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 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 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 passing 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.] [Illustration: Fig. 21. Locus of the Point of Maximum Motion.]