NEWTON S PRINCIPIA. 225 



recede from each other with forces that are as T and V, 

 and let the particles of the medium C be entirely destitute 

 of such forces. Let four equal bodies move in these 

 media, viz. 



D in the medium [A ,] and E in [B] 1 

 F and G in [C], J ; 



and let 



vel. of D vel. of F AT . 



vel. of E vel. of G = V V 



then since the forces are as the squares of the velocities,, 

 and the diameters of the particles are equal, therefore the 

 resistances in the two fluids are as the squares of the ve 

 locities, that is 



Res, to D Res, to F T ( . 



Kes.toE == Kes.toG V 



Let us suppose also that 



vel. of D = vel. of F 

 .-. vel. ofE = vel. of G 



augment the velocities of D and F in any ratio, and di 

 mmish the force V of the particles in the medium B in the 

 duplicate of that ratio, the medium B will approach to the 

 form and condition of the medium C, and therefore the 

 resistances to the equal and equally swift bodies E and G 

 moving in those media will approach equality. Hence by 

 (2.) the bodies D and F, when they move with great swift 

 ness, meet with resistances nearly equal. Hence the re 

 sistance to a body moving very swiftly in an elastic fluid is 

 almost the same as if the parts of the fluid were destitute 

 of their centrifugal forces and did not tend to fly from 

 each other. So that the resistance to similar bodies moving 

 very swiftly in an elastic medium vary as the squares of 

 the velocities and the squares of the diameters. 



Q 



