NEWTON S PRINCIPIA. 



261 



velocity, and A the area of a great circle of a sphere 

 moving in a fluid of density p, that the resistance will be 

 A v 2 p. The globe and particles are supposed perfectly 

 elastic, and thus endued with the utmost force of reflexion. 

 But if, on the contrary, they are perfectly hard, and with 

 out any reflecting force, the above expression for the 

 resistance must be diminished one half. &quot; But in continued 

 mediums the cylinder as it passes through them does not 

 immediately strike against all the particles of the fluid that 

 generate the resistance made to it, but presses only the 

 particles that lie next to it, which press the particles be 

 yond, which press other particles, and so on, and in these 

 mediums the resistance is diminished one other half.&quot; 



If in the centre of the hole E F a small circle P Q, of 

 area C, is placed, the weight of water which it sustains 

 will be greater than the weight of 

 a cone whose base is P Q and alti 

 tude H G, and less than that of a 

 spheroid on the same base and of 

 the same altitude. For let HP 

 and H Q be the boundaries of the 

 cataract. The cataract falls freely, 

 and therefore there is no pressure 

 on the sides of the mass of still 



water H Q P. The pressure on the circle P Q is the 

 weight of water H Q P. And this will still be equal 

 to the pressure if the ice which forms the sides of the 

 cataract be dissolved, and the whole water be left to flow 

 out of the orifice in any manner whatever. A little con 

 sideration will show that the mass of fluid H P Q must 

 have its boundaries meeting in a point at H, and being 

 convex to G, they also meet the sides of P Q at an acute 

 angle. Therefore these boundaries lie without the surface 



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