VOL. XLI.3 VHILOSOPHICAL TRANSACTIONS. 303 



Corol. 2. If the altitudes of the vessels be equal, or e = a ; then r = ns, 

 or n = -, hence « = — x (^ Aka + raV — no). 



Carol. 3. If the diameters of the holes be in same ratio as the altutdes; then 

 the water will spout to heights proportional to those of the vessels. For if 



r : s :: a: e, or rE := sx, and n = 1, then t = — , or t : a :: e : a, or e — e :a — a 



:: E : a, or e : a :: E : A. 



Carol. 4. Since 2p\/3Aa = \^4Aa + w'«' — nx, it will be t = — X 

 2/)V'3Aa =^^^^; hence, for \/a substituting its value above mentioned 

 9/3A, and properly reducing, « =^, or i = ^^. 



Corol. 5. Hence, by making/) = g, then £ = — -, or t: x:: rz^ : sa". That 

 is, the defects of the jets, are as the diameters of the holes inversely, and as the 

 squares of the heights of the vessels directly. 



Coral. 6. When s ■= r, then t = ^ nearly in the duplicate ratio of the 

 heights of the vessel ; which agrees with Mariotte's rule. 



Corol. 7. When e = a, then i = — nearly ; that is, the defects of the jets 

 are nearly as the diameters of the holes reciprocally. 



First General Scholium. — In examining the truth of this theory by experi- 

 ment, it will be proper, 1 . To use a very large vessel, at least in the upper 

 part, that during the time of making the experiment, the height of the water 

 may not be sensibly changed. But if the vessel be not so large, but that 

 during the efflux, the height of the water considerably decreases, then a mean 

 between the greatest and least height is to be taken for the constant height : 

 which is better than disturbing the natural motion of the fluid, by pouring 

 fresh water into it. 



2. Let the vessel be of such a depth, that when the water spouts from a hole 

 in the side, the velocity of the fluid through the centre of the hole, may be 

 safely taken for the velocity through all the hole, when there is no resistance. 



3. Let the plate, in which the hole is made, be so thin, or at least have so 

 thin an edge at the circumference of the hole, that the thickness there may be 

 accounted as nothing with respect to the diameter of the hole ; observing to 

 shave away the thickness of the plate on the outer side, leaving the inner side 

 plain next the water. 



These things being prepared, the following experiments may be made, by 



which, as so many criteria, the certainty of the above doctrine may be judged of. 



Exper. 1. When the water issues through a hole in the side of the vessel. 



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