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 Fonts 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:—