Eastern points; motion in inches 15 18 19 Western " " " " 13 15 17 183. 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 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:-- _When a glacier moves through a sinuous valley, the locus of the points 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.