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At this moment Bill Todhunter was foreman of Repair Section No. II on the “Great Alleghanian,”–a position which needed a man of first-rate promptness, of great resource, of good education in engineering. Such a man had the “Great Alleghanian” found in him, by good luck; and they had promoted him to their hardest-worked and best-paid section,–the section on which, as it happened, was this Chamoguin run, and the long bend which I have described, by which the road “headed” that stream.

The younger Todhunter did meet his brother at Faber’s Mills, where the repair-train had hauled out of the way of the express, and where the express took wood. The brothers always looked for each other on such occasions; and Bill promised to examine the paper which Joslyn had carefully written out, and which his brother brought to him.

I have never repeated in detail the mass of calculations which Bill Todhunter made on the suggestion thus given to him. If I had, I would not repeat them here, for a reason which has been suggested already. He became fascinated with the problem presented to him. Stated in the language of the craft, it was this:

Given a moving body, with a velocity eight thousand eight hundred feet in a minute, what should be its elevation that it may fall eleven hundred feet in the transit of five-eighths of a mile?” He had not only to work up the parabola, comparatively simple, but he had to allow for the resistance of the air, on the supposition of a calm, according to the really admirable formulas of Robins and Coulomb, which were the best be had access to. Joslyn brought me, one day, a letter from Bill Todhunter, which shows how carefully he went into this intricate inquiry.

Unfortunately for them all, it took possession of this spirited and accomplished young man. You see, he not only had the mathematical ability for the calculation of the fatal curve, but, as had been ordered without any effort of his, he was in precisely the situation of the whole world for trying in practice his own great experiment. At each of the two X X of Joslyn’s map, the company had, as it happened, switches for repair-trains or wood-trains. Had it not, Bill Todhunter had ample power to make them.

For the “experiment,” all that was necessary was, that under the pretext of re-adjusting these switches, he should lay out that at the upper X so that it should run, on the exact grade which he required, to the western edge of the ravine, in a line which should be the direct continuation of the long, straight run with which the little map begins.

An engine, then, running down that grade at the immense rapidity practicable there, would take the switch with its full speed, would fly the ravine at precisely the proper slopes, and, if the switch had been rightly aligned, would land on the similar switch at the lower X. It would come down exactly right on the track, as you sit precisely on a chair when you know exactly how high it is.

“If.” And why should it not be rightly aligned, if Bill Todhunter himself aligned it? This he was well disposed to do. He also would align the lower switch, that at the lower X, that it might receive into its willing embrace the engine on its arrival.

When the bold engineer had conceived this plan, it was he who pushed the others on to it, not they who urged him. They were at work on their daily duty, sometimes did not meet each other for a day or two. Bill Todhunter did not see them more than once in a fortnight. But whenever they did meet, the thing seemed to be taken more and more for granted. At last Joslyn observed one day, as he ran down, that there was a large working-party at the switch above Drums, and he could see Bill Todhunter, in his broad sombrero, directing them all. Joslyn was not surprised, somehow, when he came to the lower switch, to find another working-party there. The next time they all three met, Bill Todhunter told them that all was ready if they were. He said that he had left a few birches to screen the line of the upper switch, for fear some nervous bungler, driving an engine down, might be frightened, and “blow” about the switch. But he said that any night when the others were ready to make the fly, he was; that there would be a full moon the next Wednesday, and, if there was no wind, he hoped they would do it then.