from Fourneaux to trace a line in the supposed direction of Bardonnêche. This first line came out in the valley of Rochemolles at a point too far off from that fixed upon, but with its help a second line was drawn which came sufficiently near to the proposed entry. These lines were subsequently still further corrected. These operations occupied the months of August and September 1857."
"The observations were made with a theodolite which had been constructed with the greatest care, and which read to 10" on the vernier. The line has been verified several times by different observers, and the results show that a straight line has been laid out. Supposing that the greatest error" (due to the instrument) "had been made, the deviation from the straight line would not amount to more than one foot. MM. Borelli and Copello make—personally—the observations for the direction and for the verification of the actual course of the tunnel, and we may imagine that they will not readily leave to others such delicate work, upon which the success of the enterprise depends. All the marks on the southern side, and the most important ones on the northern side, were fixed by the first days of October 1857; snowfalls and 'tourmentes' retarded the work, but it was nevertheless completed by the end of the month."
"In 1858 the triangulations and levellings were undertaken, and they were terminated at the end of the year."
"The trigonometrical work has for a base one of the sides of the triangles of the Etat Major, and upon it two sets of triangles have been constructed, one towards the southern and the other towards the northern side. The two systems are formed of twenty-eight triangles, and the number of angles measured is eighty-six. The majority of the angles have been repeated at least twenty times; those of the principal triangles have been taken fifty times, and, of the small ones, at least ten times. The theodolite employed read to 5"."
"One can hardly give an idea of the difficulties that the observers have experienced in the course of their work. At heights like those from which they worked, meteorological changes occur with the greatest rapidity; violent winds overturned their instru-
