the angle of the extremity were a b f, it would make one 

 revolution in the distance a f, or two in that of its own cir- 

 cumference, and so on ; if the other oblique lines represented 

 the angle of the extremity of the vane of the wheel, the 

 wheel would revolve once in the distance from a, to where its 

 corresponding oblique line intersected the line a c. I have 

 proved these to be facts by a variety of experiments. In the 

 first instance, I procured three tin models ten inches diameter 

 and two-and-a-half inches deep, which had each six vanes, 

 but at different angles, from which I found that a revolution 

 was made by each wheel upon being passed through the 

 water, in distances proportionate to the tangent of the angles, 

 as already described. From this I inferred that the principle 

 would prove a correct one for measuring the velocity of 

 currents of water, or of vessels through the water ; I had, 

 therefore, two wheels constructed, the circumference of each 

 of which was the 1000th part of a mile: the vanes of one 

 were made with the periphery at an angle of 45°, or a b g 

 Fig. 3, and the other at an angle of 26" 34', or a b f, the 

 intention being that the first should make 1,000, and the latter 

 2,000 revolutions in a mile. Wheel work was attached to 

 each, so arranged as to cause an index to make one revolution 

 round a dial plate fixed a little above each of the wheels in 

 one mile, which dial plates were subdivided to mark furlongs 

 and chains. To test these wheels I measured the distance 

 of half-a-mile on the straight bank of a canal, leaving a mark 

 at each furlong ; and, afterwards getting into a boat, I was 

 hauled along the canal parallel to the measured distance, each 

 wheel being successively submerged through that distance ; 

 when the distance recorded by the index of each wheel was 



given distance ; through this point of intersection draw a radius line parallel to 

 A B, and oblique lines drawn from b, to the several points of intersection of the 

 vertical lines thus found, will be the angle which the vane should make at those 

 several distances from the centre line b d. 



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