As we were leaving, Mr. Allen asked me if I would call some time and see him--he had something he thought I would be interested in. I called soon after. He told me he had a plan for a variable cut-off with positive movements, which he thought would avoid defects in the liberating gear. He had had it in his mind a good while, but did not think it could be used, because the governor could not handle the block in his link so as to maintain uniform motion, and he had been inclined to abandon the idea; but when he heard me describing my governor to Mr. Burr, it occurred to him that that governor would do it, and he would like to explain his plan to me. He had no drawing, not a line; the design existed only in his mind. He put down his ideas, as he fitly expressed it, with chalk on the engine-room floor, and that rude sketch represented the perfect system. When his plan came to be analyzed, it was found that everything had been thought out and provided for, with a single exception afterwards provided by Mr. Allen, as will be described. But the wonder did not stop there. Mr. Allen had remedied the defect in the link motion of making a narrow opening for admission when cutting off early, by employing a four-opening admission valve of unique design at each end of the cylinder, and also by greatly enlarging the opening movements. The four-opening valve required four seats in one plane, and it was important that these should be as narrow as possible. For this purpose Mr. Allen employed the Corliss wrist-plate movement to reduce the lap of the valve, and, by an elegant improvement on this movement, he made it available also to enlarge the openings. This improvement consisted in the employment of two rockers having a common axis and separate driving-arms, as well as driven arms, for each valve. The driving-arms were made to vibrate a long way towards their dead points, and the increased opening movement in arc thus obtained was imparted directly to the valve. This combination of an enlarged opening with a reduced lap was perhaps the most surprising feature of Mr. Allen’s system. The four-opening equilibrium valve, afterwards invented by Mr. Allen and since 1876 always employed, requires but two seats in one plane. These could therefore be made wider. The division of the driving-arm was then dispensed with, and the enlarged openings were obtained by increasing the length of the driven arms. That this remarkable system of ports and movements should have been elaborated in the mind of a man who had no knowledge of mechanics except what he had absorbed in engine-rooms must stand among the marvels of inventive power. The accompanying diagram represents the lines put down by Mr. Allen on his engine-room floor and since retained, except that it is now adapted to the more simple movement, with a single driving-arm on the rocker, as previously described.