PROF. J. D. FORBES INVITED.
M. Agassiz is a naturalist, and he appears to have devoted but little attention to the study of physics. At all events, the physical portions of his writings appear to me to be very often defective. It was probably his own consciousness of this deficiency that led him to invoke the advice of Arago and others previous to setting out upon his excursions. It was also his desire "to see a philosopher so justly celebrated occupy himself with the subject," which induced him to invite Prof. J. D. Forbes of Edinburgh to be his guest upon the Aar glacier in 1841. On the 8th of August they met at the Grimsel Hospice, and for three weeks afterwards they were engaged together daily upon the ice, sharing at night the shelter of the same rude roof. It is in reference to this visit that Prof. Forbes writes thus at page 38 of the 'Travels in the Alps':—"Far from being ready to admit, as my sanguine companions wished me to do in 1841, that the theory of glaciers was complete, and the cause of their motion certain, after patiently hearing all they had to say and reserving my opinion, I drew the conclusion that no theory which I had then heard of could account for the few facts admitted on all hands." In 1842 Prof. Forbes repaired, as early as the state of the snow permitted, to the Mer de Glace; he worked there, in the first instance, for a week, and afterwards crossed over to Courmayeur to witness a solar eclipse. The result of his week's observations was immediately communicated to Prof. Jameson, then editor of the 'Edinburgh New Philosophical Journal.'
CENTRE MOVES QUICKEST.
In that letter he announces the fact, but gives no details of the measurement, that "the central part of the glacier moves faster than the edges in a very considerable proportion;quite contrary to the opinion generally entertained." He also announced at the same time the continuous hourly advance of the glacier. This letter bears the date, "Courmayeur, Piedmont, 4th July," but it was not published until the month of October following.
Meanwhile M. Agassiz, in company with M. Wild, returned to complete his experiment upon the glacier of the Aar. On the 20th of July, 1842, the displacements of the six piles which he had planted the year before were determined by means of a theodolite. Of the three upon the Finsteraar affluent, that nearest the side had moved 160 feet, the next 225 feet, while that nearest to the centre had moved 269 feet. Of those on the Lauteraar, that nearest the side had moved 125 feet, the next 210 feet, and that nearest the centre 246 feet. These observations were perfectly conclusive as to the quicker motion of the centre: they embrace a year's motion; and the magnitude of the displacements, causing errors of inches, which might seriously affect small displacements, to vanish, justifies us in ranking this experiment with the most satisfactory of the kind that have ever been made. The results were communicated to Arago in a letter dated from the glacier of the Aar, on the 1st of August, 1842; they were laid before the Academy of Sciences on the 29th of August, 1842, and are published in the 'Comptes Rendus' of the same date.
The facts, then, so far as I have been able to collect them, are as follows:—M. Agassiz commenced his experiment about ten months before Professor Forbes, and the results of his measurements, with quantities stated, were communicated to the French Academy about two months prior to the publication of the letter of Professor Forbes in the 'Edinburgh Philosophical Journal.' But the latter communication, announcing in general terms the fact of the speedier central motion, was dated fromCourmayeur twenty-seven days before the date of M. Agassiz's letter from the glacier of the Aar.
STATE OF THE QUESTION.
The speedier motion of the central portion of a glacier has been justly regarded as one of cardinal importance, and no other observation has been the subject of such frequent reference; but the general impression in England is that M. Agassiz had neither part nor lot in the establishment of the above fact; and in no English work with which I am acquainted can I find any reference to the above measurements. Relying indeed upon such sources for my information, I remained ignorant of the existence of the paper in the 'Comptes Rendus' until my attention was directed to it by Professor Wheatstone. In the next following chapters I shall have to state the results of some of my own measurements, and shall afterwards devote a little time to the consideration of the cause of glacier-motion. In treating a question on which so much has been written, it is of course impossible, as it would be undesirable, to avoid subjecting both my own views and those of others to a critical examination. But in so doing I hope that no expression shall escape me inconsistent with the courtesy which ought to be habitual among philosophers or with the frank recognition of the just claims of my predecessors.
MY FIRST OBSERVATION.
On Tuesday, the 14th of July, 1857, I made my first observation on the motion of the Mer de Glace. Accompanied by Mr. Hirst I selected on the steep slope of the Glacier des Bois a straight pinnacle of ice, the front edge of which was perfectly vertical. In coincidence with this edge I fixed the vertical fibre of the theodolite, and permitted the instrument to stand for three hours. On looking through it at the end of this interval, the cross hairs were found projected against the white side of the pyramid; the whole mass having moved several inches downwards.
The instrument here mentioned, which had long been in use among engineers and surveyors, was first applied to measure glacier-motion in 1842; by Prof. Forbes on the Mer de Glace, and by M. Agassiz on the glacier of the Aar. The portion of the theodolite made use of is easily understood. The instrument is furnished with a telescope capable of turning up and down upon a pivot, without the slightest deviation right or left; and also capable of turning right or left without the slightest deviation up or down. Within the telescope two pieces of spider's thread, so fine as to be scarcely visible to the naked eye, are drawn across the tube and across each other. When we look through the telescope we see these fibres, their point of intersection being exactly in the centre of the tube; and the instrument is furnished with screws by means of which this point can be fixed upon any desired object with the utmost precision.
MODE OF MEASUREMENT.
In setting a straight row of stakes across the glacier, our mode of proceeding was in all cases this:—The theodolite was placed on the mountain-side flanking the glacier, quite clear of the ice; and having determined the direction of a line perpendicular to the axis of the glacier, a well-defined object was sought at the opposite side of the valley as close as possible to this direction; the object being, in some cases, the sharp edge of a cliff; in others, a projecting corner of rock; and, in others, a well-defined mark on the face of the rock. This object and those around it were carefully sketched, so that on returning to the place it could be instantly recognized. On commencing a line the point of intersection of the two spiders' threads within the telescope was first fixed accurately upon the point thus chosen, and an assistant carrying a straight bâton was sent upon the ice. By rough signalling he first stood near the place where the first stake was to be driven in; and the object end of the telescope was then lowered until he came within the field of view. He held his staff upright upon the ice, and, in obedience to signals, moved upwards or downwards until the point of intersection of the spiders-threads exactly hit the bottom of the bâton; a concerted signal was then made, the ice was pierced with an auger to a depth of about sixteen inches, and a stake about two feet long was firmly driven into it. The assistant then advanced for some distance across the glacier; the end of the telescope was now gently raised until he and his upright staff again appeared in the field of view. He then moved as before until the bottom of his staff was struck by the point of intersection, and here a second stake was fixed in the ice. In this way the process was continued until the line of stakes was completed.
Before quitting the station, a plummet was suspended from a hook directly underneath the centre of the theodolite,and the place where the point touched the ground was distinctly marked. To measure the motion of the line of stakes, we returned to the place a day or two afterwards, and by means of the plummet were able to make the theodolite occupy the exact position which it occupied when the line was set out. The telescope being directed upon the point at the opposite side of the valley, and gradually lowered, it was found that no single stake along the line preserved its first position: they had all shifted downwards. The assistant was sent to the first stake; the point which it had first occupied was again determined, and its present distance from that point accurately measured. The same thing was done in the case of each stake, and thus the displacement of the whole row of stakes was ascertained.[A]The time at which the stake was fixed, and at which its displacement was measured, being carefully noted, a simple calculation determinedthe daily motionof the stake.
THE FIRST LINE.
Thus, on the 17th of July, 1857, we set out our first line across the Mer de Glace, at some distance below the Montanvert; on the day following we measured the progress of the stakes. The observed displacements are set down in the following table:—
First Line.—Daily Motion.
No. of stake.Inches.West1moved121/42"163/43"221/24"...5"241/26moved...7"261/48"...9"283/410"351/2East.
THE CENTRE-POINT NOT THE QUICKEST.
The theodolite in this case stood on the Montanvert side of the valley, and the stakes are numbered from this side. We see that the motion gradually augments from the 1st stake onward—the 1st stake being held back by the friction of the ice against the flanking mountain-side. The stakes 4, 6, and 8 have no motion attached to them, as an accident rendered the measurement of their displacements uncertain. But one remarkable fact is exhibited by this line; the 7th stake stood upon themiddleof the glacier, and we see that its motion is by no means the quickest; it is exceeded in this respect by the stakes 9 and 10.
The portion of the glacier on which the 10th stake stood was very much cut up by crevasses, and, while the assistant was boring it with his auger, the ice beneath him was observed, through the telescope, to slide suddenly forward for about 4 inches. The other stakes retained their positions, so that the movement was purely local. Deducting the 4 inches thus irregularly obtained, we should have a daily motion of 311/2inches for stake No. 10. The place was watched for some time, but the slipping was not repeated; and a second measurement on the succeeding day made the motion of the 10th stake 32 inches, whilst that of the centre of the glacier was only 27.
Here, then, was a fact which needed explanation; but, before attempting this, I resolved, by repeated measurements in the same locality, to place the existence of the fact beyond doubt. We therefore ascended to a point upon the old and now motionless moraine, a little above the Montanvert Hotel; and choosing, as before, a well-defined object at the opposite side of the valley, we set between it and the theodolite a row of twenty stakes across the glacier. Their motions, measured on a subsequent day, and reduced to their daily rate, gave the results set down in the following table:—
Second Line.—Daily Motion.
No. of stake.Inches.West1moved71/22"103/43"121/44"141/25"166"163/47"171/28"199"191/210"2111moved2112"221/213"2114"221/215"201/216"213/417"221/418"251/419"...20"253/4East.
CORROBORATIVE MEASUREMENTS.
As regards the retardation of the side, we observe here the same fact as that revealed by our first line—the motion gradually augments from the first stake to the last. The stake No. 20 stood upon the dirty portion of the ice, which was derived from the Talèfre tributary of the Mer de Glace, and far beyond the middle of the glacier. These measurements, therefore, corroborate that made lower down, as regards the non-coincidence of the point of swiftest motion with the centre of the glacier.
But it will be observed that the measurements do not show any retardation of the ice at the eastern extremity of the line of stakes—the motion goes on augmenting from the first stake to the last. The reason of this is, that in neither of the cases recorded were we able to get the line quite across the glacier; the crevasses and broken ice-ridges, which intercepted the vision, compelled us to halt before we came sufficiently close to the eastern side to make its retardation sensible. But on the 20th of July my friend Hirst sought out an elevated station on the Chapeau, or eastern side of the valley, whence he could command a view from side to side over all the humps and inequalities of the ice, the fixed point at the opposite side, upon which the telescope was directed, being the corner of a window of the Montanvert Hotel. Along this line wereplaced twelve stakes, the daily motions of which were found to be as follows:—
Third Line.—Daily Motion.
No. of stake.Inches.East1moved191/22"223/43"283/44"301/45"333/46"281/47moved241/28"259"2510"1811"...12"81/2West.
The numbering of the stakes along this line commenced from the Chapeau-side of the glacier, and the retardation of that side is now manifest enough; the motion gradually augmenting from 191/2to 331/2inches. But, comparing the velocity of the two extreme stakes, we find that the retardation of stake 12 is much greater than that of stake 1. Stake 5, moreover, which moved with themaximumvelocity, was not upon the centre of the glacier, but much nearer to the eastern than to the western side.
A NEW PECULIARITY OF GLACIER MOTION.
It was thus placed beyond doubt that the point of maximum motion of the Mer de Glace, at the place referred to, is not the centre of the glacier. But, to make assurance doubly sure, I examined the comparative motion along three other lines, and found in all the same undeviating result.
This result is not only unexpected, but is quite at variance with the opinions hitherto held regarding the motion of the Mer de Glace. The reader knows that the trunk-stream is composed of three great tributaries from the Géant, the Léchaud, and the Talèfre. The Glacier du Géant fills more than half of the trunk-valley, and the junction between it and its neighbours is plainly marked by the dirt upon the surface of the latter. In fact four medial moraines are crowded together on the eastern sideof the glacier, and before reaching the Montanvert they have strewn their débris quite over the adjacent ice. A distinct limit is thus formed between the clean Glacier du Géant and the other dirty tributaries of the trunk-stream.
Now the eastern side of the Mer de Glace is observed on the whole to be much more fiercely torn than the western side, and this excessive crevassing has been referred tothe swifter motion of the Glacier du Géant. It has been thought that, like a powerful river, this glacier drags its more sluggish neighbours after it, and thus tears them in the manner observed. But the measurement of the foregoing three lines shows that this cannot be the true cause of the crevassing. In each case the stakes which moved quickestlay upon the dirty portion of the trunk-stream, far to the east of the line of junction of the Glacier du Géant, which in fact moved slowest of all.
LAW OF MOTION SOUGHT.
The general view of the glacier, and of the shape of the valley which it filled, suggested to me that the analogy with a river might perhaps make itself good beyond the limits hitherto contemplated. The valley was not straight, but sinuous. At the Montanvert the convex side of the glacier was turned eastward; at some distance higher up, near the passages calledLes Ponts, it was turned westward; and higher up again it was turned once more, for a long stretch, eastward. Thus between Trélaporte and the Ponts we had what is called a point of contrary flexure, and between the Ponts and the Montanvert a second point of the same kind.
CONJECTURE REGARDING CHANGE OF FLEXURE.
Supposing a river, instead of the glacier, to sweep through this valley;itspoint of maximum motion would not always remain central, but would deviate towards that side of the valley to which the river turned its convex boundary. Indeed the positions of towns along the banks of a navigable river are mainly determined by this circumstance.They are, in most cases, situate on the convex sides of the bends, where the rush of the water prevents silting up. Can it be then that the ice exhibits a similar deportment? that the same principle which regulates the distribution of people along the banks of the Thames is also acting with silent energy amid the glaciers of the Alps? If this be the case, the position of the point of maximum motion ought, of course, to shift with the bending of the glacier. Opposite the Ponts, for example, the point ought to be on the Glacier du Géant, and westward of the centre of the trunk-stream; while, higher up, we ought to have another change to the eastern side, in accordance with the change of flexure.
On the 25th of July a line was set out across the glacier, one of its fixed termini being a mark upon the first of the three Ponts. The motion of this line, measured on a subsequent day, and reduced to its daily rate, was found to be as follows:—
Fourth Line.—Daily Motion.
No. of stake.Inches.East1moved61/22"83"121/24"151/45"151/26"183/47"181/48"183/49"191/210moved2111"201/212"231/413"231/414"2115"221/416"171/417"15West.
This line, like the third, was set out and numbered from the eastern side of the glacier, the theodolite occupying a position on the heights of the Echelets. A moment's inspection of the table reveals a fact different from that observed on the third line;therethe most easterly stake moved with more than twice the velocity of the mostwesterly one;here, on the contrary, the most westerly stake moves with more than twice the velocity of the most easterly one.
To enable me to compare the motion of the eastern and western halves of the glacier with greater strictness, my able and laborious companion undertook the task of measuring with a surveyor's chain the line just referred to; noting the pickets which had been fixed along the line, and the other remarkable objects which it intersected. The difficulty of thus directing a chain over crevasses and ridges can hardly be appreciated except by those who have tried it. Nevertheless, the task was accomplished, and the width of the Mer de Glace, at this portion of its course, was found to be 863 yards, or almost exactly half a mile.
Referring to the last table, it will be seen that the two stakes numbered 12 and 13 moved with a common velocity of 231/4inches per day, and that their motion is swifter than that of any of the others. The point of swiftest motion may be taken midway between them, and this point was found by measurement to lie 233 yardswestof the dirt which marked the junction of the Glacier du Géant with its fellow tributaries: whereas, in the former cases, it lay a considerable distanceeastof this limit. Its distance from the eastern side of the glacier was 601 yards, and from the western side 262 yards, being 170 yards west of the centre of the glacier.
CONJECTURE TESTED.
But the measurements enabled me to take the stakes in pairs, and to compare the velocity of a number of them which stood at certain distances from the eastern side of the valley, with an equal number which stood at the same distances from the western side. By thus arranging the points two by two, I was able to compare the motion of the entire body of the ice at the one side of the central line with that of the ice at the other side. Stake 17 stood about as far from the western side of the glacier asstake 3 did from its eastern side; 16 occupied the same relation to 4; 15, to 5; 13, to 7; and 12, to 9.
Calling each pair of points which thus stand at equal distances from the opposite sidescorresponding points, the following little table exhibits their comparative motions:—
Numbers and Velocities of Corresponding Points on the Fourth Line.
No.Vel.No.Vel.No.Vel.No.Vel.No.Vel.West171516171/415221/413231/412231/4East3121/24151/45151/27181/49191/2
WESTERN HALF MOVES QUICKEST.
The table explains itself. We see that while stake 17, which standswestof the centre, moves 15 inches, stake 3, which stands an equal distanceeastof the centre, moves only 121/2inches. Comparing every pair of the other points, we find the same to hold good; the western stake moves in each case faster than the corresponding eastern one. Hence,the entire western half of the Mer de Glace, at the place crossed by our fourth line, moves more quickly than the eastern half of the glacier.
We next proceeded farther up, and tested the contrary curvature of the glacier, opposite to Trélaporte. The station chosen for this purpose was on a grassy platform of the promontory, whence, on the 28th of July, a row of stakes was fixed at right angles to the axis of the glacier. Their motions, measured on the 31st, gave the following results:—
Fifth Line.[B]—Daily Motion.
No. of stake.Inches.West1moved111/42"131/23"123/44"155"151/46"167"171/48"191/49moved193/410"1911"191/212"171/213"1614"143/415"10East.
This line was set out and numbered from the Trélaporte side of the valley, and was also measured by Mr. Hirst, over boulders, ice-ridges, chasms, and moraines. The entire width of the glacier here was found to be 893 yards, or somewhat wider than it is at the Ponts. It will also be observed that its motion is somewhat slower.
An inspection of the notes of this line showed me that stakes 3 and 14, 4 and 12, 7 and 10, were "corresponding points;" the first of each pair standing as far from the western side, as the second stood from the eastern. In the following table these points and their velocities are arranged exactly as in the case of the fourth line.
Numbers and Velocities of the Corresponding Points on the Fifth Line.
No.Vel.No.Vel.No.Vel.West3123/44157171/4East14143/412171/21019
EASTERN HALF MOVES QUICKEST.
In each case we find that the stake on the eastern side moves more quickly than the corresponding one upon the western side: so that where the fifth line crosses the glacierthe eastern half of the Mer de Glace moves more quickly than the western half. This is the reverse of the result obtained at our fourth line, but it agrees with that obtained on our first three lines, where the curvature of the valley is similar. The analogy between a river and a glacier moving through a sinuous valley is therefore complete.
Supposing the points of maximum motion to be determined for a great number of lines across the glacier, the line uniting all these points is what mathematicians would call thelocusof the point of maximum motion. At Trélaporte this line would lie east of the centre; at the Ponts it would lie west of the centre; hence, in passing from Trélaporte to the Ponts, it must cross the axis of the glacier. Again, at the Montanvert, it would lie east of thecentre, and between the Ponts and the Montanvert the axis of the glacier would be crossed a second time. Supposing the dotted line inFig. 21to represent the middle line of the glacier, then the defined line would represent the locus of the point of maximum motion.It is a curve more deeply sinuous than the valley itself, and it crosses the axis of the glacier at each point of contrary flexure.
LOCUS OF POINT OF SWIFTEST MOTION.
Fig. 21. Locus of the Point of Maximum Motion.
To complete our knowledge of the motion of the Mer de Glace, we afterwards determined the velocity of its two accessible tributaries—the Glacier du Géant, and the Glacier de Léchaud. On the 29th of July, a line of stakes was set out across the former, a little above the Tacul, and their motion was subsequently found to be as follows:
Sixth Line.—Daily Motion.
No. of stake.Inches.1moved112"103"124"135"126moved123/47"101/28"109"910"5
The width of the glacier at this place we found to be 1134 yards, and its maximum velocity, as shown by the foregoing table, 13 inches a day.
On the 1st of August a line was set out across the Glacier de Léchaud, above its junction with the Talèfre: it commenced beneath the block of stone known as the Pierre de Béranger. The displacements of the stakes, measured on the 3rd of August, gave the following results:—
Seventh Line.—Daily Motion.
No. of stake.Inches.1moved41/22"81/43"91/24"95"81/26moved71/27"61/48"81/29"710"51/2
The width of the Glacier de Léchaud at this place was found to be 825 yards; its maximum motion, as shown by the table, being 91/2inches a day. This is the slowest rate which we observed upon either the Mer de Glace or its tributaries. The width of the Talèfre-branch, as it descends the cascade, or, in other words, before it is influenced by the pressure of the Léchaud, was found approximately to be 638 yards.
SQUEEZING AT TRÉLAPORTE.
The widths of the tributaries were determined for the purpose of ascertaining the amount of lateral compression endured by the ice in its passage through the neck of the valley at Trélaporte. Adding all together we have—
Géant1134yards.Léchaud825"Talèfre638"Total2597yards.
These three branches, as shown by the actual measurement of our 5th line, are forced at Trélaporte through a channel 893 yards wide; the width of the trunk stream is a little better than one-third of that of its tributaries, and it passes through this gorge at a velocity of nearly 20 inches a day.
THE LÉCHAUD A DRIBLET.
Limiting our view to one of the tributaries only, the result is still more impressive. Previous to its junction with the Talèfre, the Glacier de Léchaud stretches before the observer as a broad river of ice, measuring 825 yards across: at Trélaporte it is squeezed, in a frozen vice, between the Talèfre on one side and the Géant on theother, to a driblet, measuring 85 yards in width, or about one-tenth of its former transverse dimension. It will of course be understood that it is theformand not thevolumeof the glacier that is affected to this enormous extent by the pressure.
Supposing no waste took place, the Glacier de Léchaud would force precisely the same amount of ice through the "narrows" at Trélaporte, in one day, as it sends past the Pierre de Béranger. At the latter place its velocity is about half of what it is at the former, but its width is more than nine times as great. Hence, if no waste took place, itsdepth, at Trélaporte, would be atleast41/2times its depth opposite the Pierre de Béranger. Superficial and subglacial melting greatly modify this result. Still I think it extremely probable that observations directed to this end would prove the comparative shallowness of the upper portions of the Glacier de Léchaud.
FOOTNOTES:[A]Great care is necessary on the part of the man who measures the displacements. The staff ought to be placed along the original line, and the assistant ought to walk along it until the foot of aperpendicularfrom the stake is attained. When several days' motion is to be measured, this precaution is absolutely necessary; the eye being liable to be grossly deceived inguessingthe direction of a perpendicular.[B]The details of the measurement of the fourth and fifth lines are published in the 'Philosophical Transactions,' vol. cxlix., p. 261.
[A]Great care is necessary on the part of the man who measures the displacements. The staff ought to be placed along the original line, and the assistant ought to walk along it until the foot of aperpendicularfrom the stake is attained. When several days' motion is to be measured, this precaution is absolutely necessary; the eye being liable to be grossly deceived inguessingthe direction of a perpendicular.
[A]Great care is necessary on the part of the man who measures the displacements. The staff ought to be placed along the original line, and the assistant ought to walk along it until the foot of aperpendicularfrom the stake is attained. When several days' motion is to be measured, this precaution is absolutely necessary; the eye being liable to be grossly deceived inguessingthe direction of a perpendicular.
[B]The details of the measurement of the fourth and fifth lines are published in the 'Philosophical Transactions,' vol. cxlix., p. 261.
[B]The details of the measurement of the fourth and fifth lines are published in the 'Philosophical Transactions,' vol. cxlix., p. 261.
As regards the motion of thesurfaceof a glacier, two laws are to be borne in mind: 1st, that regarding the quicker movement of the centre; 2nd, that regarding the locus of the point of maximum motion. Our next care must be to compare the motion of the surface of a glacier with the motion of those parts which lie near its bed. Rendu first surmised that the bottom of the glacier was retarded by friction, and both Professor Forbes[A]and M. Martins[B]have confirmed the conjecture. Theirs are the only observations which we possess upon the subject; and I was particularly desirous to instruct myself upon this important head by measurements of my own.