118 



FIG. 1. 



riG. 2. 



The sail of a windmill will, of course, be the length of the 

 radius of a circle in which it revolves. The parallelogram 

 A B c D, Fig, 2, 

 represents this 

 radius; c B being 

 the axle, and the 

 length being di- 

 vided into six 

 equal parts. Let 

 AB, Fig. 1, equal 

 the curved line 

 of the sixth part of a circle, which the periphery of the 

 revolving sail would describe, the chord of its arc would 

 then be equal to the radius a b, Fig. 2, and the chord of 

 the several arcs 5-5, 4-4, 3-3, 2-2, 1-1, Fig. 1, would be 

 respectively equal to the lengths 5b, 4b, 3b, 2b, and 1b, 

 Fig. 2. The periphery of the sail a b. Fig. 1, being 

 placed at an angle with regard to the plane of rotation, the 

 two points would not revolve in the same line, but would 

 describe a cylinder, the depth of which may be said to be 

 D A, Fig. 2 ; and as the length of the lines a b, Fig. 1 and 2, 

 are respectively equal to each other, the angle cab, Fig. 2, 

 would be the angle of the extremity of the sail with the 

 plane of rotation. The sail being considered without fric- 

 tion, the tendency of the wind on the oblique plane a b, Fig. 1, 

 (represented by a c. Fig. 2, the arrow denoting the direction 

 of the wind,) would be to cause the sail to revolve from a to b 

 in the time the wind passed from d to a, and as the several 

 other portions of the sail would in the same time each pass 

 through the spaces 5-5, 4-4, 3-3, 2-2, 1-1, the angle which 

 the sail should present at those several points, should be 

 respectively c 5 b, c 4 b, c 3 b, c 2 b, and c 1 b. 



The form of sail which Smeaton recommends accords in 

 some measure to this principle, inasmuch as the angle of 



