THE CLEPSYDRA, OR WATER-CLOCK. 161 



Hence, the velocity of efflux through the orifice at is 



+ yW. (l) 



SCH. This formula is true for a vessel of any shape, even 

 when it is closed at the top so that the paraboloid AKB 

 cannot be completely formed. In this case also, h is the 

 depth of the orifice below the vertex K, and yu is the veloc- 

 ity of rotation of the orifice. (See Weisbach's Mechs., 

 p. 819.) 



90. The Clepsydra, or Water-Clock. This is an 



instrument consisting merely of a vessel from which the 

 water is allowed to escape through an orifice in the bottom, 

 and the intervals of time are measured by the depressions of 

 the upper surface. Thus, if we wish the clock to run 12 

 hours, we let t = 12 hours = 12x60x60 seconds; then 

 solving (4) of Art. 79 for li, we have 



h~&fl' m 



~ 2 K* ' 

 and substituting in it this value of t, we have 



h = ^(12x60x60)*, 



which gives the depth of liquid in the cylindrical vessel that 

 will empty itself in 12 hours. 



(1) To discover the manner in which the height h of the 

 vessel must be divided in order that the upper surface of 

 the liquid may descend through the several divisions of the 

 scale in equal intervals of time, we make ^in (1) successively 



equal to 12, 11, 10, 4, 3, 2, 1 hours, and get for h a 



series of values which are as 144, 121, 100, . ... 16, 9, 4, 1 ; 

 hence, if the height h be divided into 144 equal spaces, and 



