Water-Pumps. 415 



If the sucking pump were to be placed so high above the 

 usual surface of the earth (as at the top of a high mountain), or 

 so low beneath it (as in a deep mine), that the pressure of the 

 atmosphere would be sensibly different from the assumed mean 

 pressure equivalent to 34 feet of water, we must then in all the 

 preceding investigation change the co-efficient 34 to that which 

 would express the height in feet of the corresponding column of 

 water. And these equivalent columns may always be ascertain- 

 ed by means of the height of the mercurial column in the barom- 

 eter ; the proportion being this ; as 30 inches, the mean altitude of 

 the mercurial column, to 34 feet, the mean height of the column 

 of water, so is any other mercurial column in inches to its cor- 

 responding column of water in feet. 



519. In the preceding calculation the pump has been supposed 

 of a uniform bore throughout ; when this is not the case the so- 

 lution is rendered somewhat more complex, but not difficult. To 

 calculate the effort of the interior air when the water has not 

 reached the body of the pump, having only attained the height 



HJV, for example, we must use this proportion ; as the space Fig. 245, 

 QOFNMI : the space CDVNMI : : 34 feet : a fourth term, 

 which being added to the weight of the column of water whose 

 height is JVff, ought again to be equal to 34 ?/, as before. Be- 

 sides, when the sucking pipe FG is of a smaller diameter than the 

 body of the pump, if the conditions which we have before specifi- 

 ed obtain, the pump cannot fail to produce the proper effect ; for 

 the air is dilated with more facility in this latter case than when 

 the whole is of the same diameter. We need only add on this 

 point, that if the length of the stroke in a uniform pump, which 

 is requisite to render the machine effectual, be greater than can 

 conveniently be made, it maybe diminished by contracting the 

 diameter of the sucking pipe in the subduplicate ratio of the diminu- 

 tion of the length of the stroke. 



520. As to the effort of which the power ought to be capable 

 to sustain the water at a determinate height YH, it will be meas- 

 ured according to what we have said respecting the lifting pump 

 by the weight of a column of water whose base is equal to CD, 

 and height that of XY above RS. Here, too, we leave out of 

 consideration -the friction and the weight of the piston. 



