VOL. LI.] PHILOSOPHICAL TRANSACTIONS. 367 



ments, we find, that 20 revolutions of the sails raised the scale and weight 1 1 .3 

 inches; 130 revolutions will therefore raise the scale 73.45 inches, which multi- 

 plied by 17.52 lb. makes a product of 1287, for the effect of the Dutch sails in 

 their best position; that is, when the velocity of the wind is 84 feet in a second; 

 this product therefore multiplied by 3, gives 386 1 for the effect of the same sails, 

 when the velocity of the wind is 12-|- feet in a second. 



Desaguliers makes the utmost power of a man, when working so as to be able 

 to hold it for some hours, to be equal to that of raising a hogshead of water 10 

 feet high in a minute. Now, a hogshead consisting of 63 ale gallons, being 

 reduced into pounds avoirdupois, and the height into inches; the product made 

 by multiplying those two numbers will be 7 6800; which is IQ times greater than 

 the product of the sails last-mentioned, at 124- feet in a second: therefore, by 

 maxim 8th, if we multiply the square root of I9, that is 4.46, by 21 inches, 

 the length of the sail producing the effect 386 1, we shall have 93.66 inches, or 

 7 feet 9*- inches, for the radius of a Dutch sail in its best position, whose mean 

 power shall be equal to that of a man : but if they are in their common position, 

 their length must be increased in the ratio of the square root of 442 to that of 

 639, as thus appears: 



The ratio of the maximum products of N° 8 and 11, tab. 3, are as 442 : 639; 

 but by maxim 8, the effects of sails of different radii are as the square of the 

 radii : consequently the square roots of the products or effects, are as the radii 

 simply: and therefore as the square root of 442 is to that of 639, so is 93.66 

 to 112.66, or 9 feet 4|- inches. 



If the sails be of the enlarged kind, then from tab. 3, N° 11 and 15, we shall 

 have the square root of 820 to that of 639 :: 93.66 : 82.8 inches, or 6 feet lOf 

 inches: so that in round numbers we shall have the radius of a sail, of a similar 

 figure to their respective models, whose mean power shall be equal to that of a 

 man, viz. 



The Dutch sails in their common position 9^ feet. 



The Dutch sails in their best position 8 



The enlarged sails in their best position. ^ 7 



Suppose now the radius of a sail to be 30 feet, and to be constructed on the 

 model of the enlarged sails, N*^ 14 or 15, tab. 3; dividing 30 by 7, we have 

 4.28, the square of which is 18.3; and this, according to maxim 7, will be the 

 relative power of a sail of 30 feet, to one of 7 feet; that is, when working at 

 a niean rate, the 30 feet sail will be equal to the power of 18.3 men, or of 3^ 

 hotses: reckoning 5 men to a horse; whereas the effect of the common Dutch 

 sailsv of the same length, being less in the proportion of 820 : 442, will be 

 scarc%- equal to the power of 10 men, or of 2 horses. 



That these computations are not merely speculative, but will nearly hold good 



