The Brèche is 2000 feet below the summit of the Meije, and only 6000 feet above La Grave. A direct ascent from the village to the Brèche would consequently be at an angle of not much more than 20°. But it is not possible to make the ascent as the crow flies; it has to be made by an indirect and much longer route. Our track was probably double the length of a direct line between the two places. Doubling the length halved the angles, and we therefore arrive at the somewhat amazing conclusion, that upon this, one of the steepest passes in the Alps, the mean of all the angles upon the ascent could not have been greater than 11° or 12°. Of course, in some places, the angles were much steeper, and in others less, but the _mean_ of the whole could not have passed the angle above indicated. [Illustration: THE VALLON DES ETANÇONS (LOOKING TOWARDS LA BÉRARDE).(103)] We did not trouble ourselves much with these matters when we sat on the top of the Brèche. Our day’s work was as good as over (for we knew from Messrs. Mathews and Bonney that there was no difficulty upon the other side), and we abandoned ourselves to ease and luxury; wondering, alternately, as we gazed upon the Rateau and the Ecrins, how the one mountain could possibly hold itself together, and whether the other would hold out against us. The former looked [so rotten that it seemed as if a puff of wind or a clap of thunder might dash the whole fabric to pieces]; while the latter asserted itself the monarch of the group, and towered head and shoulders above all the rest of the peaks which form the great horse-shoe of Dauphiné. At length a cruel rush of cold air made us shiver, and shift our quarters to a little grassy plot, 3000 feet below—an oasis in a desert—where we lay nearly four hours admiring the splendid wall of the Meije.(104) Then we tramped down the Vallon des Etançons, a howling wilderness, the abomination of desolation; destitute alike of animal or vegetable life; pathless, of course; suggestive of chaos, but of little else; covered almost throughout its entire length with débris from the size of a walnut up to that of a house; in a word, it looked as if half-a-dozen moraines of first-rate dimensions had been carted and shot into it. Our tempers were soured by constant pitfalls [it was impossible to take the eyes from the feet, and if an unlucky individual so much as blew his nose, without standing still to perform the operation, the result was either an instantaneous tumble, or a barked shin, or a half-twisted ankle. There was no end to it, and we became more savage at every step, unanimously agreeing that no power on earth would ever induce us to walk up or down this particular valley again.] It was not just to the valley, which was enclosed by noble mountains,—unknown, it is true, but worthy of a great reputation, and which, if placed in other districts, would be sought after, and cited as types of daring form and graceful outline.(105)