NEWTON S PRINCIPIA. 263 



stagnant water with its bottom CD, and let the water run 

 out of the cylindrical canal EFTS perpendicularly to the 

 horizon, and let a small circle P Q be placed anywhere in 

 the middle of the canal with its surface horizontal. Let 

 U be the velocity of the fluid at the surface, V that at the 

 orifice, A the area of a section of the cylinder, B and C 

 that of the orifice and little circle P Q, h the altitude of 

 the cylinder. Then 



V(B - C) = UA. 



If we suppose A to be infinitely greater than B, this last 

 equation shows that U is indefinitely small, and therefore 



V 2 = 2^ft, 

 and the pressure on the little circle is 



where a is some quantity that becomes unity when 



C 



w diminishes without limit. 

 x&amp;gt; 



Now let the orifice of the canal E F S T be closed, and let 

 the little circle ascend with such a velocity that the rela 

 tive motion of the circle and fluid which is compelled to 

 rush past it may be the same as when the water fell from 

 the height HGr, and the circle was at rest. The pres 

 sure on the circle will be the same as before. The 



C 



velocity of the fluid will be =~ - p V, and that of 



the plane ^ - ~ V. Let us suppose B infinitely 



.D - O 



greater than C, then the resistance on a plane moving 

 with a velocity V in still water is i C v 2 p. If a cylinder, 



s 4 



