seen advanced to the contrary can, so far as I perceive, overturn Mr. Moseley's conclusion, that the glacier cannot descend by its weight only. The interesting experiment described by Mr. Mathews*, of a plank of ice supported horizontally at each end being deflected in the middle without any weight being applied to the ice, does not appear to me to prove any thing either in favour of the generally received theory or against Canon Moseley's conclusion, -for this very simple reason, that whatever theory we may adopt as to the cause of the motion of glaciers, the deflection of the plank in the way described by Mr. Mathews follows as a necessary consequence. Although no weight was placed upon the plank, it does not necessarily follow that the deflection was caused by the weight of the ice alone; for, according to Canon Moseley's own theory of the motion of glaciers by heat, the plank ought to be deflected in the middle, just as it was in Mr. Mathews's experiment. A solid body, when exposed to variations of temperature, will expand and contract transversely as well as longitudinally. Ice, according to Canon Moseley's theory, expands and contracts by heat. Then if the plank expands transversely, the upper half of the plank must rise and the lower half descend. But the side which rises has to perform work against gravity, whereas the side which descends has work performed upon it by gravity; consequently more of the plank will descend than rise, and this will, of course, tend to lower or deflect the plank in the middle. Again, when the plank contracts, the lower half will rise and the upper half will descend; but as gravitation, in this case also, favours the descending part and opposes the rising part, more of the plank will descend than rise, and consequently the plank will be lowered in the middle by contraction as well as by expansion. Thus, as the plank changes its temperature, it must, according to Mr. Moseley's theory, descend or be deflected in the middle, step by step-and this not by gravitation alone, but chiefly by the motive power of heat. I do not, of course, mean to assert that the descent of the plank was thus actually caused by heat; but I assert that Mr. Mathews's experiment does not necessarily prove (and this is all that is required in the mean time) that gravitation alone was the cause of the deflection of the plank. Neither does this experiment prove that the ice was deflected without shearing; for although the weight of the plank was not sufficient to shear the ice, as Mr. Mathews, I presume, admits, yet Mr. Moseley would reply that the weight of the ice, assisted by the motive power of heat, was perfectly sufficient.

Had Mr. Mathews laid his plank horizontally across an inclined plane and fixed the two ends of the plank so as to prevent them * Alpine Journal for February 1870; Nature' for March 24, 1870.

moving, everybody (whatever might be his theory as to the cause of the motion of glaciers) would at once admit that the middle of the plank (which, of course, was not fixed) would begin slowly to descend the incline in the manner that the ice of a glacier actually does, and that the plank, not being permitted to move at its ends, would become bent or deflected in the middle. Then, if everybody would admit that the plank would be deflected in the middle notwithstanding the friction of the ice on the inclined plane, and the diminished pressure of the weight of the ice in consequence of its resting on the slope, surely no one could conclude that, were the inclined plane removed and the plank suspended in the air by its two extremities, as in Mr. Mathews's experiment, it would not descend in the middle.

I shall now briefly refer to Mr. Ball's principal objections to Canon Moseley's proof that a glacier cannot shear by its weight alone. One of his chief objections is that Mr. Moseley has assumed the ice to be homogeneous in structure, and that pressures and tensions acting within it are not modified by the varying constitution of the mass. Although there is, no doubt, some force in this objection (for we have probably good reason to believe that ice will shear, for example, more easily along certain planes than along others), still I can hardly think that Canon Moseley's main conclusion can ever be materially affected by this objection. The main question is this, Can the ice of the glacier shear by its own weight in the way generally supposed? Now the shearing-force of ice, take it in whatever direction we may, so enormously exceeds that required by Mr. Moseley in order to allow a glacier to descend by its weight only, that it is a matter of indifference whether ice be regarded as homogeneous in structure or not. Mr. Ball objects also to Mr. Moseley's imaginary glacier lying on an even slope and in a uniform rectangular channel. Surely Mr. Ball does not suppose that a glacier would descend more easily in an irregular and broken channel having a variable slope and direction than it would do in a straight channel uniform in width and slope. And if he does not, why advance such an objection? Canon Moseley assumed, as he had a perfect right to do, that if the glacier could not descend by its weight in his imaginary channel, it could much less do so in its actual one.

That a relative displacement of the particles of the ice is involved in the motion of a glacier, is admitted, of course, by Mr. Ball; but he states that the amount of this displacement is but small, and that it is effected with extreme slowness. This may be the case; but if the weight of the ice be not able to overcome the mutual cohesion of the particles, then the weight of the ice cannot produce the required displacement, however small it may be. Mr. Ball then objects to Mr. Moseley's method of determin

ing the unit of shear on this ground:-The shearing of the ice in a glacier is effected with extreme slowness; but the shearing in Canon Moseley's experiment was effected with rapidity; and although it required 75 lbs. to shear one square inch of surface in his experiment, it does not follow that 75 lbs. would be required to shear the ice if done in the slow manner in which it is effected in the glacier. "In short," says Mr. Ball, "to ascertain the resistance opposed to very slow changes in the relative positions of the particles, so slight as to be insensible at short distances, Mr. Moseley measures the resistance opposed to rapid disruption between contiguous portions of the same substance."

There is force in this objection; and here we arrive at a really weak point in Canon Moseley's reasoning. His experiments show that if we want to shear ice quickly a weight of nearly 120 lbs. is required; but if the thing is to be done more slowly, 75 lbs. will suffice*. In short, the number of pounds required to shear the ice depends to a large extent on the length of time that the weight is allowed to act; the longer it is allowed to act, the less will be the weight required to perform the work. "I am curious to know," says Mr. Mathews when referring to this point, "what weight would have sheared the ice if a day had been allowed for its operation." I do not know what would have been the weight required to shear the ice in Mr. Moseley's experiments had a day been allowed; but I feel pretty confident that, should the ice remain unmelted, and sufficient time be allowed, shearing would be produced without the application of any weight whatever. There are no weights placed upon a glacier to make it move, and yet the ice of the glacier shears. If the shearing is effected by weight, the only weight applied is the weight of the ice; and if the weight of the ice makes the ice shear in the glacier, why may it not do the same thing in the experiment? Whatever may be the cause which displaces the particles of the ice in a glacier, they, as a matter of fact, are displaced without any weight being applied beyond that of the ice itself; and if so, why may not the particles of the ice in the experiment be also displaced without the application of weights? Allow the ice of the glacier to take its own time and its own way, and the particles will move over each other without the aid of external weights, whatever may be the cause of this; well, then, allow the ice in the experiment to take its own time and its own way, and it will probably do the same thing. There is something here unsatisfactory. If, by the unit of shear, be meant the pressure in pounds that must be applied to the ice to break the connexion of one square inch of two surfaces frozen together and

* Philosophical_Magazine for January 1870, p. 8; Proceedings of the Royal Society for January 1869.

cause the one to slip over the other, then the amount of pressure required to do this will depend upon the time you allow for the thing being done. If the thing is to be done rapidly, as in some of Mr. Moseley's experiments, it will take, as he has shown, a pressure of about 120 lbs. ; but if the thing has to be done more slowly, as in some other of his experiments, 75 lbs. will suffice. And if sufficient time be allowed, as in the case of glaciers, the thing may be done without any weight whatever being applied to the ice, and, of course, Mr. Moseley's argument, that a glacier cannot descend by its weight alone, falls to the ground. But if, by the unit of shear, be meant not the weight or pressure necessary to shear the ice, but the amount of work required to shear a square inch of surface in a given time or at a given rate, then he might be able to show that in the case of a glacier (say the Mer de Glace) the work of all the resistances which are opposed to its descent at the rate at which it is descending is greater than the work of its weight, and that consequently there must be some cause, in addition to the weight, urging the glacier forward. But then he would have no right to affirm that the glacier would not descend by its weight only; all that he could affirm would simply be that it could not descend by its weight alone at the rate at which it is descending.

Mr. Moseley's unit of shear, however, is not the amount of work performed in shearing a square inch of ice in a given time, but the amount of weight or pressure requiring to be applied to the ice to shear a square inch. But this amount of pressure depends upon the length of time that the pressure is applied. Here lies the difficulty in determining what amount of pressure is to be taken as the real unit. And here also lies the radical

defect in Canon Moseley's result. Time as well as pressure enters as an element into the process. The key to the explanation of this curious circumstance will, I think, be found in the fact to which reference has already been made, viz. that the rate at which a glacier descends depends in some way or other upon the amount of heat that the ice is receiving. This fact shows that heat has something to do in the shearing of the ice of the glacier. But in the communication of heat to the ice time necessarily enters as an element. There are two different ways in which heat may be conceived to aid in shearing the ice: (1) we may conceive that heat acts as a force along with gravitation in producing displacement of the particles of the ice; or (2) we may conceive that heat does not act as a force in pushing the particles over each other, but that it assists the shearing processes by diminishing the cohesion of the particles of the ice, and thus allowing gravitation to produce displacement. The former is the function attributed to heat in Canon Moseley's theory of glacier

motion; the latter is the function attributed to heat in the theory of glacier-motion which I ventured to advance some time ago*. It results, therefore, from Canon Moseley's own theory, that the longer the time that is allowed for the pressure to shear the ice, the less will be the pressure required; for, according to his theory, a very large proportion of the displacement is produced by the motive power of heat entering the ice; and, as it follows of course, other things being equal, the longer the time during which the heat is allowed to act, the greater will be the proportionate amount of displacement produced by the heat; consequently the less will require to be done by the weight applied. In the case of the glacier, Mr. Moseley concludes that at least thirty or forty times as much work is done by the motive power of heat in the way of shearing the ice as is done by mere pressure or weight. Then, if sufficient time be allowed, why may not far more be done by heat in shearing the ice in his experiment than by the weight applied? In this case how is he to know how much of the shearing is effected by the heat and how much by the weight. If the greater part of the shearing of the ice in the case of a glacier is produced, not by pressure, but by the heat which necessarily enters the ice, it would be inconceivable that in his experiments the heat entering the ice should not produce, at least to some extent, a similar effect. And if a portion of the displacement of the particles is produced by heat, then the weight which is applied cannot be regarded as the measure of the force employed in the displacement, any more than it could be inferred that the weight of the glacier is the measure of the force employed in the shearing of it. If the weight is not the entire force employed in shearing, but only a part of the force, then the weight cannot, as in Mr. Moseley's experiment, be taken as the measure of the force.

How, then, are we to determine what is the amount of force required to shear ice? in other words, how is the unit of shear to be determined? If we are to measure the unit of shear by the weight required to produce displacement of the particles of the ice, we must make sure that the displacement is wholly effected by the weight. We must be certain that heat does not enter as an element in the process. But if time be allowed to elapse during the experiment, we can never be certain that heat has not been at work. It is impossible to prevent heat entering the ice. We may keep the ice at a constant temperature, but this would not prevent heat from entering the ice and producing molecular work. True that, according to Moseley's theory of glacier-motion, if the temperature of the ice be not permitted to vary, then no displacement of the particles can take place from * Philosophical Magazine for March 1869.