ON THE REGULATION OF HYDRAULIC FORCES. 323 



tiou between pressure and mechanical power. It may be demonstrated that 

 the greatest possible pressure of the wind or water, on a given oblique sur- 

 face at rest, tending to turn it in a direction perpendicular to that of the wind, 

 is obtained when the surface forms an angle of about 55° with the wind ; but 

 that the mechanical power of such a pressure, which is to be estimated from 

 a combination of its intensity with the velocity of the surface, may be in- 

 creased without limit by increasing the angle of inclination, atid consequently 

 the velocity. The utmost effect that could be thus obtained would be equal 

 to that of the same wind or stream acting on the floatboards of an undershot 

 wheel : but since in all practical cases the velocity is limited, the effect will 

 be somewhat smaller than this : for example, if the mean velocity of the sails 

 or floatboards be supposed equal to that of the wind, the mechanical power 

 will be more than four fifths as great as that of an undershot wheel, that is, in 

 the case of a windmill, more than four fifths of the utmost effect that can be 

 obtained from the wind. In such a case Maclaurin has shown that the sails 

 ought to make an angle of 74° with the direction of the wind: but in practice 

 it is found most advantageous to make the angle somewhat greater than this, 

 the velocity of the extremities of the sails being usually, according to Mr. 

 Smeaton, more than twice as great as that of the wind. It appears, there- 

 fore, that the oblique sails of the common windmill are in their nature almost 

 as well calculated to make the best use of any hydraulic force as an undershot 

 wheel ; and since they act without intermission throughout their whole revo- 

 lution, they have a decided advantage over such machines as require the sails 

 or fans to be exposed to a more limited stream of the wind, during one half only 

 of their motion; which is necessary in the horizontal windmill, where a screen is 

 employed for covering them while they are moving in a direction contrary to 

 that of the wind : and such machines, according to Smeaton, are found to per- 

 form little more than one tenth of the work of those which are more usually 

 employed. The sails of a common windmill are frequently made to change their 

 situation according to the direction of the wind, by means of a small wheel, with 

 sails of the same kind, which turns round whenever the wind strikes, on 

 either side of it, and drives a pinion turning the whole machinery; ithe sails 

 are sometimes made to furl or unfurl themselves, according to the velocity of 

 the wind, by means of a revolving pendulum, which rises to a greater or less 

 height,in order to prevent the injury which the flour would suffer frorn too great 

 a rapidity in the motion, or any other accidents which might happen in a mill 



