VOL. LXXIU.] fHILOSOPHICAL TUANSAC TIONS. 3t)5 



and other mathematicians, have fallen into the same mistake. No demonstra- 

 tion of this sort was more commonly known or received among practical mecha- 

 nics, than that the best angle for the sails of a wind-mill, at the beginning of 

 their motion, was an angle of 45 degrees ; and that the maximum of an under- 

 shot water-wheel was when it moved with -±- of the velocity of the water: but 

 Mr. Smeaton, in an excellent paper in the Phil. Trans, has refuted this opinion 

 by the clearest experiments. 



I had intended to diversify these experiments, and to extend them to a more 

 interesting subject of inquiry, to determine the best shape of sails, and the angle 

 to which they should be set, to obtain the greatest progressive effect with the 

 least leeway ; but, as a more complicated apparatus than I could at present pro- 

 cure is necessary for this purpose, I determined to offer the slight progress I have 

 made, in hopes that some gentleman, more conversant and more interested than 

 myself in these inquiries, may pursue them with success and advantage to the 

 public. I shall only remark, that the general cause of the different resistance of 

 the air on surfaces of different shapes, is the stagnation of that fluid near the 

 middle of the plane on which it strikes. The shape and size of the portion thus 

 stagnated, differs from the shape and angle of the plane. The elasticity of the 

 air permits the parts in motion to compress those which are first stopped or re- 

 tarded by the plane, and forms, as it were, a new surface of a different shape, 

 for the reception of those particles which succeed. With the assistance of a good 

 solar microscope the curves of the air striking against different surfaces may be 

 delineated, and when the general facts are once clearly ascertained, mathemati- 

 cians will have an ample field for curious and useful speculation. 



TABLE.* 



Turns. Time. Weight. 

 Machine alone 5 4 2 8 



With a parallelogram of 9 inches long and 4 broad, one of its longer sides 



parallel to the horizon and the parallelogram inclined to an angle of 45°, 5 4 7 



Ditto, with one of its shorter sides downwards 5 4 7 9 



With a lozenge 9 inches long and 4 broad, with its longer side parallel to 



the horizon 5 4 5 8 



Ditto reversed 5 4 6 



With a square piece of tin, four inches each side 5 4 5 



Ditto, 8 inches square 5 4 16 6" 



With the former parallelogram, placed with one of its shortest sides down- 

 wards, inclined to an angle of 45°, and bent into an arch whose chord 

 was 8 inches long 5 4 8 



Ditto bent to an arch, the chord of which was 1\ inches 5 4 8 5 



\ 



* See a great many more experiments of this nature in Dr. Hutton's Dictionary, vol. 1, 

 pp. 364, 365. 



