414 Hydrodynamics* 



517. Resuming the equation 



and finding thence the value of ?/, we have 

 _ x 2 a x -f- 34 p 



y - - - 



Fig.248.Now let AB represent the greatest height of the piston above the 

 2494 surface of the water in the reservoir, and AD the play of the pis- 

 ton ; suppose the different portions AP of the line JlBio represent 

 the successive values of a?, and lay down upon the perpendicu- 

 lars PMthe values ofy which correspond to these assumed values 

 of x ; so shall we have a curve MMC, which, while j a 2 is greater 



PJ 248( than 34/>,will cut AB in two points / and /', in such manner that 

 the ordinates PM will lie on different sides of AB ; the ordinates 

 which are on the right/iZ? shewing the positive values of 7/,and those 

 which are on the left AB the negative values. We see, therefore, 

 that so long as I a 2 is greater than 34 p the pressure of the ex- 

 terior air is strongest, until the water has attained the height BI'. 

 At this point I' it will stop (the motion acquired being left out of 

 consideration,) because the value of y is = 0. But if the water 

 by the motion it has acquired continues to rise till it reaches 

 some point between /' and /, it will not stop there, but will des- 

 cend, if the valve does not oppose its descending motion ; because 

 the value of?/, being there negative, indicates that the pressure of 

 the exterior air is weaker than the united pressures of the water 

 and the interior air. If the water reaches the point /, it will stop 

 there, for the same reason that it would at the point I 1 ; but if it 

 rises above /, there is then no reason to fear that it will descend ; 

 for all the ordinates PM between / and A being positive, shew 

 that in that portion of the pump the pressure of the exterior air 

 exceeds the combined efforts of the interior air and water. 



518. When, on the contrary, the value of \ a 2 is less than 



Fig.249. tnat O f 34 p^ t h e curve will intersect the axis AB ; all the ordi- 



nates are positive, and consequently the pressure of the exterior 



air is always the strongest. This confirms and illustrates what 



has been laid down in article 515. 



