262 NEWTON S PRINCIPIA. 



of the cone and within the surface of the spheroid described 

 on the base PQ, and with an altitude HGr. 



The weights of these two solids are respectively 



1 2 



- Chgp, and ^ 



where p is the density of the fluid, and h the altitude HG. 

 Therefore the weight supported by the little circle lies 

 between these two quantities. If the circle be very small, 

 both these will be small, and we may take the weight sup 

 ported as being very nearly equal to their arithmetic mean, 

 that is 



where P is the pressure on the little circle. If, however, 

 C be not very small, compared with B, let us assume that 

 the pressure is 



P = 



where B is the area of the orifice EF. 



Then when C is very small, this must agree with the pre 

 vious result, hence /3 = 1, and when C = B the weight 

 supported is that of a cylinder whose base is C and altitude 

 hy hence = ^. Moreover, so long as C is less than half 

 B, the expression 



- 



makes P lie between the limits assigned above. 



Newton next proceeds to point out the analogy between 

 the pressure on the circle and the resistance to a circle 

 moving in a still fluid. Let the vessel touch the surface of 



