From William Hopkins   Jan. 29/61

22 Grand Parade, | Brighton. | Jan. 29/61

Dear Tyndall,

I have just been reading the review of “Forbes & Tyndall” in the Edinburgh¹—a holy alliance I scarcely expected to see cemented in the North. The whole tone is marvelously modified from the former denunciations which have hitherto proceeded from that quarter against every opponent of Viscosity. The viscous theory² is in fact departed. The claim for a presentiment on the part of Forbes of the property of ice made out by Faraday and yourself is simply ludicrous. The reviewer, too, effectively gives up Forbes’s theory of the veined structure, though not venturing to state the real reason why it cannot possibly be maintained. How Forbes will like this I don’t know because it is quite certain that it was the part of his theory on which he prided himself most. I suppose I have the honor of the reviewer’s notice as ‘an ingenious critic’ in the note on the sliding of glaciers (p. 323) where he makes the absurd assertion that the surface of a glacier would move very nearly in the same way whether it should adhere to its bed or not. Even Forbes never dared to make this assertion. How singularly unjust those northern reviewers are to Agassiz.³ The ‘Nouvelles Etudes’⁴ of the latter are but just noticed, and yet for details of glacial phenomena there is nothing at all comparable to it. I have no idea who the reviewer is. Can you tell me? He seems to me to be standing forth as a sort of mediator with the olive branch in his hand, and I should rather infer that Forbes himself may intend to withdraw from further controversy within the dignity of his new station at St. Andrews.⁵

But we must not suppose that because certain of Forbes’s theories may be passing away, the theory of glacier motion is complete. There are one or two points to which I wish to draw your attention.

There is a fallacy or misrepresentation which has pervaded all that Forbes and others have written on the points to which it relates. When glacial ice conforms itself to the contracted form of the glacial valley, it must of course do so by virtue of a certain degree of plasticity, which it displays in consequence of the enormous compressing forces both a tergo⁶ and laterally to which it is necessarily subjected in such cases. This is the kind of plasticity which is common in a greater or less degree to all solid bodies. Now it has been always tacitly assumed that admitting this degree of plasticity in glacial ice, a glacier if placed on a smooth level plane would be crushed, or squeezed out, by its own weight so as to produce in it a lateral motion; or in other words, its component molecules instead of remaining fixed with respect to each other would move inter se, and the cohesive power be entirely overcome. Now this would certainly not be necessarily the case for that degree of plasticity which would allow a glacier to be squeezed into a narrower portion of its valley; and one obvious reason is this—that we may conceive the force à tergo in this squeezing process, to be much greater than the crushing weight of the superincumbent mass in the case in which the lateral motion is produced. This last case might require a much greater degree of plasticity, or a nearer approach to viscidity than the other. Now it is asserted (as in the note above alluded to in the review) that there could be no sliding without plasticity, by which it is here (as it is usually) meant, without that degree of plasticity which would under the ordinary conditions of a glacier, be an independent cause of continuous motion. Forbes obviously never admitted the notion of a solid body with a certain amount of compressibility; but glacial ice, according to his views, was either rigid, or possessed a degree of plasticity which implied a molecular cohesion sufficiently feeble to be overcome entirely by the crushing superincumbent weight of the upper portions of the glacial mass, and this not only in the deeper portions of the mass, cut in nearly all portions of it generally. Now I maintain, on the contrary, that there may be, and probably is a wide interval between that degree of plasticity (compressibility) which may admit of a glacier being squeezed into a smaller volume, and that degree of plasticity (approximate viscosity) which, under the pressure to which a glacier at rest and without any sliding motion, would be commonly subjected, would be an independent cause of continuous progressive motion. But let us consider the different forces which exert a tendency to crack and break the glacial mass, with the view of ascertaining which are the most important.

The external force producing an active tendency to dislocate the mass is that of gravity or the weight of the mass. Resistance arising from friction on projecting obstacles being considered to act as it were, passively. Let us take as the approximate type and for the simplicity of explanation, a glacier descending a canal shaped glacier at a constant inclination (α) to the horizon, α being small. We may resolve the weight (W) of the glacier into W sin α parallel to the bottom of the valley and W cos α perpendicular to it. The tendency of the latter force will be to crush the mass, or rather its lower parts, by the superincumbent weight of the upper portion. I much doubt, however, whether this tendency can ever be very considerable. For suppose we could, for instance, remove Mont Blanc, and form for it a new pedestal by a horizontal stratum of crystalline limestone, and replace the mountain upon it. The limestone I imagine would be crushed and its crystalline structure destroyed. But if a bed of limestone had been originally found there and gradually hardened and crystallized under its mountain load, that same load would not suffice to crush it again. And so with glacier ice. In all those parts of a glacier on which the principal observations on its motion have been made, the ice must have been generally crystallized under a greater superincumbent weight than that to which it can be subsequently exposed. It is for this reason that I doubt much whether the superincumbent portion of a glacial mass can ever produce, by the compressing force (W cos α) of its weight alone, any material effect in crushing the subsequent portion.

Let us next consider what the force W sin α acting parallel to the bed of the glacier will do—i.e. supposing the previous absence of any internal constraint, what tendency will this force exert to crack and break the mass. And first let us suppose the mass to have the same amount of cohesion to the sides and bottom of the glacial valley as the constituent particles of the ice have to each other. Then in consequence of the supposed degree of plasticity of the mass, the force now considered (W sin α) will move the upper portion more than the lower, and the central more than the lateral parts, and thus the general form of the mass will be changed, and every part of it will be brought into a state of internal constraint; i.e. it will be subjected to internal pressure and tension tending to tear and crush it. By this means a plane transverse section of a glacier will be made to bulge forward into a curved surface, but it is manifest that the general tendency to produce this effect will be partly counteracted by the adhesion to the bed of the valley, and this counteracting force will be very large. But now let us conceive the adhesion to the bottom of the valley to be destroyed, while that on the flanks to the sides of the valley still remains. The bulging forward of our original plane transverse section will now be as great at the lower as at the upper surface of the glacier, and the whole of the internal pressure and tension produced in this case, and arising from the deformation of the general mass, will obviously be much greater than in the preceding case, on account of the removal of the opposing force of cohesion to the bottom of the valley. This is in fact the case in which the form W sin α would exert its maximum tendency to rupture the mass. It would act at the same kind of mechanical advantage in breaking the ice as that with which one acts when one places a stick against one’s knee and pulls at both ends to break it.

If the adhesion to the sides of the valley or the obstacles it affords to the motion be considerably smaller than here supposed, but still sufficient to impede the motion of the flanks compared with the centre, the reasoning and conclusion will be still the same.

You will recollect that my early experiment on the uniform sliding of ice down an inclined plane, showed that the statical form of friction, or that exerted to impede (not the accelerated but) the uniform motion, was extremely small, so that the second of the above cases modified as in the preceding paragraph, will be the type of the actual case of a glacier which (as I suppose to be admitted) does slide over its bed. It is to the wide difference between the tendencies to rupture the mass in the two cases above discussed that I want to direct your special attention. In the case of the glacier sliding you will observe that a very large portion of the force W sin α is employed in deforming the glacier and therefore in rending and compressing it, whereas in the case of the glacier not sliding, the force employed in the same work is only the difference between W sin α and the effect of cohesion to the bed of the glacier (which must be nearly equal to W sin α and therefore only a comparatively small portion of W sin α is effective).

Hence if a glacier slide over its bed, and slide faster in the central than in the lateral portions there will be a force always tending to produce the crevasses, together with the minuter cracks and fissures which your theory of regelation, requires, indefinitely greater than if the glacier were attached to its bed by the same cohesion as that by which one part is attached to another. According to this view sliding and regelation are the essential parts of the same true glacial theory. We have nothing to do with the inconceivable property of viscosity in ice. On the contrary, according to this theory it cracks and breaks as one would suppose a brittle substance to do in an infinite variety of ways, and thus obtains its freedom of motion, while all its broken bones become healed and united again by the happy process of regelation.

By similar reasoning we see that when a glacier is forced thro’ a gorge where its motion is retarded, there will be an enormous pressure acting on it à tergo, and very much greater than if the glacier did not slide pretty freely over its bed. Mere local obstacles on the sides of the valley will be as nothing to arrest the motion of the glacier under such circumstances. The ice will only be broken the more and pass on.

There is a glacial yarn for you. Examine it carefully to see if there be any flaws in it. If not I am disposed to think that it will render the theory of glacier motion pretty nearly complete as to the sufficiency of the causes assigned for it. Still experiment may do something more in pointing out the modus operandi in breaking and crushing the ice. Will it yield first to the internal tensions or to the crushing power of the internal pressures (by the bye those produced by the distortion of the mass will probably be much greater than those produced by the weight of any superincumbent on a subjacent portion) Or will the mass yield as Forbes supposes (not assuredly in the directions he supposes) by one vertical slice sliding past another? Experiment might tell us a good deal on these points. I will suggest two or three

Suppose two vessels A and B were filled with water

and placed with their open ends in contact at C. If the water

were completely frozen and the vessel A were firmly fixed

vertically, what weight suspended to B would be just sufficient to pull the vessels asunder. This would give the power of the ice to resist tension. Its extensibility might also be measured in some similar manner probably.

Possibly you may have made some experiments of this kind.

Again supposing A to be firmly fixed as before and the axes of the two vessels in the same vertical line, what force applied to B horizontally would be sufficient to rupture the ice along the section at C by making the ice in B slide horizontally past that in A. This would determine the amount of the tangential force of cohesion, as the former experiment would give the normal force of cohesion. Again if we take a short cylinder of ice what pressure would be required to crush it? What would it be also if the cylinder of ice were congeled under great pressure? as in some of your experiments.

Such experiments would probably enable us to give a very explicit answer to the question—how would the ice yield to the above forces acting upon it? Would it as I have already asked, be crushed by its own weight, or by the internal pressure superinduced by the unequal motions of the sides and centre? or would it rather yield to the superinduced internal tensions? or rather by one portion sliding past another according to Forbes’s notion?

Can you make some such experiments as those suggested?⁷ You might present them to the Royal Society as a fitting supplement to your former communications; and I would also write a short memoir⁸ embodying my present views, with such remarks as I might deem necessary on opposing views, and as such as might be made without giving too much of a controversial character to the communication. It would at all events be no more than Forbes’s paper in the Royal Transactions.⁹

My knee has made so little progress of late¹⁰ that I have been induced to come here to place myself under the great bone quack Harrop.¹¹ He promises much, but how he will perform I have not yet had the time to determine.

I began this long epistle several days ago, but have not had time to finish it till today (Feb. 3).

Believe me | Yours very truly | W. Hopkins.

RI MS JT/1/TYP/2/633–8

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