304 VHILOSOPHICAL TRANSACTIONS. [aNNO 173Q. 



measure carefully the diameter of the contracted vein, observing whether it re- 

 mains always the same, however the altitude of the water may vary. 



Exper. 1. Observe whether this diameter has always the same ratio to the 

 diameter of the hole, in using different sizes of apertures. 



Exper. 3. Observe the quantity of water issuing in a given time, through the 

 same hole, either in the bottom or the side of the vessel, with different altitudes 

 of the water. 



Exper. 4. Observe the same, with holes of various sizes, but the same alti- 

 tudes of the water. 



Exper. 5. Observe how much water issues in a given time, in two different 

 cases, in each of which there is the same ratio of the diameter of the hole to 

 the height of the water. For if the quantities be found in a ratio compounded 

 of the duplicate ratio of the diameters, and the simple ratio of the altitudes, as 

 in cor. 3, prob. 9, it will be a great confirmation of our theory. 



Exper. 6. In the same two cases, observe to what altitudes the water will 

 jet upwards, through a large tube fitted to the side of the vessel, and perforated 

 in its upper part. For if these altitudes be found proportional to those of the 

 water in the vessel, as in cor. 3, prob. 12, it will be another sure confirmation 

 of this theory. 



Exper. 7. Observe also the height of the jet, with the same hole, but various 

 heights of the water. 



Exper. 8. Observe also the same, by varying the hole, but with the same 

 height of the vessel. 



Second General Scholium. — Till those experiments be carefully tried, we must 

 avail ourselves of the experiments hitherto made. These are of three kinds : 

 for they measure either, 1 . The diameter of the contracted vein ; or, 2. The 

 measure of the effluent water ; or, 3. The height to which the water jets. 

 As to the 



1st. The radius of the contracted vein, as measured by Sir I. Newton, is 

 0.84r, when the diameter 2r is ^ of an inch ; and by Poleni, it is O.JSr nearly, 

 when the diameter of the hole is 2^ Paris inches. But by the calculation in 

 this theory it isO.BlSr nearly, for any diameter of the hole; being nearly a 

 medium between those two. 



2. As to the 2d, none of the quantities, measured by any one, are of any 

 use, except those by Poleni, when the water issues through the above size of 

 hole made in a thin plate, which he informs us is much less than when it 

 passes through a pipe of the same diameter. And the medium among 10 such 

 measured quantities, is 2mr'A X 0.57 1, when the height of the vessel is 33 

 Paris inches 



