Hermann von Helmholtz; Translated by Edmund Atkinson
THE THEORY of the regelation of ice has led to scientific discussions between Faraday and Tyndall on the one hand, and James and Sir W. Thomson on the other. In the text I have adopted the theory of the latter, and must now accordingly defend it.
Faradays experiments show that a very slight pressure, not more than that produced by the capillarity of the layer of water between two pieces of ice, is sufficient to freeze them together. James Thomson observed that in Faradays experiments pressure which could freeze them together was not utterly wanting. I have satisfied myself by my own experiments that only very slight pressure is necessary. It must, however, be remembered that the smaller the pressure the longer will be the time required to freeze the two pieces, and that then the junction will be very narrow and very fragile. Both these points are readily explicable on Thomsons theory. For under a feeble pressure the difference in temperature between ice and water will be very small, and the latent heat will only be slowly abstracted from the layers of water in contact with the pressed parts of the ice, so that a long time is necessary before they freeze. We must further take into account that we cannot in general consider that the two surfaces are quite in contact; under a feeble pressure which does not appreciably alter their shape, they will only touch in what are practically three points. A feeble total pressure on the pieces of ice concentrated on such narrow surfaces will always produce a tolerably great local pressure under the influence of which some ice will melt, and the water thus formed will freeze. But the bridge which joins them will never be otherwise than narrow.
Under stronger pressure, which may more completely alter the shape of the pieces of ice, and fit them against each other, and which will melt more of the surfaces that are first in contact, there will be a greater difference between the temperature of the ice and water, and the bridges will be more rapidly formed, and be of greater extent.
A glass flask with a drawn-out neck was half filled with water, which was boiled until all the air in the flask was driven out. The neck of the flash was then hermetically sealed. When cooled, the flask was void of air, and the water within it freed from the pressure of the atmosphere. As the water thus prepared can be cooled considerably below 0° C. before the first ice is formed, while when ice is in the flask it freezes at 0° C., the flask was in the first instance placed in a freezing mixture until the water changed into ice. It was afterwards permitted to melt slowly in a place the temperature of which was +2° C., until the half of its was liquefied.
The flask thus half filled with water, having a disc of ice swimming upon it, was placed in a mixture of ice and water, being quite surrounded by the mixture. After an hour, the disc within the flask was frozen to the glass. By shaking the flask the disc was liberated, but it froze again. This occurred as often as the shaking was repeated.
The flask was permitted to remain for eight days in the mixture, which was kept throughout at a temperature of 0° C. During this time a number of very regular and sharply defined ice crystals were formed, and augmented very slowly in size. This is perhaps the best method of obtaining beautifully formed crystals of ice.
While, therefore, the outer ice which had to support the pressure of the atmosphere slowly melted, the water within the flask, whose freezing point, on account of a defect of pressure, was 0.0075° C. higher, deposited crystals of ice. The heat abstracted from the water in this operation had, moreover, to pass through the glass of the flask, which, together with the small difference of temperature, explains the slowness of the freezing process.
Now as the pressure of one atmosphere on a square millimetre amounts to about ten grammes, a piece of ice weighing ten grammes, which lies upon another and touches it in three places, the total surface of which is a square millimetre, will produce on these surfaces a pressure of an atmosphere. Ice will therefore be formed more rapidly in the surrounding water than it was in the flask, where the side of the glass was interposed between the ice and the water. Even with a much smaller weight the same result will follow in the course of an hour. The broader the bridges become, owing to the freshly formed ice, the greater will be the surfaces over which the pressure exerted by the upper piece of ice is distributed, and the feebler it will become; so that with such feeble pressure the bridges can only slowly increase, and therefore they will be readily broken when we try to separate the pieces.
It cannot, moreover, be doubted that in Faradays experiments, in which two perforated discs of ice were placed in contact on a horizontal glass rod, so that gravity exerted no pressure, capillary attraction is sufficient to produce a pressure of some grammes between the plates, and the preceding discussions show that such a pressure, if adequate time be given, can form bridges between the plates.
If, on the other hand, two of the above-described cylinders of ice are powerfully pressed together by the hands, they adhere in a few minutes so firmly that they can only be detached by the exertion of a considerable force, for which indeed that of the hands is sometimes inadequate.
In my experiments I found that the force and rapidity with which the pieces of ice united were so entirely proportional to the pressure that I cannot but assign this as the actual and sufficient cause of their union.
In Faradays explanation, according to which regelation is due to a contact action of ice and water, I find a theoretical difficulty. By the water freezing, a considerable quantity of latent heat must be set free, and it is not clear what becomes of this.
Finally, if ice in its change into water passes through an intermediate viscous condition, a mixture of ice and water which was kept for days at a temperature of 0° must ultimately assume this condition in its entire mass, provided its temperature was uniform throughout; this however is never the case.
As regards what is called the plasticity of ice, James Thomson has given an explanation of it in which the formation of cracks in the interior is not presupposed. No doubt when a mass of ice in different parts of the interior is exposed to different pressures, a portion of the more powerfully compressed ice will melt; and the latent heat necessary for this will be supplied by the ice which is less strongly compressed, and by the water in contact with it. Thus ice would melt at the compressed places, and water would freeze in those which are not pressed: ice would thus be gradually transformed and yield to pressure. It is also clear that, owing to the very small conductivity for heat which ice possesses, a process of this kind must be extremely slow, if the compressed and colder layers of ice, as in glaciers, are at considerable distances from the less compressed ones, and from the water which furnishes the heat for melting.
To test this hypothesis, I placed in a cylindrical vessel, between two discs of ice of three inches in diameter, a smaller cylindrical piece of an inch in diameter. On the uppermost disc I placed a wooden disc, and this I loaded with a weight of twenty pounds. The section of the narrow piece was thus exposed to a pressure of more than an atmosphere. The whole vessel was packed between pieces of ice, and left for five days in a room the temperature of which was a few degrees above the freezing point. Under these circumstances the ice in the vessel, which was exposed to the pressure of the weight, should melt, and it might be expected that the narrow cylinder on which the pressure was most powerful should have been most melted. Some water was indeed formed in the vessel, but mostly at the expense of the larger discs at the top and bottom, which being nearest the outside mixture of ice and water, could acquire heat through the sides of the vessel. A small welt, too, of ice, was formed round the surface of contact of the narrower with the lower broad piece, which showed that the water, which had been formed in consequence of the pressure, had again frozen in places in which the pressure ceased. Yet under these circumstances there was not appreciable alteration in the shape of the middle piece which was most compressed.
This experiment shows that although changes in the shape of the pieces of ice must take place in the course of time in accordance with J. Thomsons explanation, by which the more strongly compressed parts melt, and new ice is formed at the places which are freed from pressure, these changes must be extremely slow when the thickness of the pieces of ice through which the heat is conducted is at all considerable. Any marked change in shape by melting in a medium the temperature of which is everywhere 0°, could not occur without access of external heat, or from the uncompressed ice and water; and with the small differences in temperature which here come into play, and from the badly conducting power of ice, it must be extremely slow.
That on the other hand, especially in granular ice, the formation of cracks, and the displacement of the surfaces of those cracks, render such a change of form possible, is shown by the above-described experiments on pressure; and that in glacier ice changes of form thus occur, follows from the banded structure, and the granular aggregation which is manifest on melting, and also from the manner in which the layers change their position when moved, and so forth. Hence, I doubt not that Tyndall has discovered the essential and principal cause of the motion of glaciers, in referring it to the formation of cracks and to regelation.
I would at the same time observe that a quantity of heat, which is far from inconsiderable, must be produced by friction in the larger glaciers. It may be easily shown by calculation that when a mass of firn moves from the Col du Géant to the source of the Arveyron, the heat due to the mechanical work would be sufficient to melt a fourteenth part of the mass. And as the friction must be greatest in those places that are most compressed, it will at any rate be sufficient to remove just those parts of the ice which offer most resistance to motion.
I will add, in conclusion, that the above-described granular structure of ice is beautifully shown in polarised light. If a small clear piece is pressed in the iron mould, so as to form a disc of about five inches in thickness, this is sufficiently transparent for investigation. Viewed in the polarising apparatus, a great number of variously coloured small bands and rings are seen in the interior; and by the arrangement of their colours it is easy to recognize the limits of the ice granules, which, heaped on one another in irregular order of their optical axes, constitute the plate. The appearance is essentially the same when the plate has just been taken out of the press, and the cracks appear in it as whitish lines, as afterwards when these crevices have been filled up in consequence of the ice beginning to melt.
In order to explain the continued coherence of the piece of ice during its change of form, it is to be observed that in general the cracks in the granular ice are only superficial, and do not extend throughout its entire mass. This is directly seen during the pressing of the ice. The crevices form and extend in different directions, like cracks produced by a heated wire in a glass tube. Ice possesses a certain degree of elasticity, as may be seen in a thin flexible plate. A fissured block of ice of this kind will be able to undergo a displacement at the two sides which form the crack, even when these continue to adhere in the unfissured part of the block. If then part of the fissure at first formed is closed by regelation, the fissure can extend in the opposite direction without the continuity of the block being at any time disturbed. It seems to me doubtful, too, whether in compressed ice and in glacier ice, which apparently consists of interlaced polyhedral granules, these granules, before any attempt is made to separate them, are completely detached from each other, and are not rather connected by ice bridges which readily give way; and whether these latter do not produce the comparatively firm coherence of the apparent heap of granules.
The properties of ice here described are interesting from a physical point of view, for they enable us to follow so closely the transition from a crystalline body to a granular one; and they give the causes of the alteration of its properties better than in any other well-known example. Most natural substances show no regular crystalline structure; our theoretical ideas refer almost exclusively to crystallised and perfectly elastic bodies. It is precisely in this relationship that the transition from fragile and elastic crystalline ice into plastic granular ice is so very instructive.