Helmholtz On Ice And Glaciers
( Originally Published 1897 )
SWITZERLAND has attractions for the scientific philosophers of Germany, and around the Titlis, Bunsen, Helmholtz, Kirchhoff, and Wiedemann are not unfamiliar names. Nor have their visits to the Alps been unproductive of results. Some time ago I was favoured by Professor Helmholtz with the First Part of his ' Popular Scientific Lectures.' It contains four of them—the first, ' On the Relation of the Natural Sciences to Science in general ;' the second, ' On Goethe's Labours in Natural Science ;' the third, ' On the Physiological Origin of Musical Harmony ;' and the fourth, ' On Ice and Glaciers.' The lectures are in German, and it is much to be desired that some competent person should under-take their translation into English.'
I turned with natural interest to the last-mentioned discourse, to see how my notions and experiments on the formation and motion of glaciers were regarded by so eminent a man. I will here endeavour to give a summary of the scientific portion of the lecture.
Professor Helmholtz refers the cold of the upper regions of the atmosphere to the causes generally assigned ; but he adds a remark important at the present moment, when the origin of the hot wind called Fohn in Switzerland is the subject of so much discussion. This wind, as Helmholtz justly observes, may not only be a cold wind upon the mountain-summits, but a wet one, and it may deposit its moisture there. A wind thus dried upon the heights, and warmed by its subsequent fall into the valleys, would possess the heat and dryness of the Fohn. These qualities are, therefore, no proof that the origin of the Fohnwind is Sahara.
It will probably be remembered that I deduced the formation of glaciers, and their subsequent motion through valleys of varying width and flexure, from the fact that when two pieces of ice are pressed together they freeze together at their places of contact. This fact was first mentioned to me verbally by its discoverer, Faraday. Soon after-wards, and long before I had occasion to reflect upon its cause, the application of the fact to the formation and motion of glaciers flashed upon me. Snow was in the yard of the Royal Institution at the time; stuffing a quantity of it into a steel mould, which I had previously employed to demonstrate the influence of pressure on magnetic phenomena, I squeezed the snow, and had the pleasure of seeing it turn out from the mould as a cylinder of translucent ice. I immediately went to Faraday, and expressed the conviction that his little outlying experiment would be found to constitute the basis of a true theory of glaciers. It became subsequently known to me that the Messrs. Schlagintweit had made a similar experiment with snow ; but they did not connect with it the applications which suggested themselves to me, and which have since been developed into a theory of glacier-motion.
A section of the mould used in the experiment above referred to is given in the foregoing figure. A n is the solid base of the mould ; c D E F a hollow cylinder let into the base ; P is the solid plug used to compress the snow. When sufficiently squeezed, the bottom, A B, is removed, and the cylinder of ice is pushed out by the plug. The mould closely resembles one of those employed by Professor Helmholtz.
The subsequent development of the subject by the moulding of ice into various forms by pressure is too well known to need dwelling upon here. In applying these results to glaciers, I dwelt with. especial emphasis upon the fact that while the power of being moulded by pressure belonged in an eminent degree to glacier ice, the power of yielding, by stretching, to a force of tension, was sensibly wanting. On this point Prof. Helmholtz speaks as follows : ' Tyndall in particular maintained, and proved by calculation and measurement, that the ice of a glacier does not stretch in the smallest degree when subjected to tension—that when sufficiently strained it always breaks and he adds, in another place, that the property thus revealed establishes ' an essential difference between a stream of ice, and one of lava, tar, honey, or mud.'
In the beautiful experiments of M. Tresca recently executed, the power of ice to mould itself under pressure has been very strikingly illustrated. Professor Helmholtz also, in the presence of his audiences at Heidelberg and Frankfort, illustrated this property in various ways. From snow and broken fragments of ice he formed cakes and cylinders ; and uniting the latter, end to end, he permitted them to freeze together to long sticks of ice. Placing, moreover, in a suitable mould a cylinder of ice of the shape represented in fig. 7, he squeezed it into the cake represented in fig. 8. In fact he corroborated, by a series of striking experimental devices of his os n the results previously obtained by myself.
With regard to the application of these results to the phenomena of glaciers, Professor Helmholtz, after satisfying himself of the insufficiency of other hypotheses, thus finally expresses his conviction : ' I do not doubt that Tyndall has assigned the essential and principal cause of glacier-motion, in referring it to fracture and regelation.'
It is perhaps worth stating that the term ' re-gelation' was first introduced in a paper published by Mr. Huxley and myself more than seven years after the discovery of the fact by Faraday, and that it was suggested to us by our friend Dr. Hooker, . Director of the Royal Gardens at Kew. As already remarked, the formation and motion of glaciers, and other points of a kindred nature, had been referred to regelation long before I occupied myself with the cause of regelation itself. This latter question is not once referred to in the memoir in which the regelation theory was first developed.' The enquiries, though related, were different. In referring the motion of glaciers to a fact experimentally demonstrated, I referred it to its proximate cause. To refer that cause to its physical antecedents formed the subject of a distinct enquiry, in which, because of my belief in the substantial correctness of Faraday's explanation, I took comparatively little part.
Five persons, however, mingled more or less in the enquiry—viz. Professor Faraday, Principal Forbes, Professor James Thomson, Professor (now Sir) William Thomson, and myself.' Professor James Thomson explained regelation by reference to an important deduction, first drawn by him,' and almost simultaneously by Professor Clausius, from the mechanical theory of heat. He had shown it to be a consequence of this theory that the freezing-point of water must be lowered by pressure ; that is to say, water when subjected to pressure will remain liquid at a temperature below that at which it would freeze if the pressure were removed. This theoretic deduction was confirmed in a remarkable manner by the experiments of his brother. Regelation, according to James Thomson's theory, was thus accounted for : 'When two pieces of ice are pressed together, or laid the one upon the other, their compressed parts liquefy. The water thus produced has rendered latent a portion of the heat of the surrounding ice, and must therefore be lower than 0° C. in temperature. On escaping from the pressure this water refreezes and cements the pieces of ice together.
I always admitted that this explanation dealt with a 'true cause.' But considering the infinitesimal magnitude of the pressure sufficient to produce re-gelation, in common with Professor Faraday and Principal Forbes, I deemed the cause an insufficient one. Professor James Thomson, moreover, grounded upon the foregoing theory of regelation a theory of glacier-motion, in which he ascribed the changes of form which a glacier undergoes to the incessant liquefaction of the ice at places where the pressure is intense, and the refreezing, in other positions, of the water thus produced.' I endeavoured to show that this theory was inapplicable to the facts, Professor Helmholtz has recently subjected it to the test of experiment, and the conclusions which he draws from his researches are substantially the same as mine.
Thus, then, as regards the incapacity of the ice on which my observations were made to stretch in obedience to tension, and its capacity to be moulded to any extent by pressure—as regards the essential difference between a glacier, and a stream of lava, honey, or tar—as regards the sufficiency of pressure and regelation to account for the formation of glaciers, and of fracture and regelation to account for their motion—as regards, finally, the insufficiency of the theory which refers the motion to liquefaction by pressure, and refreezing, the views of Professor Helmholtz and myself appear to be identical.
But the case is different with regard to the cause of regelation itself. Here Professor Helmholtz, like M. Jamie, accepts the clear and definite explanation of Professor James Thomson as the most satisfactory that has been advanced ; and he supports this view by an experiment so beautiful that it cannot fail to give pleasure even to those against whose opinions it is adduced. But before passing to the experiment, which is described in the Appendix to the lecture, it will be well to give in the words of Professor Helmholtz the views which he expresses in the body of his discourse.
'You will now ask with surprise,' he says, ' how it is that ice, the most fragile and brittle of all known solid substances, can flow in a glacier like a viscous mass ; and you may perhaps be inclined to regard this as one of the most unnatural and paradoxical assertions that ever was made by a natural philosopher. I will at once admit that the enquirers themselves were in no small degree perplexed by the results of their investigations. But the facts were there, and could not be dissipated by denial. How this kind of motion on the part of ice was possible remained long an enigma—the more so as the known brittleness of ice also manifested itself in glaciers by the formation of numerous fissures. This, as Tyndall rightly maintained, constituted an essential difference between the ice-stream, and a stream of lava, tar, honey, or mud.
' The solution of this wonderful enigma was found —as is often the case in natural science-in an apparently remote investigation on the nature of heat, which forms one of the most important conquests of modern physics, and which is known under the name of the mechanical theory of heat. Among a great number of deductions as to the relations of the most diverse natural forces to each other, the principles of the mechanical theory of heat enable us to draw certain conclusions regarding the dependence of the freezing-point of water on the pressure to which the ice and water are subjected.'
Professor Helmholtz then explains to his audience what is meant by latent heat, and points out that, through the circulation of water in the fissures and capillaries of a glacier, its interior temperature must remain constantly at the freezing-point.
'But,' he continues, ' the temperature of the freezing-point of water can be altered by pressure. This was first deduced by James Thomson, and almost simultaneously by Clausius, from the mechanical theory of heat ; and by the same deductions even the magnitude of the change may be predicted.
For the pressure of every additional atmosphere, the freezing-point sinks 00.0075 C. The brother of the gentleman first named, William Thomson, the celebrated Glasgow physicist, verified experimentally the theoretic deduction by compressing a mixture of ice and water in a suitable vessel. The mixture became colder and colder as the pressure was augmented, and by the exact amount which the mechanical theory of heat required.
If, then, by pressure a mixture of ice and water can be rendered colder without the actual abstraction of heat, this can only occur by the liquefaction of the ice and the rendering of heat latent. And this is the reason why pressure can alter the point of congelation.
In the experiment of William Thomson just referred to ice and water were enclosed in a solid vessel from which nothing could escape. The case is somewhat different when, as in the case of a glacier, the water of the compressed ice can escape through fissures. In this case the ice is compressed, but not the water which escapes. The pressed ice will become colder by a quantity corresponding to the lowering of its freezing-point by the pressure. But the freezing-point of the uncompressed water is not lowered. Here, then, we have ice colder than 0° C. in contact with water at 0° C. The con-sequence 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 (wahrend dafür ein Theil des gepressten Eises fortschmilzt).
This occurs, for instance, when two pieces of ice are simply pressed together. By the water which freezes at the points of contact they are firmly united to a continuous mass. When the pressure is considerable, and the chilling consequently great, the union occurs quickly, but it may also be effected by a very slight pressure if sufficient time be afforded. Faraday, who discovered this phenomenon, named it the vegetation of ice.' Its explanation has given rise to considerable controversy : I have laid that explanation before you which I consider to be the most satisfactory.
In the Appendix, Professor Helmholtz returns to the subject thus handled in the body of his discourse. The theory of the regelation of ice, he observes, ' has given rise to a scientific discussion between Faraday and Tyndall on the one hand, and James and William Thomson on the other. In the text of this lecture I have adopted the theory of the latter, and have therefore to justify myself for so doing.' He then analyses the reasonings on both sides, points out the theoretic difficulties of Faraday's explanation, shows what a small pressure can accomplish if only sufficient time be granted to it, draws attention to the fact that when one piece of ice is placed upon another the pressure is not distributed over the whole of the two appressed surfaces, but is concentrated on a few points of contact. He also holds, with Professor James Thomson, that in an experiment devised by Principal Forbes even the capillary attraction exerted between two plates of ice is sufficient, in due time, to produce regelation. To illustrate the slow action of the small differences of temperature which here come into play Professor Helmholtz made the following experiment, to which reference has been already made.
' A glass flask with a drawn-out neck was half filled with water, which was boiled until all the air above it was driven out. The flask 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. [why ? J. T.], the flask was in the first instance placed in a freezing mixture until the water was changed into ice. It was afterwards permitted to melt slowly in a place the temperature of which was + 2° C., until the half of it was liquefied.
' The flask thus half filled with water having a disk of ice swimming upon it was placed in a mixture of ice and water, being quite surrounded by the mixture. After an hour the disk within the flask was frozen to the glass. By shaking the flask the disk 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 preserved 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 00.0075 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.'
A single additional condition in connection with this beautiful experiment I should like to have seen fulfilled—namely, that the water in which the flask was immersed, as well as that within it, should be purged of its air by boiling. It is just possible that the point of congelation may not be entirely independent of the presence of air in the water.
The revival of this subject by Professor Helmholtz has cased me to make a few additional experiments on the moulding and regelation of ice. The following illustrates both : A quantity of snowy powder was scraped from a block of clear ice and placed in a boxwood mould having a shape like the foot of a claret-glass. The ice-powder being squeezed by a hydraulic press, a clear mass of ice of the shape shown in section at the bottom of fig. 9 was the result. In another mould the same powder was squeezed so as to form small cylinders, three of which are shown separate in fig. 9. A third mould was then employed to form a cup of ice, which is shown at the top of fig. 9. Bringing all the parts into contact, they were cemented through regelation to form the claret-glass sketched in fig.10, from which several draughts of wine might be taken, if the liquid were cooled sufficiently before pouring it into the cup of ice.
There are brass shapes used for the casting of flowers and other objects which answer admirably for experiments on the regelation of ice. One of them was purchased for me by Mr. Becker. Ice-powder squeezed into it regelated to a solid mass and came from the mould in the sharply defined form sketched in fig. 11.
The submerged morsel was so small that the vertical pressure was almost infinitesimal. It froze, not-withstanding, to the under surface of the superior piece of -ice. Two pieces of ice were placed in a basin of warm water, and allowed to come together. They froze as soon as they touched each other. The parts surrounding the place of contact rapidly melted away, but the two pieces continued for a time united by a narrow bridge of ice. The bridge finally melted away, and the pieces were for a moment separated. But bodies which water wets, and against which it rises by capillary attraction, move spontaneously together upon water. The ice morsels did so, and immediately regelation again set in. A new bridge was formed, which in its turn was dissolved, and the pieces closed up as before. Thus a kind of pulsation was kept up by the two pieces of ice. They touched, froze, a bridge was formed and melted, leaving an interval between the pieces. Across this they moved, touched, froze, the same process being repeated over and over again.
We have here the explanation of the curious fact that when several large lumps of ice are placed in warm water and allowed to touch each other, regelation is maintained among them as long as they remain undissolved. The final fragments may not be the one-hundredth part of the original ones in size ; but through the process just described, they incessantly lock themselves together until they finally disappear.
According to Professor James Thomson's theory, to produce regelation the pieces of ice have to exercise pressure, in order to draw from the surrounding ice the heat necessary for the liquefaction of the compressed part; and then this water must escape and be refrozen. All this requires time. In the fore-going experiments, moreover, the water liquefied by the pressure issued into the surrounding warm water, but notwithstanding this the floating fragments regelated in a moment. It is not necessary that the touching surfaces should be flat ; for in this case a film of water might be supposed to exist between them of the temperature 0°C. The surfaces in contact may be convex : they may be virtual points that are about to touch each other, clasped all round by the warm liquid, which is rapidly dissolving them as they approach. Still they freeze immediately when they touch.
There are two points urged by Helmholtz—one in favour of the view he has adopted, and the other showing a difficulty associated with the view of Faraday—on which a few words may be said. 'I found,' says Helmholtz, 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.'
But, according to Faraday's explanation, the strength and quickness of the regelation must also go hand in hand with the magnitude of the pressure employed. Helmholtz rightly dwells upon the fact that the appressed surfaces are usually not perfectly congruent—that they really touch each other in a few points only, the pressure being, therefore, concentrated. Now the effect of pressure exerted on two pieces of ice at a temperature of 0° C. is not only to lessen the thickness of the liquid film between the pieces, but also to flatten out the appressed points, and thus to spread the film over a greater space. On both theories, therefore, the strength and quickness of the regelation ought to correspond to the magnitude of the pressure.
The difficulty referred to above is thus stated by Helmholtz : ' In the explanation given by Faraday, according to which the regelation is caused by a contact action of ice and water, I find a theoretic difficulty. By the freezing of the water a very sensible quantity of heat would be set free ; and it does not appear how this is to be disposed of.'
On the part of those who accept Faraday's explanation, the answer here would be that the free heat is diffused through the adjacent ice. But against this it will doubtless be urged that ice already at a temperature of 0° C. cannot take up more heat without liquefaction. If this be true under all circumstances, Faraday's explanation must undoubtedly be given up. But the essence of that explanation seems to be that the interior portions of a mass of ice require a higher temperature to dissolve them than that sufficient to cause fusion at the surface. When therefore two moist surfaces of ice at the temperature 0° are pressed together, and when, in virtue of the contact action assumed by Faraday, the film of water between them is frozen, the adjacent ice (which is now in the interior, and not at the surface as at first) is in a condition to with-draw by conduction, and without prejudice to its own solidity, the small amount of heat set free. Once granting the contact action claimed by Faraday, there seems to be no difficulty in disposing of the heat rendered sensible by the freezing of the film.
When the year is advanced, and after the ice imported into London has remained a long time in store, if closely examined, parcels of liquid water will be found in the interior of the mass. I enveloped ice containing such water-parcels in tinfoil, and placed it in a freezing mixture until the liquid parcels were perfectly congealed. Removing the ice from the freezing mixture, I placed it, covered by its envelope, in a dark room, and found, after a couple of hours' exposure to a temperature somewhat over 0° C., the frozen parcels again liquid. The heat which fused this interior ice passed through the firmer surrounding ice without the slightest visible prejudice to its solidity. But if the freezing temperature of the ice-parcels be 0° C., then the freezing temperature of the mass surrounding them must be higher than 0° C., which is what the explanation of Faraday requires.
In a quotation at p. 389 I have attached to the description of a precaution taken by Professor Helmholtz the query ' why ?' He states that water freed of its air sinks, without freezing, to a temperature far below 0° C.; while when a piece of ice is in the water it cannot so sink in temperature, but is invariably deposited in the solid form at 0° C. This surely proves ice to possess a special power of solidification over water. It is needless to say that the fact is general—that a crystal of any salt placed in a saturated solution of the salt always provokes crystallisation. Applying this fact to the minute film of water enclosed between two appressed surfaces of ice, it seems to me in the highest degree probable that the contact action of Faraday will set in, that the film will freeze and cement the pieces of ice together.
Apart from the present discussion, the following observation is perhaps worth recording : It is well known that ice during a thaw disintegrates so as to form rude prisms whose axes are at right angles to the planes of freezing. I have often observed this action on a large scale during the winters that I spent as a student on the banks of the Lahn. The manner in which these prisms are in some cases formed is extremely interesting. On close inspection, a kind of cloudiness is observed in the interior of a mass of apparently perfect ice. Looked at through a strong lens, this cloudiness appears as striae at right angles to the planes of freezing, and when the direction of vision is across these planes the ends of the striae are apparent. The spaces between the striae are composed of clear unclouded ice When duly magnified, the objects which produce the striae turn out to be piles of minute liquid flowers, whose planes are at right angles to the direction of the striae.
Since writing the above, I have been favoured with a copy of a discourse delivered by Professor De la Rive, at the opening of the forty-ninth meeting of the Société Helyétique, which assembled in 1865 at Geneva. From this admirable résumé of our present knowledge regarding glaciers I make the following extract, which, together with those from the lecture of Helmholtz, will show sufficiently how the subject is now regarded by scientific men: 'Such, gentlemen,' says M. De la Rive, ' is a description of the phenomena of glaciers, and it now remains to explain them, to consult observation, and deduce from it the fundamental character of the phenomena. Observation teaches us that gravity is the motive force, and that this force acts upon a solid body—ice—imparting to it a slow and continuous motion. What are we to conclude from this ? That ice is a solid which possesses the property of flowing like a viscous body—a conclusion which appears very simple, but which was nevertheless announced for the first time hardly five-and-twenty years ago by one of the most distinguished philosophers of Scotland, Professor James D. Forbes. This theory, for it truly is a theory, basing itself on facts as numerous as they are well observed, enunciates the principle that ice possesses the characteristic properties which belong to plastic bodies. Although he did not directly prove it, to Professor Forbes belongs not the less the great merit of insisting on the plasticity of ice, before Faraday, in discovering the phenomenon of regelation, enabled Tyndall to prove that the plasticity was real, at least partially.
' The experiment of Faraday is classical in connexion with our subject. It consists, as you knew, in this, that if two morsels of ice be brought into contact in water, which may be even warm, they freeze together. Tyndall immediately saw the application of Faraday's experiment to the theory of glaciers ; he comprehended that, since pieces of ice could thus solder themselves together, the substance might be broken, placed in a mould, compressed, and thus compelled to take the form of the cavity which contained it. A wooden mould, for example, embraces a spherical cavity ; placing in it fragments of ice and squeezing them, we obtain an ice sphere ; placing this sphere in a second mould with a lenticular cavity and pressing it, we transform the sphere into a lens. In this way we can impart any form whatever to ice.
Such is the discovery of Tyndall, which may well be thus named, particularly in view of its consequences. For all these moulds magnified become the borders of the valley in which a glacier flows. Here the action of the hydraulic press which has served for the experiments of the laboratory is re-placed y the weight of the masses of snow and ice collected on the summits, and exerting their pressure on the ice which descends into the valley. Supposing, for example, between the spherical mould and the lenticular one, a graduated series of other moulds to exist, each of which differs very little from the one which precedes and from that which follows it, and that a mass of ice could be made to pass through all these moulds in succession, the phenomenon would then become continuous. Instead o rudely breaking, the ice would be compelled to change by insensible degrees from the spherical to the lenticular form. It would thus exhibit a plasticity which might be compared to that of soft wax. But ice is only plastic under pressure ; it is not plastic under tension : and this is the important point which the vague theory of plasticity was unable to explain. While a viscous body, like bitumen or honey, may be drawn out in filaments by tension, ice, far from stretching in this way, breaks like glass under this action. These points well established by Tyndall, it became easy for him to explain the mechanism of glaciers, and by the aid of an English geometer, Mr. William Hopkins, to show how the direction of the crevasses of a glacier are the necessary consequences of its motion.'
I have quite recently had a mould constructed for me by Mr. Becker,' and yesterday (November 16, 1865) made with it an experiment which, on account of the ease with which it may be performed, will interest all those who care about exhibiting in a striking and instructive manner the effects of regelation.
The mould is shown in fig. 12. It consists of two pieces of cast iron, A B C and D F G, slightly wedge-shaped and held together by the iron rectangle R B which is slipped over them. The inner face of A B c is shown in fig. 13. In it is hollowed out a semi-ring m N, with a semicylindrical passage o leading into it. The inner face of D F G is similarly hollowed out, so that when both faces are placed together, as in fig. 12, they enclose a ring 4 inches in external diameter, from m to N, and f of an inch in thickness, with the passage o, 1 inch in diameter, into which fits the polished iron plug r. At q and r, fig. 13, are little pins which, fitting into holes corresponding to them, keep the slabs A B C and D F G from sliding over each other.
The mould being first cooled by placing it for a short-time in a mixture of ice and water, fragments of ice are stuffed into the orifice o and driven down with a hammer by means of the plug p. The bruised and broken ice separates at x, one portion going to the right, the other to the left. Driving the ice thus into the mould, piece after piece, it is finally filled By removing the rectangle R E, the two halves of the mould are then separated, and a perfect ring of ice is found within. Two such rings soldered by regelation at a are shown in fig. 14. It would be easy thus to construct a chain of ice. An hydraulic press may of course be employed in this experiment, but it is not necessary; with the hammer and plug beautiful rings of ice are easily obtained by the regelation of the crushed fragments.
I have now to add the description of an experiment which suggested itself to my ingenious friend Mr. Duppa, when he saw the ice-rings just referred to, and which was actually executed by him yesterday (the 16th) in the laboratory of the Royal Institution. Pouring a quantity of plaster of paris into a proper vessel, an ice-ring was laid upon the substance, an additional quantity of the cement being then poured over the ring. The plaster ' set,' enclosing the ring within it : the ring soon melted, leaving its perfect matrix behind. The mould was permitted to dry, and, molten lead being poured into the space previously occupied by the ice, a leaden ring was produced. Now ice can be moulded into any shape : statuettes, vases, flowers, and innumerable other ornaments can be formed from it. These enclosed in cement, in the manner suggested by Mr. Duppa, remain intact sufficiently long to enable the cement to set around them ; they afterwards melt and disappear, leaving behind them perfect plaster moulds, from which casts can be taken.