344 .PHILOSOPHICAL TRANSACTIONS. [anNO J/SQ. 



in a second, equal to 107.5 inches, or 8.96 feet, which is due to a head of 15 

 inches ;* and this we call the virtual or effective head. 



The area of the head being 105.8 inches, this multiplied by the weight of 

 the water of the inch cubic, equal to the decimal .5/9 o^ the ounce avoirdupois, 

 gives 6 1.26 ounces for the weight of as much water as is contained in the head, 

 on 1 inch in depth, -^ of which is 3.83 pounds; this multiplied by the depth 

 21 inches, ' gives 80.43 lb. for the value of 12 strokes; and by proportion, 394-, 

 the number made in a minute, will give 264.7 lb. the weight of water expended 

 in a minute. 



Now as 264.7 lb. of water may be considered as having descended through a 

 space of 15 inches in a minute, the product of these two numbers 3970 will 

 express the power of the water to produce mechanical effects ; which were as 

 follows. 



The velocity of the wheel at the maximum, as appears above, was 30 turns a 

 minute ; which multiplied by 9 inches, the circumference of the cylinder makes 

 270 inches ; but as the scale was hung by a pulley and double line, the weigtit 

 was only raised half of this, viz. 135 inches. 



The weight in the scale at the maximum 8 lb. O oz. 



Weight of the scale and pulley O 10 



Counterweight, scale, and pulley O 12 



Sum of the resistance 9 6 



or lb. 9.375. 

 Now as 9.375 lb. is raised 135 inches, these two numbers being multiplied to- 

 gether, the product is 1266, which expresses the effect produced at a maximum : 

 so that the proportion of the power to the effect is as 3970 : 1266, or as 10: 

 3.18. 



But though this is the greatest single effect producible from the power men- 

 tioned, by the impulse of the water on an undershot wheel ; yet as tlie whole 

 power of the water is not exhausted by it, this will not be the true ratio between 

 the power of the water, and the sum of all the effects producible from it : for as 

 the water must necessarily leave the wheel with a velocity equal to the wheel's 

 circumference, it is plain that some part of the power of the water must remain 

 after quitting the wheel. 



The velocity of the wheel at the maximum is 30 turns a minute ; and conse- 

 quently its circumference moves at the rate of 3.123 feet a second, which an- 

 swers to a head 1 .82 inches ; this being multiplied by the expence of water in a 



• This is determined on the connroon maxim of hydrostatics, that the velocity of spouting waters, 

 is equal to the velocity that a heavy body would acquire in falling from the height of the reservoir; 

 and is proved by the rising of jets to the height of their reservoirs nearly. — Orig. 



