142 FERGUSON'S LECTURES. 



the spring. So that the same force, which would raise 

 ^ water to the height A B in the upright pipe A i k I m 

 n o p q B, will raise it to the same height or level BIH 

 in the oblique pipe A E FG H. For the pressure of 

 the water at the end A of the latter is no more than its 

 pressure against the end A of the former. 



The weight or pressure of water at the lower end of 

 the pipe, is always as the sine of the "angle to which the 

 pipe is elevated above the level parallel to the horizon. 

 For, although the water ,in the upright pipe A B would 

 require a force applied immediately to the lower end A 

 equal to the weight of all the water in it, to support 

 the water, and a little more to drive it up, and out of 

 the pipe ; yet, if that pipe be inclined from its upright 

 position to an angle of 80 degrees (as in A 80) the force 

 required to support or to raise the same cylinder of wa- 

 ter will then be as much less, as the sine 80 h is less 

 than the radius A B ; or as the sine of 80 degrees is 

 less than the sine of 90. And so, decreasing as the sine 

 of the angle of elevation lessens, until it arrives at its level 

 A C or place of rest, where the force of the water is no- 

 thing at either end of the pipe. For, although the abso- 

 lute weight of the water is the same in all positions, yet 

 its pressure at the lower end decreases, as the sine of 

 the angle of elevation decreases ; as will appear plainly 

 by a farther consideration of the figure. 



Let two pipes, A B and AC, (Plate III.) of equal lengths 

 and bores, join each other at A ; and let the pipe A B be 

 divided into 100 equal parts, as the scale 5 is ; whose 



wjien the solid piston covered with leather, exactly fills the barrel, and 

 is even pressed a little to it, there is no such risk ; and now that part 

 of the leather band which reaches beyond the solid piston performs its 

 office in the completes! manner. We do not hesitate, therefore, to 

 recommend this form of a piston, which is the most common and sim 

 pie of all, as preferable, when well executed, to many of those more 

 artificial, and frequently very ingenious, constructions, which we 

 have met with in the works of the first engineers. Vide Gregory on 

 Practical Mechanics. 



