162 THE VENA CONTRACTA. 



marked upwards from the bottom of the vessel, then the 

 marks 121, 100, ..... 16, 9, 4, 1, 0, will give the water level 

 at 1, 2, ..... 8, 9, 10, 11, 12 hours after the water begins to 

 flow. 



(2) Any vessel may serve for a clepsydra, but that form is 

 most convenient in which the upper surface of the liquid 

 descends uniformly. 



Let x = the height of the liquid in the vessel, K the 

 area of the descending surface, v its velocity, and k the area 

 of the orifice. Then from (a) of Art. 78, we have 



v = tye. (2) 



And since the surface is to descend uniformly, this value 

 of v must be equal to some constant a, which will depend 

 upon the whole height and the time in which the clepsydra 

 will be emptied ; hence (2) becomes 



K* = --3F; (3) 



a 3 



and supposing the area of the descending surface of the 

 liquid to be a circle = try*, (3) becomes 



which is a parabola of the fourth order. 



Hence, the heights of the sections must v^ry as the 

 fourth power of their radii. 



91. The Tena Contracta. The laws of efflux that 

 have been deduced are founded on the hypothesis that the 

 liquid particles descend in straight lines to the orifice, and 

 all issue in parallel lines with a velocity due to the height 



