ON THE REGULATION OF HYDRAULIC FORCES. 247 



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 t as great as that of the wind. It appears, 

 therefore, 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 revolution, 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 perform 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 ; the 

 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 from too great a rapidity in the motion, or any other accidents which 

 might happen in a mill of a different nature. The inclination of the axis 

 of a windmill to the horizon is principally intended to allow room for the 

 action of the wind at the lower part, where it would be weakened if the 

 sails came too nearly in contact with the building, as they must do if they 

 were perfectly upright. When it is necessary to stop the motion of a 

 windmill, a break is applied to the surface of a large* wheel, so that its 

 friction operates with a considerable mechanical advantage. Water wheels 

 with oblique floatboards are sometimes used with good effect in China and 

 in the south of France : for tide wheels, such floatboards have the advan- 

 tage that they may be easily made to turn on a hinge with the stream, so 

 as to impel the wheel in the same direction whether the tide be flowing or 

 ebbing. (Plate XXII. Fig. 293.) 



A smoke jack is a windmill in miniature ; a kite affords a very familiar 

 example of the effect of the oblique impulse of the air, of which the action 

 first causes a pressure perpendicular to the surface of the kite, and this 

 force, combined with the resistance of the string, produces a vertical result 

 capable of counteracting the weight of the kite. (Plate XXII. Fig. 294.) 



* Maclaurin's Account of Sir I. Newton's Philos. Discoveries, art. 29. 

 f Nearer three times. See Smeaton, Ph. Tr. 1759, li. 163. 

 t Ibid. p. 172. 



