376 Hydrodynamics. 



exerted upon the particle. Hence the squares of the times be- 

 ing as the spaces, or the times simply as the square roots of the 

 spaces, s/BG is to \,'GD as the time employed in describing BG 

 to the time required to reach the horizontal plane DF. But in 

 the time employed in describing UG, the particle would be car- 

 ried uniformly and horizontally by the velocity thus acquired, 

 through a space equal to 2 BG ; therefore, to find the amplitude 

 or horizontal range DE of the jet, we have the proportion 



215. 



= 2 \/BG -GD = 2 GH. 



As the same reasoning may be used with respect to any other 

 point in J5D, if upon the height of the fluid BD as a diameter we 

 describe a semicircle BKD, the horizontal distance to which the fluid 

 will spout from any point will be twice the ordinate of the circle drawn 

 through this point, the distance being measured on the plane of the 

 bottom of the vessel. 



486. It will hence be perceived, that if apertures be made at 

 equal distances G, L, from the top and bottom of the vessel, 

 the horizontal distances DE to which the fluid will spout from 

 these apertures will be equal ; and that the point 7, bisect- 

 ing the altitude, is that from which the fluid will spout to the 

 greatest distance, this distance DF being equal to twice the radi- 

 us of the semicircle or to the altitude BD of the fluid. 



487. If the fluid issue obliquely instead of horizontally, the 

 curve described will still be parabolic, and the horizontal range, 

 &c. of the jet may be calculated as in the case of other projectiles. 



Fig.237. Let the aperture C be inclined, for example, upward at different 



angles. CB will be equal to s, the space through which a body 



must fall to acquire the velocity of projection, and equal to the dis- 



477. tance CF, CF', of the foci of the several parabolas, traced by 



particles issuing with different angles of elevation. Hence BE 



Trlg.172 is the directrix to these parabolas, and the circle described from 

 the centre C, and with the radius BC, will pass through the sev- 

 eral foci F, F x , &c. Let CE, for instance, be the direction of 

 the jet, and draw CF making the angle ECF equal to BCE-, let 



