vol.. 'XLI.] PHILOSOPHICAL TRANSACTIONS. 28) 



have no common velocity. Though mathematicians have hitherto taken the 

 contrary to be certain. 



g. At a small distance from the hole, the diameter of the vein of water is 

 much less than that in the hole. For instance, if the diameter of the hole be 

 J , the diameter of the vein of water will be 44 or 0.84, according to Sir I. New- 

 ton's measure, who first observed this wonderful phenomenon ; but according to 

 Poleni's measure -|4 or '-/-r* ; '^hat is, if you take the mean diameter, 0.78 nearly. 



We should now proceed to the solution of these phaenomena ; but before 

 doing this, it wiil be convenient to notice the following particulars. 



1. We consider water no otherwise than as a fluid and continuous body, 

 the parts of which yield to the least force, and are thereby moved among 

 themselves. 



2. By efRuent water, is understood that quantity of It, which actually passes 

 out of the hole; and though it may seem unnecessary, yet it may he proper to 

 mention, that in my dissertation on the motion of running waters, inserted 

 about 24 years ago, in the Philos. Trans, by defluent water I understood that 

 whole quantity of water, which is put in motion within the vessel, and descends 

 towards the hole. jirr. 



3. We consider the amplitude of the vessel as infinite, or at least so great, 

 that the decrease of the depth of water, during the whole space of time in 

 which the water flows out of the hole, is imperceptible. 



4. We consider water as running out with a constant velocity. At the be- 

 ginning indeed of the motion it runs out, for a very small space of time, with 

 a less velocity than afterwards. But we pass over the very beginning of the 

 motion, and investigate the measure and motion of water, when it has acquired 

 its utmost velocity. Now this must necessarily be constant, as long as the 

 height of the superincumbent water remains the same. 



5. We conceive the bottom of the vessel no otherwise than as a mathe- 

 matical plane, or at least as so thin a plate, that its thickness is little or nothing, 

 with regard to the diameter of the hole. 



6. By the measure of effluent water in the following pages, we always under- 

 stand that quantity of water which flows out of the hole in the same space of 

 time that a heavy body, falling in vacuo, would take in passing through the 

 height of the water above the hole. , 



7. By the motion of effluent water, we understand the sum of the motions 

 of all the particles of water, which run out of the hole in the abovementioned 

 space of time. But the motion of every particle^ is as the factum of the par- 

 ticle itself, and of the velocity with which it bursts out of the hole. 



8. That what we shall say hereafter may be the more easily ajnceived, we 



VOL. VIII. O o 



