OF HYDRAULIC ENGINES. 145 



which will be equal to the heights A m, A n, A o, A p, 

 and A q : and these heights, measured upon the scale 

 v will be 64.3, 76.6, 86.6, 94.0, and 98.5; which ex- 

 press the pressures at A in all these elevations, consi- 

 dering the pressure in the upright pipe A B as 100. 



Because it may be of use to have the lengths of all 

 the sines of a quadrant from degrees to 90, we have 

 given the foregoing table, shewing the length of the 

 sine of every degree in such parts as the whole pipe 

 (equal to the radius of the quadrant) contains 1000. 

 Then the sines will be integral or whole parts in length. 

 But if you suppose the length of the pipe to be divided 

 only into 100 equal parts, the last figure of each part or 

 sine must be cut off as a decimal ; and then those which 

 remain at the left hand of this separation will be integral 

 or whole parts. 



Thus, if the radius of the quadrant (supposed to be 

 equal to the length of the pipe A C) be divided into 

 1000 equal parts, and the elevation be 45 degrees, the 

 sine of that elevation will be equal to 707 of these parts : 

 but if the radius be divided only into 100 equal parts, 

 the same sine will be only 70.7, or 70Tr of these parts. 

 For, as 1000 is to 707, so is 100 to 70.7. 



As it is of great importance to all engine-makers, to 

 know what quantity and weight of water will be con- 

 tained in an upright round pipe of a given diameter and 

 height, so that, by knowing what weight is to be raised, 

 they may proportion their engines to the force which 

 they can afford to work them ; we shall subjoin tables 

 shewing the number of cubic inches of water contained 

 in an upright pipe of a round bore, of any diameter 

 from one inch to six and a half; and of any height from 

 one foot to two hundred : together with the weight of 

 the said number of cubic inches, both in troy and avoir- 

 dupoise ounces. The number of cubic inches divided 

 by 231, will reduce the water to gallons in wine mea- 

 sure ; and divided by 282 will reduce it to the measure 

 10 L 



