368 PHILOSOPHICAL TRANSACTIONS. [aNNO IJdQ. 



when applied to works in large, I have had an opportunity of verifying: for in a 

 mill with the enlarged sails of 30 feet, applied to the crushing of rape seed, by 

 means of two runners on the edge, for making oil ; I observed, that when the 

 sails made 1 1 turns in a minute, in which case the velocity of the wind was 

 about 1 3 feet in a second, according to article 6th, that the runners then made 

 7 turns in a minute: whereas 2 horses, applied to the same 2 runners, scarcely 

 worked them at the rate of 3^ turns in the same time. Lastly, with regard to 

 the real superiority of the enlarged sails, above the Dutch sails, as commonly 

 made, it has sufficiently appeared, not only in those cases where they have been 

 applied to new mills, but where they have been substituted instead of the others. 



VI] J. On Horizontal IVindmills and Water-wheels, tvitk Oblique Vanes. 



Observations on the effects of common windmills with oblique vanes, have led 

 many to imagine, that could the vanes be brought to receive the direct impulse, 

 like a ship sailing before the wind, it would be a very great improvement in 

 point of power; while others, attending to the extraordinary and even unex- 

 pected effects of oblique vanes, have been led to imagine, that oblique vanes ap- 

 plied to water-mills, would as much exceed the common water-wheels, as the 

 vertical windmills are found to have exceeded all attempts towards a horizontal 

 one. Both these notions, but especially the first, have so plausible an appear- 

 ance, that of late years there has seldom been wanting those, who have assidu- 

 ously employed themselves to bring to bear designs of this kind : it may not 

 therefore be unacceptable to endeavour to set this matter in a clear light. 



In pi. 13, fig. 13, let ab be the section of a plane, on which let the wind 

 blow in the direction cd, with such a velocity as to describe a given space be, in 

 a given time, suppose 1 second; and let ab be moved parallel to itself, in the 

 direction cd. Now, if the plane ab moves with the same velocity as the wind, 

 that is, if the point b moves through the space be in the same time that a par- 

 ticle of air would move through the same space; it is plain that in this case there 

 can be no pressure or impulse of the wind on the plane: but if the plane moves 

 slower than the wind, in the same direction, so that the point b may move to p, 

 while a particle of air, setting out from b at the same instant, would move to e, 

 then BF will express the velocity of the plane, and the relative velocit) of the 

 wind and plane will be expressed by the line fe. Let the ratio of pe to be be 

 given, suppose 2:3; let the line ab represent the impulse of the wind on the 

 plane ab, when acting with its whole velocity be; but when acting with its rela- 

 tive velocity pe, let its impulse be denoted by some aliquot part of ab, as for in- 

 stance -^ab: then will *- of the parallelogram af represent the mechanical power 

 of the plane; that is, ^ab X -]-be. 



2dly, Let in be the section of a plane, inclined in such a manner, that the 



