the middle line of the glacier. The demonstration that the point of swiftest motion wanders to and fro across the axis, as the flexure of the valley changes, is, therefore, shall I say complete? 180. Not yet. For if surer means are open to us we must not rest content with estimates by the eye. We have with us a surveying chain: let us shake it out and measure these lines, noting the distance of every stake from the side of the glacier. This is no easy work among the crevasses, but I confide it confidently to Mr. Hirst and you. We can afterwards compare a number of stakes on the eastern side with the same number of stakes taken at the same distances from the western side. For example, a pair of stakes, one ten yards from the eastern side and the other ten yards from the western side; another pair, one fifty yards from the eastern side and the other fifty yards from the western side, and so on, can be compared together. For the sake of easy reference, let us call the points thus compared in pairs, equivalent points. 181. There were five pairs of such points upon our fourth line, D D', and here are their velocities: In every case here the stake at the western side moved more rapidly than the equivalent stake at the eastern side. 182. Applying the same analysis to our fifth line, E E', we have the following series of velocities of three pairs of equivalent points :— 183. Here the three points on the eastern side move more rapidly than the equivalent points on the western side. 184. It is thus proved : 1. That opposite the Montanvert the eastern half of the Mer de Glace moves more rapidly than the western half. 2. That opposite les Ponts the western half of the glacier moves more rapidly than the eastern half. 3. That opposite Trélaporte the eastern half of the glacier again moves more rapidly than the western half. 4. That these changes in the place of greatest motion are determined by the flexures of the valley through which the Mer de Glace moves. § 25. New Law of Glacier Motion. 185. Let us express these facts in another way. Supposing the points of swiftest motion for a very great number of lines crossing the Mer de Glace to be determined; the line joining all those points together is what mathematicians would call the locus of the point of swiftest motion. 186. 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 would cross the centre. But at the Montanvert it would again lie east of the centre; hence between the Ponts and the Montanvert the centre must be crossed a second time. If there were further sinuosities upon the Mer de Glace there would be further crossings of the axis of the glacier. 187. The points on the axis which mark the transition from eastern to western bending, and the reverse, may be called points of contrary flexure. 188. Now what is true of the Mer de Glace is true of all other glaciers moving through sinuous valleys; so that the facts established in the Mer de Glace may be expanded into the following general law of glacier motion : When a glacier moves through a sinuous valley, the locus of the point of maximum motion does not coincide with the centre of the glacier, but, on the contrary, always lies on the convex side of the central line. The locus is therefore a curved line more deeply sinuous than the valley itself, and crosses the axis of the glacier at each point of contrary flexure. 189. The dotted line on the Outline Plan (page 68) represents the locus of the point of maximum motion, the firm line marking the centre of the glacier. 190. Substituting the word river for glacier, this law is also true. The motion of the water is ruled by precisely the same conditions as the motion of the ice. 191. Let us now apply our law to the explanation of a difficulty. Turning to the careful measurements executed by M. Agassiz on the glacier of the Unteraar, we notice in the discussion of these measurements a section of the 'Système glaciaire' devoted to the 'Migrations of the Centre.' It is here shown that the middle of the Unteraar glacier is not always the point of swiftest motion. This fact has hitherto remained without explanation; but a glance at the Unteraar valley, or at the map of the valley, shows the enigma to be an illustration of the law which we have just established on the Mer de Glace. § 26. Motion of Axis of Mer de Glace. 192. We have now measured the rate of motion of five different lines across the trunk of the Mer de Glace. Do they all move alike? No. Like a river, a glacier at different places moves at different rates. Comparing together the points of maximum motion of all five lines, we have this result : 198, There is thus an increase of rapidity as we desoond the glacier from Trélaporte to the Montanvert; *This is probably under the mark. I think it likely that the swiftest on of this portion of the Mer de Glace in 1857 amounted to a yard in uty four hours. the maximum motion at the Montanvert being fourteen inches a day greater than at Trélaporte. § 27. Motion of Tributary Glaciers. 194. So much for the trunk glacier; let us now investigate the branches, permitting, as we have hitherto done, reflection on known facts to precede our attempts to discover unknown ones. 195. As we stood upon our 'cleft station,' whence we had so capital a view of the Mer de Glace, we were struck by the fact that some of the tributaries of the glacier were wider than the glacier itself. Supposing water to be substituted for the ice, how do you suppose it would behave? You would doubtless conclude that the motion down the broad and slightly-inclined valleys of the Géant and the Léchaud would be comparatively slow, but that the water would force itself with increased rapidity through the narrows' of Trélaporte. Let us test this notion as applied to the ice. 196. Planting our theodolite in the shadow of Mont Tacul, and choosing a suitable point at the opposite side of the Glacier du Géant, we fix on July 29 a series of ten stakes across the glacier. The motion of this line in twenty-four hours was as follows:: MOTION OF GLACIER DU GÉANT. SIXTH LINE: HH' UPON SKETCH. 1 2 3 4 5 6 7 8 Stake 99 10 5 |