VOL. Ll.l PHILOSOPHICAL TRANSACTIONS. 36 1 



the sail is broader at the extremity, than near the centre, this shape is more ad- 

 vantageous than that of a parallelogram.* 



Many have imagined, that the more sail the greater the advantage, and have 

 therefore proposed to fill up the whole area : and by making each sail a sector of 

 an ellipsis, according to M. Parent, to intercept the whole cylinder of wind, 

 and so to produce the greatest effect possible. We have therefore proceeded to 

 inquire how far the effect could be increased by a further enlargement of the 

 surface, on the same radius of which N° 18 and IQ are specimens. The sur- 

 faces indeed were not made planes, and set at an angle of 35°, as Parent pro- 

 posed ; because, from N° 1 we learn, that this position has nothing to do, when 

 we intend them to work to the greatest advantage. We therefore gave them 

 such an angle as the preceding experiments indicated for such sort of sails, viz. 

 12° at the extremity, and 22° for the greatest weather. By N° 18 we have the 

 product 1059, greater than N° 15, in the ratio of 7 : Q; but then the augmen- 

 tation of cloth is almost 7 : 12. By N* IQ we have the product 11 65, that is 

 greater than N^ 15 as 7 : 10 ; but the augmentation of cloth is nearly as 7 : l6 ; 

 consequently had the same quantity of cloth as in N° 18 been disposed in a 

 figure similar to that of N" 15, instead of the product 1059, ^ve should have 

 had the product 1386; and in N° 19, instead of the product U65, we should 

 have had a product of I860 ; as will be further made appear in the course of the 

 following deductions. Hence it appears, that beyond a certain degree, the more 

 the area is crowded with sail, the less effect is produced in proportion to the 

 surface : and by pursuing the experiments still further, it was found, that though 

 in N° 19 the surface of all the sails together were not more than ^ of the cir- 

 cular area containing them, yet a further addition rather diminished than 

 increased the effect. " So that when the whole cylinder of wind is intercepted, 

 it does not then produce the greatest effect, for want of proper interstices to 

 escape." It is certamly desirable, that the sails of vvindmills should be as short 

 as possible ; but at the same time it is equally desirable, that the quantity of 

 cloth should be the least that may be, to avoid damage by sudden squalls of 

 wind. The best structure therefore for large mills, is that where the quantity of 

 cloth is the greatest, in a given circle, that can be: on this condition, that the 

 effect holds out in proportion to the quantity of cloth ; for otherwise the effect 

 can be augmented in a given degree by a less increase of cloth on a larger radius, 



* The figure and proportion of the enlarged sails, which Mr. S. found best to answer at large, 

 are represented in the figure, where the extreme bar is ^ of the radius (or whip, as it is called by 

 the workmen,) and is divided by the whip in the proportion of 3 to 5. The triangular or leading 

 sail is covered with board from the point downwards ^ of its height, the rest with cloth as usual. 

 The angles of weather in the preceding note are best for the enlarged sails also j for in pract ice it is 

 found, that the sails had better have too little than too much weather. — Orig. 

 VOL. XI. 3 A 



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