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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

as the screens absorb or reflect heat: a screen of tinfoil will not allow a deposit to be formed; but if the screen be of brown paper, there will be an abundant furthest deposit. So also if a bottle have attached to it disks and rings of tinfoil, paper of various colours, &c., no deposit will be formed in and about such disks, because they keep the bottle warm by preventing radiation, and even by absorbing heat. A disk of black paper put on a deposit already formed will clear away a much larger space than tinfoil will do.

The author found that crude camphor was more sensitive in its action than refined; but that the experiments succeed with ordinary camphor, Borneo camphor, artificial turpentine camphor, camphoric acid, iodine, naphthaline, chloral, water, alcohol, ether, &c.

ELECTRICITY, MAGNETISM.

On the Mechanical Power of Electro-Magnetism, with special reference to the Theory of Dr. Joule and Dr. Scoresby. By JAMES CROLL, Glasgow.

In an article by Dr. Joule and Dr. Scoresby on the mechanical power of Electromagnetism*, it is stated that when the electro-magnetic engine is set in motion and the current in consequence reduced from a to b, the heat manifested in the circuit is reduced from a2 to b2, but the heat which is produced by the oxidation of the zinc is only reduced from a to b; hence they conclude that the quantity of heat equal a-b produced by the zinc plates, but which does not appear in the circuit, is consumed in the production of mechanical effects. That this conclusion is not satisfactory will appear, the author thinks, from the following considerations, viz. if we reduce the current from a to b by merely reducing the consumption of the zinc from a to b, the heat evolved in the circuit will in this case also be reduced from a2 to b2. The question now arises, what becomes of the amount of force a-b which disappears in the circuit here also? It is not consumed in work, for no mechanical effect takes place. Hence, from the disappearance of heat when the electro-magnetic machine is set in motion, we are not warranted to conclude that it went to produce mechanical effects; for it equally disappears in the other case when no mechanical effect is produced. The true explanation of the matter, he thinks, is this: when we reduce the current from a to b, we reduce the heat evolved in the conducting wire from a2 to b2, but we only reduce the heat evolved in the entire circuit from a to b; hence there is no disappearance of heat whatever. The simple fact is, the heat which is missing in the conductor will be found in the battery; however, when the engine is in motion there will be a deficiency in the total heat evolved equal to the thermal equivalent of the mechanical work performed. When the engine being at rest the current is equal b, the total heat evolved is also equal b; but when the current is reduced to 6 by the motion of the machine, the total heat evolved will then be equal b-x; x being the equivalent of the mechanical work performed. The value of x, therefore, is not determined by the theory of Dr. Joule and Dr. Scoresby.

Let us consider the theory in relation to the origin of the mechanical work. When the current is equal b, without mechanical work being performed, the heat evolved in the conductor is b2; when the current is b, and mechanical work performed, according to the theory the heat evolved in the conductor is also equal b2. In this case there is no reduction of heat in the conductor corresponding to the mechanical effect produced; for the heat is as great when the mechanical effect takes place as when it does not, being in both cases equal b2. This would lead to the conclusion that the mechanical effect is not derived from the current b, for it could not possibly produce its full equivalent of work, in the shape of heat b2 and amount of work in addition. The work a must, therefore, according to this theory, be derived directly either from the chemical action in the battery or from the heat evolved. That it is not directly dependent upon chemical action is evident from

* Philosophical Magazine, June 1846.

the fact that, if the current exist, x will arise the same as before, whether there be chemical action or not, as, for example, when the current has a thermal origin; and that it is not derived from the heat evolved is evident also from the fact that it has no existence when the heat is present in the circuit without the current. The mechanical work is therefore, contrary to the above theory, derived directly from the electric current; and it follows from hence that when we have two currents equal in every respect, the one performing mechanical work and the other producing nothing but heat, less heat must be evolved by the former current than by the latter; consequently the law involved in the theory, viz. that the heat evolved in similar conductors is proportional to the square of the currents, does not hold true when one of the currents produces magnetical effects.

Facts seem to lead to the following theory as a true explanation of the mechanical power of electro-magnetism. Whatever our views may be regarding the nature of the electric current, we must allow that the molecules of bodies offer a certain amount of resistance to the passage of the current, which amount differs according to the nature of the body through which the electricity is propagated. It must also be admitted that the molecules of the body, in consequence of the resistance which they offer, become heated. Let us take now the case of the conducting wire connecting the pole of a battery. Suppose it to be composed of a succession of molecules A, B, C, D, &c. The chemical action in the battery communicates a certain amount of motion to the atom A, in consequence of which its equilibrium is destroyed, and to regain this state it transmits motion to the next adjoining atom B; but B offers resistance to A, and the consequence is that A is unable to communicate to it the full amount of motion necessary to restore its own equilibrium, so that A must still retain a portion of the disturbing force or motion received from the battery; but on account of its position in space being limited by its relations to surrounding molecules, it can only retain motion or force in itself by vibrating, and in virtue of these vibrations we affirm it to be hot. Bin like manner, to regain its equilibrium, transmits motion to C, but C likewise offers resistance to B, and, of course, B must also retain a portion of the disturbing force in the form of heat, and what holds true of A, B, and C, holds equally true in regard to all the other molecules of the conductor.

Let us now observe what takes place when work is being performed by an electro-magnetic engine. We have, in the first place, a continual evolution of force arising from chemical action in the battery. This chemical force becomes immediately transformed into electric current, and the electric force must in turn be constantly transformed into some other form of force, or else we should instantly have an accumulation of current. When the current is allowed simply to circulate in the conductor without producing any work, either chemical or magnetical, its entire force is transformed into heat, and the heat in turn is transmitted to surrounding objects and radiated into space. This, as we have shown, is the effect of forces tending to a state of equilibrium. When the soft iron of the electro-magnetic engine is brought into the presence of the conductor, another channel or outlet is then offered to the molecules of the conductor, whereby they may get rid of the disturbing force, the electric current; a portion of this force will be transferred to the molecules of the iron, causing them to assume the magnetic state, and, of course, whatever is consumed in work upon the molecules of the iron cannot appear in the molecules of the conductor in the shape of heat. The moment the molecules of the iron assume the magnetic state, no further transference of force in this direction can take place; but if they are allowed to perform mechanical work while they are assuming this state, as is the case when the electro-magnetic engine is in motion, then a constant outlet is afforded in this direction to the disturbed molecules of the conductor to regain their equilibrium. But it must be observed that the relative proportions of the force which pass through each of the two channels or outlets, heat and magnetical work, do not remain the same, as Dr. Joule and Dr. Scoresby's theory implies; for as the force will always tend to the path of least resistance, the relative proportion passing through each outlet will be determined by the relative resistance offered the quantity passing through each being inversely as the resistance to be overcome. Now the quantity x of mechanical work that can be produced by an electro-magnetic engine from a given quantity of elec

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