Their motions, measured on the 31st, gave the following results:--

Fifth Line.[B]--Daily Motion.

No. of stake. Inches.

West 1 moved 11-1/4 2 " 13-1/2 3 " 12-3/4 4 " 15 5 " 15-1/4 6 " 16 7 " 17-1/4 8 " 19-1/4 9 moved 19-3/4 10 " 19 11 " 19-1/2 12 " 17-1/2 13 " 16 14 " 14-3/4 15 " 10 East.

This line was set out and numbered from the Trelaporte 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.

West 3 12-3/4 4 15 7 17-1/4 East 14 14-3/4 12 17-1/2 10 19

[Sidenote: 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 glacier _the 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 a.n.a.logy 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 the _locus_ of the point of maximum motion. At Trelaporte this line would lie east of the centre; at the Ponts it would lie west of the centre; hence, in pa.s.sing from Trelaporte to the Ponts, it must cross the axis of the glacier. Again, at the Montanvert, it would lie east of the centre, and between the Ponts and the Montanvert the axis of the glacier would be crossed a second time.

Supposing the dotted line in Fig. 21 to 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._

[Sidenote: LOCUS OF POINT OF SWIFTEST MOTION.]

[Ill.u.s.tration: 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 Geant, and the Glacier de Lechaud. 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.

1 moved 11 2 " 10 3 " 12 4 " 13 5 " 12 6 moved 12-3/4 7 " 10-1/2 8 " 10 9 " 9 10 " 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 Lechaud, above its junction with the Talefre: it commenced beneath the block of stone known as the Pierre de Beranger. The displacements of the stakes, measured on the 3rd of August, gave the following results:--

Seventh Line.--Daily Motion.

No. of stake. Inches.

1 moved 4-1/2 2 " 8-1/4 3 " 9-1/2 4 " 9 5 " 8-1/2 6 moved 7-1/2 7 " 6-1/4 8 " 8-1/2 9 " 7 10 " 5-1/2

The width of the Glacier de Lechaud at this place was found to be 825 yards; its maximum motion, as shown by the table, being 9-1/2 inches a day. This is the slowest rate which we observed upon either the Mer de Glace or its tributaries. The width of the Talefre-branch, as it descends the cascade, or, in other words, before it is influenced by the pressure of the Lechaud, was found approximately to be 638 yards.

[Sidenote: SQUEEZING AT TReLAPORTE.]

The widths of the tributaries were determined for the purpose of ascertaining the amount of lateral compression endured by the ice in its pa.s.sage through the neck of the valley at Trelaporte. Adding all together we have--

Geant 1134 yards.

Lechaud 825 "

Talefre 638 "

Total 2597 yards.

These three branches, as shown by the actual measurement of our 5th line, are forced at Trelaporte 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 pa.s.ses through this gorge at a velocity of nearly 20 inches a day.

[Sidenote: THE LeCHAUD A DRIBLET.]

Limiting our view to one of the tributaries only, the result is still more impressive. Previous to its junction with the Talefre, the Glacier de Lechaud stretches before the observer as a broad river of ice, measuring 825 yards across: at Trelaporte it is squeezed, in a frozen vice, between the Talefre on one side and the Geant on the other, 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 the _form_ and not the _volume_ of the glacier that is affected to this enormous extent by the pressure.

Supposing no waste took place, the Glacier de Lechaud would force precisely the same amount of ice through the "narrows" at Trelaporte, in one day, as it sends past the Pierre de Beranger. 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, its _depth_, at Trelaporte, would be at _least_ 4-1/2 times its depth opposite the Pierre de Beranger. 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 Lechaud.

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 a.s.sistant ought to walk along it until the foot of a _perpendicular_ from 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 in _guessing_ the 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.

ICE-WALL AT THE TACUL.

VELOCITIES OF TOP AND BOTTOM.

(11.)

As regards the motion of the _surface_ of 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 r.e.t.a.r.ded 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.

[Sidenote: FIRST ATTEMPT AT MEASUREMENT.]

During the summer of 1857 the eastern side of the Glacier du Geant, near the Tacul, exposed a nearly vertical precipice of ice, measuring 140 feet from top to bottom. I requested Mr. Hirst to fix two stakes in the same vertical plane, one at the top of the precipice and one near the bottom. This he did upon the 3rd of August, and on the 5th I accompanied him to measure the progress of the stakes. On the summit of the precipice, and running along it, was the lateral moraine of the glacier.

The day was warm and the ice liquefying rapidly, so that the boulders and debris, deprived incessantly of their support, came in frequent leaps and rushes down the precipice. Into this peril my guide was about to enter, to measure the displacement of the lower stake, while I was to watch, and call out the direction in which he was to run when a stone gave way. But I soon found that the initial motion was no sure index of the final motion. By striking the precipice, the stones were often deflected, and carried wide of their original direction. I therefore stopped the man, and sent him to the summit of the precipice to remove all the more dangerous blocks. This accomplished, he descended, and while I stood beside him, executed the required measurement. From the 3rd to the 5th of August the upper stake had moved twelve inches, and the lower one six.

Unfortunately some uncertainty attached itself to this result, due to the difficulty of fixing the lower stake. The guide's attention had been divided between his work and his safety, and he had to retreat more than a dozen times from the falling boulders and debris. I, on the other hand, was unwilling to accept an observation of such importance with a shade of doubt attached to it. Hence arose the desire to measure the motion myself. On the 11th of August I therefore reascended to the Tacul, and fixed a stake at the top of the precipice, and another at the bottom. While sitting on the old moraine looking at the two pickets, the importance of determining the motion of a point midway between the top and bottom forcibly occurred to me, but, on mentioning it to my guide, he promptly p.r.o.nounced any attempt of the kind absurd.

[Sidenote: STAKES FIXED AT TOP, BOTTOM, AND CENTRE.]

On scanning the place carefully, however, the value of the observation appeared to me to outweigh the amount of danger. I therefore took my axe, placed a stake and an auger against my breast, b.u.t.toned my coat upon them, and cut an oblique staircase up the wall of ice, until I reached a height of forty feet from the bottom. Here the position of the stake being determined by Mr. Hirst, who was at the theodolite, I pierced the ice with the auger, drove in the stake, and descended without injury. During the whole operation however my guide growled audibly.

On the following morning we commenced the ascent of Mont Blanc, a narrative of which is given in Part I. We calculated on an absence of three days, and estimated that the stakes which had just been fixed would be ready for measurement on our return; but we did not reach Chamouni until the afternoon of Friday, the 14th. Heavy clouds settled, during our descent, upon the summits behind us, and a thunder-peal from the Aiguilles soon heralded a fall of rain, which continued without intermission till the afternoon of the 16th, when the atmosphere cleared, and showed the mountains clothed to their girdles with snow.

The Montanvert was thickly covered, and on our way to it we met the servants in charge of the cattle, which had been driven below the snow-line to obtain food.

[Sidenote: THROUGH GLOOM TO THE TACUL.]

On Monday morning, the 17th, a dense fog filled the valley of the Mer de Glace. I watched it anxiously. The stakes which we had set at the Tacul had been often in my thoughts, and I wished to make some effort to save the labour and peril incurred in setting them from being lost. I therefore set out, in one of the clear intervals, accompanied by my friend and Simond, determined to measure the motion of the stakes, if possible, or to fix them more firmly, if they still stood. As we pa.s.sed, however, from l'Angle to the glacier, the fog became so dense and blinding that we halted. At my request Mr. Hirst returned to the Montanvert; and Simond, leaving the theodolite in the shelter of a rock, accompanied me through the obscurity to the Tacul. We found the topmost stake still stuck by its point in the ice; but the two others had disappeared, and we afterwards discovered their fragments in a snow-b.u.t.tress, which reared itself against the base of the precipice.

They had been hit by the falling stones, and crushed to pieces. Having thus learned the worst, we descended to the Montanvert amid drenching rain.