On the 6th February 1843, or almost twenty-two years ago, I had the honour of laying before this Society an account of a topographical survey of the Mer de Glace of Chamouni and its neighbourhood, together with the detailed map founded upon it, being probably the first map of a glacier on such a scale ever constructed. Since that time I have never ceased to interest myself in the improvement and extension of this survey. Two subsequent editions of the map appeared, containing the results of my continued observations with the theodolite in 1843, 1844, 1846, and 1850. The last edition (on a reduced scale), in 1853, included the whole of the glacier of Bossons and the results of an extended triangulation, in which the Flegère and the Breven formed the extremities of a new base connected with the stations L, M, and I of my former survey.