We have digressed somewhat from our immediate historical continuity, because not merely is it essential to appreciate some of the difficulties which the ship-man of to-day has to encounter, but in order to show that, though Fulton was very far from comprehending all the details of the relations between resistance and hull which recent experiments alone are determining, yet he was working on right lines, and with a certainty of aim that was positively unique for the beginning of the nineteenth century. Reverting, then, to the illustration on page 64, he explains in his footnote that a nice calculation must be made on the velocities of the wheels which drive the paddle-wheels, whilst the same regard must also be had for the rate at which the paddle-wheels and the boat herself are to move. Thus, he says, supposing a boat is calculated to run at the rate of four miles an hour, the paddles and bow presenting equal surfaces in the water, then the circumference of the wheel must run eight miles an hour, of which four strike water back equal to the water divided by the boat, the other four miles, so to speak, _overtaking_ the boat. But, he adds, if the paddles were made twice as large the engine would stand still. In the illustration, much of which has necessarily suffered through having to be reduced, we see an arrangement of pulleys and lines, and a weight. To the left of the diagram, _A_ represents the boat which is to be propelled through the water, while _B_, shown at the extreme right of the illustration, is the paddle which is to send the ship along. Both present a flat front of four feet to the water. By the known resistance, Fulton argued, each would require twelve pounds to draw each one mile per hour, so that if the pulley and weight marked _C_ weighed 24 pounds, and descended to where it is marked “No. 1,” then the boat _A_ would be drawn to the point marked 2 (seen just to the right of it) and the paddle would be drawn to that spot marked 3, each moving through equal spaces in equal times, twelve of the 24 pounds being consumed by the boat and twelve by the paddles. Thus half of the power is actually consumed by the paddles. Next, he says, suppose that the flat front of the paddle is reduced to one foot while the boat still remains four. “The paddle being one-fourth the size of the boat must move 2 miles an hour to create a resistance for the boat to move one mile in the same time.” Finally, as we said, he concludes that the paddles acting in the water should, if possible, present more surface than the bow of the boat, and power will thus be saved.