VOL. 



XLI.] 



HHILOSOFHICAL TRANSACTIONS. 



305 



But the measure taken to this altitude, by our calculation, fron) Mariotte's 

 fundamental experiments, is 2ffjr*A X O.5768, exceeding Poleni's measure about 

 the 98th part only. 



3. As Poleni rendered all the experiments of his predecessors useless, con- 

 cerning the measure of the effluent water, because they took no account of the 

 thickness of the plate through which the water issued ; it might be suspected 

 that the like fault enters into the experiments concerning the height of the jet 

 of water. But Poleni has removed this doubt, by another excellent observa- 

 tion ; viz. that water issuing through short tubes, or through holes in a thin 

 plate, spout nearly to the same horizontal distance, or issue with nearly the 

 same velocity. 



Therefore, to try the certainty of our theory, let us make use of Mariotte's 

 experiments concerning the altitudes of jets ; assuming some one of them, as 

 a foundation, for trying the heights in the rest of the experiments, by our 1 2th 

 problem. Taking therefore that experiment, in which the diameter of the hole 

 was 6 lines, and the depth of water in the vessel 34 feet 11-^ lines, or 4 1 94. 

 inches, in which case Mariotte found the jet spouted to the height of 31 feet 

 8 or 9 inches, or 380^ inches. Here then, A = 4194- inches, a = 380-|-, and 

 ft = 39. But, in another experiment, where e, or the depth of water in the 

 vessel, was 26 feet 1 inch, the water rose, through the same hole, to the 

 height of 24 feet '1\ inches ; and by our cor. 1, prob. 12, the height of the jet, 

 or the value of e, comes out 24 feet 3 inches, which is nearly the same. 



Other cases are exhibited in the following tables, where it appears how nearly 

 the calculated heights of the jets, computed by our theory, agree with those 

 observed in Mariotte's experiments, when made with holes of various sizes, and 

 with vessels of different heights. 



I. With the Hole of 6 lines Diameter. 



II. The Hole of 4 lines Diameter. 

 Alt. of the Height of the Jet, 



Kr 



