f 355 3 
be creded on the Orifice equal to the Quantity of 
Water that iffues at the Orifice in the former of thofe 
Times, the Height of this Column will be to the 
Space defcribed by the defcending Body in the latter 
Time, in the fame Ratio as the Orifice to the Area 
of the Bafe. The Ratio of the'Force that ads on the 
Bottom of the VefTel to the Force that generates the 
Motion of the Water iftuing at the Orifice, is de- 
duced from Sir Ifaac Newtons Catarad, and is the 
lame that follows from the Principle concerning the 
Equality of the Afcent and Defcent of the Centre of 
Gravity, which was firft applied to this Inquiry by 
Mr .'Daniel Bernouilli Comment. Acad. Retrop. T om. 
2. But there are feveral Precautions to be taken in 
applying this Dodrine. 
After fome other Theorems concerning the Centre 
of Gravity, and feveral Obfervations concerning the 
Curvature of Lines, and the Angles of Contad ; the 
Author reprefents four general Propofitions in one 
View, that the Analogy between them may appear. 
The Firft gives the Property of the Trajedories that 
are defcribed by any centripetal Forces, how variable 
foever thefe Forces, or their Diredions, may be. The 
Second gives a like general Property of the Lines of 
fwifteft Defcent. The Third gives the Property of 
the Line that is defcribed in lefs time than any other 
of an equal Perimeter. And the Fourth gives the 
Property of the Figure that is alfumed by a flexible 
Line or Chain, in confequence of any fuch Forces 
ading upon it. If we fuppofe a Body to fet out from 
any Point in the Trajedory, or in the Line of fwifteft 
Defcent, with the Velocity which it has acquired 
there, and to move in the right Line which is the 
Z z Di- 
