MECHANICS. 



25 



any solid body, which obstructs its 

 course. (PNEUMATICS, Art. 9.) This 

 force is used as a first mover, by means 

 analogous to water-wheels, viz. by flat 

 surfaces exposed to the impact of the 

 wind, by that impact made to revolve 

 on a centre. When this rotator}- motion 

 is once produced, it maybe easily trans- 

 mitted, and modified by machinery, and 

 applied to any required purpose. 



If the sails of a windmill be con- 

 structed in a manner analogous to the 

 float-boards of an undershot -water- 

 wheel, the plane of the wheel must be 

 in the direction of the wind ; and it is 

 evident that one half of the wheel must 

 be sheltered from the action of the wind, 

 for otherwise equal forces would tend 

 to turn the wheel in opposite directions, 

 and no motion would ensue. Besides 

 this, the wind would act with very little 

 advantage on those sails whose planes 

 are nearly in its own direction. For 

 this reason windmills of this construc- 

 tion are not generally used. On the 

 other hand, the arms which carry the 

 sails revolve in a plane fac-ins: the wind. 

 In this arrangement, if the sails were in 

 the same plane with the arms, the wind 

 would fall perpendicularly upon them, 

 and merely press the arms against the 

 building perpendicular to the plane in 

 which they are designed to move. If, 

 on the other hand,lhe sails were per- 

 pendicular to the plane in which the 

 arms move, their edges would be pre- 

 sented to the wind, and would, there- 

 fore, offer no resistance, and there 

 would be no motion. In order to 

 make the arms revolve, the sails must, 

 therefore, be placed in some direction 

 intermediate between those of the w ind 

 and the plane in which the arms re- 

 volve. 



The most accurate experimentalists 

 and the most profound mathematicians 

 have instituted inquiries, practical and 

 theoretical, to determine that position 

 which should be given to sails of wind- 

 mills, in order to produce the best 

 effect. Most of the theoretical calcula- 

 tions on this difficult subject have been 

 vitiated by conditions and hypotheses, 

 which are inadmissible in* practice. 

 The angle which Parent and others 

 deduced from mathematical calculation 

 to be the best at which the planes of 

 the sails could be inclined to the axis of 

 motion or the direction of the wind, 

 was found to be one of the worst in 

 Mr. Smeaton's experiments. The posi- 

 tion determined by Parent, was the best 



at the beginning of motion, but his cal- 

 culation proceeded on the supposition, 

 that the w ind struck the sail at rest ; 

 and was, therefore, inapplicable to the 

 continuance of its action. 



When the wind acts upon the sail in 

 motion, it is necessary to take into ac- 

 count the velocities both of the sail 

 and the wind. For if the sail moved 

 before the wind with a speed equal to 

 that of the wind itself, no effect would 

 be produced. The effect will depend 

 on the difference of the velocities, that 

 being the velocity with which the wind 

 strikes the sail. Now as the obliquity 

 of the sail to the wind should depend 

 on the force with which the wind acts 

 upon it, and as those parts of the sail 

 which are nearer to the centre of motion 

 move more slowly than those which are 

 more remote, it follows that the posi- 

 tion of the sail should vary at different 

 distances from the centre of rotation. 

 From several experiments executed on 

 a large scale, Mr. Smeaton concluded 

 the following positions to be among the 

 best.* Let the radius be conceived to 

 be divided into six equal parts, and let 

 the first part, beginning from the centre, 

 be called 1 ; the second 2, and so on ; 

 the extreme part being 6. 



Angle with 

 the axis. 



72 

 71 

 72 

 74 



77* 

 83 



Angle with the plane 

 of the motion. 



18 

 19 

 18 

 16 



12* 



7 



(56.) The last property, in virtue of 

 which we have stated that air becomes a 

 mechanical agent, is its elasticity. The 

 nature of this property, and the laws 

 by which it acts, have already been ex- 

 plained in our treatise on PNEUMATICS, 

 Chap. IV. When this property is con- 

 sidered as a mechanical agent, it is 

 subject to nearly the same observations 

 as we have already applied to the w eight 

 and pressure of the atmosphere. To 

 give effect to the elastic force of air, it 

 is necessary that it should predominate 

 over the w'eisrht of the atmosphere, a 

 pressure to which, as we have before 

 stated, all bodies in their ordinary state 



* The general resemblance which the best form of 

 windmill sails bears to the arrangement of the 

 feathers in the wings of birds is very striking, and 

 one of those beautiful instances of the truly mathe- 

 matical principles on which the works of the creation 

 are constructed. 



