OF WINDMILLS. 397 



Let WV represent the direction and velocity of the wind ; 

 SV, SV &c. that of the sail at those distances from the centre 

 of motion, and perpendicular to WV; draw the parallel TW, 

 also NB' in the middle and MC' either at 4. the distance be- 

 tween N and S, according to Maclaurin's, or at 4. the distance, 

 by the last hypothesis. Then to find the angle of weather cor- 

 responding to any velocity or distance TW, draw SW, on which 

 describe a semicircle SVBW, and draw SC, SB, to where it meets 

 tire parallels MC', NB'; then will CSV r , be the angle of weather ac- 

 cording to Maclaurin, if at ~ distance; or according to the last hy- 

 pothesis, if MC' be at L the distance between N and S; and BSV, 

 equal to half the angle oj limit WSV, will be the angle of weather 

 according to Waring, if any constant portion of wind could be 

 intercepted ; and for Mr. Hall Gower's hypothesis, take TW, 

 as the whole lengtb of the vane, and assuming any angle at 

 the extremity as most advantageous, suppose TW'H = 10 de- 

 grees, then any other line drawn from H, to any other distance 

 on TW, will sbew the corresponding angle of iv eat her ; but this 

 principle will be found evidently erroneous. 



The calculation of the different angles of weather is also much 

 easier from this construction, than from Maclaurin's theorem 

 for that purpose ; for taking WV = 1, as the winds velocity; 

 then the sails' velocity TW is = contangent of the angle of 

 limit = twice the angle of weather according to Waring; and 

 either 4. or L the sine of the angle of limit SN, will give the 

 sine of the arc BC, which arc subtracted from the angle of limit 

 (BW =) B V will give the arc VC = twice the angle of weather ac- 

 cording to either of the two hypotheses. — By this method, the 

 following table is calculated shewing the different angles of 

 weather, and the effective force of the wind to turn the sail ; 

 but it must be understood that the proportionate velocity of the 

 extreme part of the sail to the wind can be assumed at pleasure, 

 if the interior mechanism be adapted to it; the greater the an- 

 gle of weather the less will be the sails' velocity, but the force 

 greater; and also, on either hypothesis, if the same angle of wea- 

 ther be assumed at the extremity, the difference of all the other 

 angles would in practice be imperceptible, until we approach 

 towards the centre, where they approximate to either 30°, 35° 

 16', 45° or 90°; the last, evidently erroneous. 



