OF HYDRAULIC 1INGIXES. 143 



length is equal to the length of the pipe. Upon this LKCT. 

 length, as a radius, describe the quadrant B D C, and N - 

 divide it into 90 equal parts or degrees. 



Let the pipe A C be elevated to 10 degrees upon the 

 quadrant, and filled with water ; then part of the water 

 that is in it will rise in the pipe A B, and if it be kept 

 full of water, it will raise the water in the pipe A B 

 from A to i ; that is, to a level i 10 with the mouth of 

 the pipe at 10 : and the upright line a 10 equal to A i, 

 will be the sine of 10 degrees' elevation ; which, being 

 measured upon the scale <S, will be about 17.4 of such 

 parts as the pipe contains 100 in length : and therefore? 

 the force or pressure of the water at A in the pipe A 10, 

 will be to the force or pressure at A in the pipe A B, 

 as 17.3 to 100. 



Let the same pipe be elevated to 20 degrees in the 

 quadrant, and if it be kept full of water, part of that 

 water will run into the pipe A B, and rise therein to 

 the height A k, which is equal to the length of the up- 

 right line b 20, or to the sine of 20 degrees' elevation ; 

 which, being measured upon the scale S, will be 34.2 

 of such parts as the pipe contains 100 in length. And 

 therefore, the pressure of the water at A, in the full 

 pipe A 20, will be to its pressure, if that pipe were 

 raised to the perpendicular situation A B, as 34.2 

 to 100. 



Elevate the pipe to the position A 30 on the quadrant, 

 and if it be supplied with water, the water will rise 

 from it ir.to the pipe A B, to the height A I, or to the 

 same level with the mouth of the pipe at 30. The sine 

 of this elevation, or of the angle of 30 degrees, is c 30 ; 

 which is just equal to half the length of the pipe, or to 

 50 of such parts of the scale, as the length of the pipe 

 contains 100. Therefore, the pressure of the water at 

 A, in a pipe elevated 30 degrees above the horizontal 

 level, will be equal to one half of what it would be if 

 the same pipe stood upright in the situation A B. 



