Chap. 3.] througbfma.ll Apertures. 47t 



with a number of holes; if each o~ thefe holes is re- 

 garded as particular and infulared, the rapidity of the 

 flow through each will be according to the corrt \\-> n- 

 dent height of the fluid; then if the irvmber of holes 

 are multiplied ad infinitum, or, which will ,10,011,14: to 

 the fame thing, if the plate is fuppofed t > be en- 

 tirely taken away, the velocity at each point of ihe 

 fuppofed orifice will be according to the corrcfno: nc 

 height of the fluid ; and in eftimating the quantity of 

 water difc barged, fome attention mufl be paid to the 

 inequality of the motion ; yet it muft not be alft-rred 

 that this reaibning is entirely conclufive. In propor- 

 tion as the fum of the fmall holes made in the plate is 

 fmail in comparifon with the fize of the refervoir, the 

 portions of water which flow through each hole are 

 forced out by the .abfolme weight of the column 

 above ; but the moment that the number of apertures 

 augment ad infinitum, and the ft reams of water which, 

 run through'- them -become contiguous, it cannot be 

 clearly faid that.the-lid.uid flows in the fame manner as 

 through final! iniuiatcd holes ; yet as this hypothecs 

 gives a refult fufficicntly conformable to experiments, 

 it may be ufeful to preferve it, and the more fo, as it 

 leads to very fimple calculations, and in all common 

 queftions this ftmplicitv may be preferable to the mi- 

 nutenefs of fractional operations. 



The quantity of water which iffues from thefe aper- 

 tures in a given time is not fo great as their -fize 

 might at firft fugged, becaufe the itream is contracted 

 by running out of each orifice, and that contraction 

 extends to a diftance nearly equal to half the diameter 

 of the aperture; and the diameter of the contracted 

 ftream is to the diameter of the aperture a little more 

 than as three to four, or as three and one-iixth to four, 

 or nineteen to twenty- four ; fo that its area is to that 



of 



