In the winter of 1863 and the spring of 1864, Mr. Reilly constructed an entirely original map from his newly-acquired data. The spaces between his trigonometrically determined points he filled in after photographs, and a series of panoramic sketches which he made from his different stations. The map so produced was an immense advance upon those already in existence, and it was the first which exhibited the great peaks in their proper positions. This extraordinary piece of work revealed Mr. Reilly to me as a man of wonderful determination and perseverance. With very small hope that my proposal would be accepted, I invited him to take part in renewed attacks on the Matterhorn. He entered heartily into my plans, and met me with a counter-proposition, namely, that I should accompany him on some expeditions which he had projected in the chain of Mont Blanc. The unwritten contract took this form:—I will help you to carry out your desires, and you shall assist me to carry out mine. I eagerly closed with an arrangement in which all the advantages were upon my side. At the time that Mr. Reilly was carrying on his survey, Captain Mieulet was executing another in continuation of the great map of France; for about one-half of the chain of Mont Blanc (including the whole of the valley of Chamounix) had recently become French once more. Captain Mieulet was directed to survey up to his frontier only, and the sheet which was destined to include his work was to be engraved, of course, upon the scale of the rest of the map, viz., 1/80000 of nature. But upon representations being made at head-quarters that it would be of great advantage to extend the survey as far as Courmayeur, Captain Mieulet was directed to continue his observations into the south (or Italian) side of the chain. A special sheet on the scale of 1/40000 was promptly engraved from the materials he accumulated, and was published in 1865, by order of the late Minister of War, Marshal Randon.(124) This sheet was admirably executed, but it included the central portion of the chain only, and a complete map was still wanting. Mr. Reilly presented his MS. map to the English Alpine Club. It was resolved that it should be published; but before it passed into the engraver’s hands its author undertook to revise it carefully. To this end he planned a number of expeditions to high points which up to that time had been regarded inaccessible, and upon some of these ascents he invited me to accompany him. Before I pass on to these expeditions, it will be convenient to devote a few lines to the topography of the chain of Mont Blanc.