The first rough tracing out of the line was completed before the winter of the year 1857, and it was considered sufficiently correct to permit the commencement of the tunnel at each end by the ordinary means--manual labor. In the autumn of 1858, the corrected line was traced, and the observatories definitely fixed, and all other necessary geodetic operations completed. Contemporaneously was undertaken a careful levelling between the two ends, taken along the narrow path of the Colle di Frejus, and bench-marks were established at intervals along the whole line. All the data necessary for an exact profile of the work were now obtained. The exact length of the future tunnel was found to be twelve thousand two hundred and twenty metres, or about seven and a half English miles; and the difference of level between the two mouths was ascertained to be two hundred and forty metres, or seven hundred and eighty feet, the Southern or Bardonnêche end being the highest. Under these circumstances, it would have been easy to have established a {63} single gradient from Bardonnêche down to Fourneaux of about two centimètres per metrè--that is, of about one in fifty. But a little reflection will show, that in working both ends of the gallery at once, in order to effect the proper drainage of the tunnel, it would be necessary to establish two gradients, each inclining toward the respective mouths, and meeting in some point in the middle. This, in fact, has been done, and the two hundred and forty metres' difference of level has been distributed in the following manner: From Bardonnêche, the gradient mounts at the rate of 0.50 per one thousand mètres--that is, one in two thousand as far as the middle of the gallery; here it descends toward Fourneaux with a gradient of 22.20 mètres per one thousand, or about one in forty-five. The highest point of the Grand Vallon perpendicularly over the axis of the tunnel is 1615.8 mètres, or 5251.31 feet.