VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 2Q3 



Schol. I. — It was supposed above, that the motion of the water running 

 through the contracted vein, is equal to the motion of that which runs through 

 the hole. But this is not true in mathematical strictness. For the motion of 

 the water running through the hole, is equal both to the motion of the water 

 through the contracted vein, and to the motion of the ring of air surrounding 

 the vein, which air is drawn into motion by the water running through the 

 vein. But the motion of the ring of air is considered as little or nothing, since 



its thickness is not greater than ^^^, and its density not greater than the gOOth 



part of the density of the water. And thus the equations are rendered much 

 simpler than otherwise they would be. 



Sckol. 2. — By corol. 1, prob. 5, when the water issues into a vacuum, the 

 same ratio continues between the radius of the hole, and the radius of the con- 

 tracted vein, whether the motion of the effluent water be in any degree dimi- 

 nished by resistance, or not. Hence, as to a physical quantity, it is accounted 

 sufficiently true, that the ratio between those radii be considered as given, even 

 when the water flows through air, however the motion of the effluent water 

 may be diminished by resistance, or at least that the said ratio is varied the least 

 possible. And the same is found to be true by the experiments hitherto made. 



Also if the ratio is given between r and f, the ratio between r and r is also 

 given, or the ratio between the radius of the hole, and the imaginary radius, 

 by which the velocity u, by gradually decreasing, is reduced to nothing. For 

 by eliminating u from the two equations above, we come to an equation which 



gives R = Aj -f — ■====-^. Besides, from one of the two equations we ob- 

 tain 3r^R : p^(3r — 2p) :: u :g\: and since the former ratio is given, the latter 

 ratio is also given, that is, the quantity — is given. 



Of two remarkable Caverns, the one Icy, and the other emitting noxious Effluvia. 

 By Matthias Belius,* F.R.S. N° 452, p. 41. Abridged from the Latin. 



The icy cavern opens from the frozen Carpathian mountain, near the village of 

 Szelicze, the mouth, which faces the north, being 18 fathom high, and Q wide. 

 When the cold is severe in the country, M. B. says, the air within the cavern is 

 warm ; but that it freezes within the cavern, when on the outside the sun shines 

 with the greatest heat. When spring begins, and the snow melts, the water 

 trickles down into the inside of the cavern, and is there frozen into transparent 

 ice, by the power of the internal cold, forming large clusters of icicles, as 



• Authorof a history of Hungary in 4 vols, folio, with plates, entitled Notitia Hungariae Historico- 

 geographica. Viennee Austr. 1735 — IZ^S. 



