Still the difficulty remains of the disposal of the heat of liquidity of the frozen water. Professor Tyndall is no doubt right in assuming that the interior portions of a mass of ice require a higher temperature to liquefy than the surfaces, and consequently that they may conduct and transmit heat without melting. But as this very fact supposes them to be less susceptible of individual molecular motion, it is difficult to imagine that they can absorb or retain heat, unless from a source of appreciably higher temperature-that is to say, a temperature above the margin which distinguishes the capability of liquefaction between. the free and the confined particles, no cause of which is given; and it is not supposed that the film of water between the appressed surfaces is subject to any other cause of freezing than the mere sympathetic action tending to induce synchronism of molecular motion, or identity of condition in the neighbouring particles.

The explanation given by Professor James Thomson is based on his interesting discovery of the lowering of the freezing-point of water by compression, and is briefly as follows:-"The two pieces of ice, on being pressed together at their points of contact, will at that place, in virtue of the pressure, be in part liquefied and reduced in temperature, and the cold evolved in their liquefaction will cause some of the liquid film intervening between the two masses to freeze." Of course a sufficient cause of the pressure should be shown; and moreover it must be supposed that the liquid film between the appressed solid surfaces is free (or comparatively free) from pressure. With this condition the explanation seems satisfactory; and Helmholtz supposes this condition to obtain in the case of glacier-motion, as the water of the compressed ice can escape through fissures. This seems questionable as a general fact; but, supposing that in general the water is confined and retained in the internal fissures, the phenomena might still be explained by supposing the degree of pressure to be continually varying in any given spot in the mass from the extensive process of internal fracture and change of shape always going on in the glacier from its descending motion through a mould of very irregular conformation. When a block of ice is compressed, layers of liquid water are formed in the substance of the solid at right angles to the direction of pressure. The temperature of the ice must be lowered by a quantity corresponding to the heat of liquefaction of the water produced; and the water, being under the same pressure, remains liquid in contact with the cooled ice, because its freezing-point is lowered by the pressure. On the removal of the pressure (supposing the ice to return to its former dimensions, not by elasticity, but by a

again and throws out the heat of liquidity of the frozen particles into the surrounding ice.

But in the case of instantaneous regelation in fragments of ice merely touching each other, and even when floating in warm water, there does not seem to be sufficient cause of the pressure required by J. Thomson's explanation, even keeping in mind the fact pointed out by Helmholtz, that the pressure is not equally distributed over the whole of the two appressed surfaces, but is concentrated on a few points of contact. Moreover, in the case of wet surfaces, or when the fragments of ice are floating in warm water, it is not easy to imagine how any pressure acting on the pieces of ice should not at the same time act on the films of water interposed between the surfaces of contact.

It must therefore be allowed that, in such cases of regelation, a sufficient cause of pressure is not apparent; yet Helmholtz insists on the probability of pressure being the proximate cause of regelation. He says, "I find the strength and rapidity of the union of the pieces of ice in such complete correspondence with the amount of pressure employed, that I cannot doubt that the pressure is actually the sufficient cause of the union." On this, Tyndall remarks that Faraday's contact-action would also increase under pressure, from the greater extent of surface which would be brought into play; and he insists on the difficulty of imagining any sufficient cause of pressure in the regelation of fragments of ice floating in warm water which freeze together at their points of contact "in a moment"- -convex surfaces freeze together" virtual points that touch each other, clasped all round by the warm liquid which is rapidly dissolving them as they approach each other." (Phil. Mag., December 1865.)

Evidently the chief difficulty in the inquiry is to explain the existence of a sufficient cause of pressure on the surfaces of solid contact, while at the same time the liquid films enclosed between these surfaces should be free from pressure; and as none of the explanations hitherto given seem to satisfy these conditions, the following hypothesis is offered as apparently meeting the physical requirements of the case.

It seems probable that all bodies are continually sending off particles of their substance into the surrounding atmosphere. Ice certainly is known to evaporate at all temperatures, from the freezing-point to the lowest temperature which has been observed; and the "disgregation" or "metamorphic" action constituting the phenomenon may be supposed to involve an expenditure of heat (or other energy) equal to convert the particles of solid ice into particles of gaseous steam, though we should imagine the motion of the disgregated particles to be straight-line motion, or the true motion of free gaseous particles in space, the

distance of the particles from each other being too great to admit of any appreciable mutual interaction between them. The evaporating surface of the ice is therefore a field of active molecular operation; in whatever way heat may be getting in, it is certainly going out with each disgregrated or metamorphosed particle which flies off from the surface of the solid.

Water, within a small range above its freezing-point, expands with cold; and as it gives this marked evidence of being in an • exceptional state of thermic susceptibility under these circumstances, we might naturally suppose that in this condition its thermic properties generally were in an inverted state. It is certain, at least, that between 3910 and 32° water contracts with heat. Very thin liquid films on the surfaces of ice may be supposed to be at the maximum limit of this inverted state of thermometric action, and would certainly contract on being slightly heated.

When two pieces of ice are brought together, we should imagine that the motion of translation of the escaping disgregated particles being mutually stopped, local heat must be the result. In the case of two fragments of wet ice touching each other without any appreciable pressure artificially applied, the actual points of solid contact may be supposed to be very minute, with comparatively large surfaces of water-films between; and the smallest extent of "spherical surfaces" which we can imagine practically to come to touch each other should, when conceived of molecularly, give the idea of considerable space, including many of the "virtual points that touch other," as described by Tyndall, with very shallow water-spaces between. Now the sudden generation of heat, developed, between the pieces of ice in the act of contact, from the arrested motion of translation of the disgregated particles flying off from the surfaces, must raise the temperature of the surfaces where it acts. The sudden melting of the projecting prominences of solid ice would probably be an action of very limited extent compared with the heating of the intervening liquid films, which, shut in from free communication with the exterior, and instantly contracting with the increase of temperature, would cause locally a partial vacuum between the contiguous solid points of support, while the atmospheric pressure acting on the back of each piece of ice might cause a very considerable amount of pressure on the solid points, in addition, perhaps, to a kind of capillary attraction existing between surfaces in contact.

The effects of the pressure thus brought into action may be conceived of as results of the interesting fact of the lowering of the freezing-point of water by compression. Helmholtz (quoted

quantity corresponding to the lowering of its freezing-point by the pressure. But the freezing-point of the uncompressed water is not lowered. [This is said of the glacier-water supposed to be free to escape through fissures; but it applies here, as the cause assigned to the pressure on the ice is the shrinking of the intervening water.] Here, then, we have ice colder than 0° C. in contact with water at 0° C. [the water of liquefaction]. The consequence is, that round the place of pressure the water will freeze and form new ice, while, on the other hand, a portion of the compressed ice continues to be melted." The water of liquefaction would in the first place form zones round the solid points of contact, displacing laterally the surrounding water of the liquid films, while the particles of ice simultaneously forming round the solid prominences would act as wedges or props to compensate the lowering of the points by liquefaction, and so maintain the original distance of the surfaces (approximately), and consequently the partial vacuum originally formed by the shrinking of the liquid films. Meanwhile the heat thrown out by the forming ice, and the heat of the enclosed films which are at a temperature above that of the surrounding ice, would pass into the solid mass,—perhaps quite through it without causing liquefaction, according to Tyndall's idea; but at least, in the case under consideration, the heat should naturally pass from the water into the ice, because the temperature of the water should be sensibly higher.

When fragments of ice are floating in warm water with the appressed surfaces submerged, we must suppose that before contact took place the surfaces were melting and sending off liquid particles at or very little above 32° at the moment of their separation from the solid mass, which particles would be floating away with a certain amount of vis viva in their motion of translation. On the contact of the two pieces of ice this motion would be stopped and changed into heat, which would act locally on the liquid film formed by the arrested particles themselves, converting their previous motion of translation into heat-motion; and hence the shrinking of the liquid films, and consequent pressure on the solid points of contact required to explain the fact of regelation.

Palermo, December 24, 1865.

IN

XVII. Studies on Gases.

By Dr. H. W. SCHROEDER VAN der Kolk*.

[§ I. Introduction.

N so far as the principle of the mechanical theory of heatthat the condition of a body only depends on two given magnitudes can be considered to hold good, the formula pv=kT, where p is the pressure, v the volume, and 7 the absolute temperature, may be regarded as valid for all bodies. In general, k is then a variable magnitude dependent on temperature and pressure; if it is made constant, the formula is obtained of the body which is called an ideal gas. Actual gases approximate to this condition; the changes which temperature and pressure here produce in the value of k arc very small. For some gases, especially for hydrogen, air, carbonic acid, and nitrogen, Regnault's determinations render it possible to determine more accurately the changes in k. From his experiments in reference to Mariotte's law, I have calculated for these gases the formula which indicates the connexion between k and p at the mean temperature of 4, as I have already communicated in a former memoirt. From the coefficients of expansion between 0° and 100° under different pressures, the same formula may be calculated for 100°. It was found that in the case of hydrogen, at any rate within the limits of the accuracy of Regnault's experiments, k does not alter with the temperature, while in the case of the other gases it is a function of both variables. Other determinations of Regnault rendered it possible to test the accuracy of the formula thus obtained.

If the principle that the condition of a body is determined by means of two magnitudes, and therefore by means of the changes in k, be compared with Regnault's result, that the specific heat of water and of air scarcely changes at all with the temperature, while that of carbonic acid, in which k undergoes a far greater alteration, changes considerably, it is natural to investigate whether these changes of the specific heat are not connected with changes in k.

This investigation is connected with an accurate determination of the mechanical equivalent of heat. Hence I repeated the calculation of Moll and van Beek's experiments on the velocity of sound, in order to have a more accurate determination of the coefficient. The ordinary formula for calculating the con

* Translated from Poggendorff's Annalen, vol. cxxvi. † Poggendorff's Annalen, vol. cxvi. p. 429.

p. 333.