steam, to the conclusion that μ cannot in all cases be expressed by the above formula.

May not the deviations, however, be entirely due to the influence of cohesion ? It is evident that cohesion must affect the value of this function in the following manner: if a mutual attraction exist between the particles of a gas at a given temperature, then that gas in cooling itself down one degree below that temperature, by performing mechanical work in expanding, will execute less work than it would otherwise do did no cohesion between the particles exist; for a portion of the heat must be consumed in work against the cohesion. The quantity consumed by cohesion will continually increase as the temperature diminishes; for as the temperature diminishes the cohesion increases. But in regard to steam and all other saturated vapours, the reverse holds true, for the cohesion of the particles of vapours increases as their temperature rises, because their density increases with rise of temperature. In the case of a perfect gas, the function will agree with the formula at all temperatures; but in imperfect gases and vapours the function will deviate from the formula, but in opposite directions. In both cases the actual function will fall short of the theoretical.

On the Supernumerary Bows in the Rainbow. By the Rev. J. DINGLE. The author gave a method of approximating to the size of the drops of rain corresponding to any given position of the supernumerary bows produced by the interference of the two luminiferous surfaces proceeding from each drop. It appeared from his tables appended to the paper that the size which Dr. Young (without giving his method of calculation) had assigned to the drops under certain conditions was withinth of an inch of the truth, and was more accurate than that assigned subsequently by Mr. Potter.

On the Duration of Fluorescence. By Dr. ESSELBACH.

The author described the apparatus by which he succeeded in 1856 in proving the duration of fluorescence ( second with uranium glass), thereby establishing a year before M. Becquerel the experimental link between this interesting phenomenon and phosphorescence.

Description of an Optical Instrument which indicates the Relative Change of Position of Two Objects (such as Ships at Sea during Night) which are maintaining Independent Courses. By J. M. MENZIES.

This instrument consisted of a lantern-shaped case, containing a lens in front and a concentric sheet of bent glass behind, at the focal distance of the lens, ruled with parallel vertical lines. This was hung up on gimbals so as to have its axis parallel to the course of the vessel, and the bright spot (the image of the light of the approaching vessel) showed by its position and shifting the relative place and course of the approaching vessel.

Experiments on Photography with Colour. By the Rev. J. B. READE, F.R.S. A recent examination of the phenomena of polarized light in their immediate connexion with the undulatory theory led the author to inquire into the causes of natural colours, and thence to the possibility of coloured objects setting up, in sensitive films on which their image is thrown, the very same causes which regulate and determine their own respective colours. This being effected, the image of an object would communicate to the eye the identical colour of the object itself.

The propositions, in general terms, are-that radiant-coloured light consists in undulations of the luminiferous ether-that all material bodies have an attraction for the ethereal medium, by means of which it is accumulated within their substance

unit, divided by the absolute temperature. The reciprocal of E must be the absolute temperature of melting ice, or the formula is erroneous.

and exerts its influence beyond them—and that the luminous phenomena are exhibited under two modifications, the vibratory or permanent, and the undulatory or transient state. This theory leads to the conclusion that the undulations within the substance of material bodies communicate their vibrations to the ethereal medium without them, and thence to the same medium within the eye. If the undulations be such as to produce red, red is seen by the eye, and so for other colours. Now, as we have films eminently sensitive to the action of reflected light, and capable occasionally of being coloured by such light, it is clearly within the laws of physical science to suppose that the several portions of the excited film may retain within themselves, in the vibratory and permanent state, the varying undulations of the coloured objects whose images they receive. A picture with the colours as in nature would be the result, instead of the mere black and white mezzotint at present obtained. The desiderata are a sensitive silver compound capable of receiving and transmitting the undulations, and energetic reflexions from the objects themselves.

Shortly before the meeting he happened to obtain unusual traces of colour in photographic portraits. The chief difference in manipulation was a slight excess of the iodizer in the collodion, and the addition of acetic acid and acetate of soda to the bath. And in order more fully to test the effect of the cadmium and bromoiodizers, he increased the quantity until natural colours ceased to be strengthened. The final proportion of iodizing solutions gave the portrait which was exhibited. The general warm colours of the forehead and face, and the tone of the coat were fairly represented in the portrait.

Remarks on the Complementary Spectrum. By J. SMITH.

The author endeavoured to explain, on the principle adopted by him in his chromatrope experiments, the well-known fact that the spectrum of a hole in the window-shutter, when received on a screen, has the violet end above and the red below, but when looked at through the prism, the red appears above and the violet below.

On the Motion of Camphor, &c. towards the Light.

By CHARLES TOMLINSON, King's College, London.

Books on chemistry from the time of Chaptal (1788) to the present, recognize the fact that salts in crystallizing move towards the light; that camphor, water, alcohol, &c. form deposits on the most illuminated side of the bottles that contain them. The history of the subject includes the names of Petit, Chaptal, Dorthes, Draper, &c. Chaptal's experiments were made with saline solutions, and he found that crystalline deposits could be determined to any point by admitting the light to that point, or prevented by shutting out the light. Dr. Draper, who named these phenomena perihelion motions, found that in the case of camphor deposits were sometimes made nearest the sun, and at other times furthest from him, the latter being termed aphelion motions; that reflected light and coloured light produced aphelion movements; that the deposits are not produced in the dark, or by artificial light, and that rings and disks of tinfoil prevent the formation of deposits. He supposed electricity to be concerned in the production of these phenomena.

Mr. Tomlinson shows that neither light nor electricity has anything to do with these effects, but that they are the simple results of cooling. By treating the vapour of camphor, &c. as dew, all the effects follow; and Chaptal's results are obtained in full sunshine without any shutting out of the light, but simply by preventing radiation by means of transparent screens. When a bottle containing camphor, &c. is exposed to light, the illuminated side is generally the colder, and hence the deposit on this side; but when the sun is shining on the bottle, the furthest side is the colder, and there the deposit takes place. Bottles of camphor kept in the dark, i. e. in a cupboard or drawer, are equally warm all round, and hence no deposit is formed; but if such a bottle be cooled on one side by means of a piece of filtering-paper dipped in ether, a deposit is instantly formed. If a bottle of camphor be plunged into water at 100° no deposit is formed, because it is equally hot all round. If a number of bottles be covered with opake substances and exposed to the sun, or to a heated cannon-ball, deposits are formed or not according

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