VOL. LI.] PHILOSOPHICAL TRANSACTIONS. 363 



swered best, the ratios will be confined between that of ?0 : 8 and of 10 : 9 ; 

 and at a medium about 10 : 8.3 or of () : 5. This ratio also agrees nearly with 

 those in col. 14 of tab. 4. However it appears, on the whole, that in those in- 

 stances, where the angle of the sails or quantity of cloth was greatest, that the 

 'id term of the ratio was less. 

 IF'. On the Effects of Sailsy according to the Different Velocity of the PVind. 



Maxim 1. The velocity of windmill sails, whether unloaded, or loaded so as 

 to produce a maximum, is nearly as the velocity of the wind ; their shape and 

 position being the same. — ^This appears by comparing together the respective 

 numbers of columns 4 and 5, tab. 4. 



Maxim 2. The load at the maximum is nearly, but somewhat less than, as 

 the square of the velocity of the wind ; the shape and position of the sails being 

 the same. — ^This appears by comparing together the numbers in col. 6 tab. 4. 



Maxim 3. The effects of the same sails at a maximum are nearly, but some- 

 what less than, as the cubes of the velocity of the wind. — It has already been 

 proved, Maxim 1st, that the velocity of sails at the maximum is nearly as the 

 velocity of the wind ; and by Maxim 2d, that the load at the maximum is nearly 

 as the square of the same velocity : if those two maximums would hold pre- 

 cisely, it would be a consequence that the effect would be in a triplicate ratio 

 thereof: how this agrees with experiment will appear by comparing together the 

 products in col. 8 of tab. 4, wherein those of N'' 2, 4, and 6, (the velocity of 

 the wind being double) ought to be octuple of those of N° 1, 3, and 5, instead 

 of which they fall short, N*' 2 by -f , N° 4 by -^V, and N° 6 by -^ part of the 

 whole. 



Maxim 4. The load of the same sails at the maximum is nearly as the squares, 

 and their effect as the cubes, of their number of turns in a given time. — This 

 maxim may be esteemed a consequence of the three preceding. 



Maxim 5. When sails are loaded so as to produce a maximum at a given ve- 

 locity, and the velocity of the wind increases, the load continuing the same ; 

 1 st. The increase of effect, when the increase of the velocity of the wind is 

 small, will be nearly as the squares of those velocities : 2dly, When the velocity 

 of the wind is double, the effects will be nearly as 10: 274- : but, 3dly, When 

 the velocities compared, are more than double of that where the given load pro- 

 duces a maximum, the effects increase nearly in a simple ratio of the velocity of 

 the wind. 



V. On the Effects of Sails of Different Magnitudes : the structure and position 

 being similar, and the velocity of the wind the same. 

 Maxim 6. In sails of a similar figure and position, the number of turns in a 

 given time will be reciprocally as the radius or length of the sail. 



3A2 



