224 NEWTON S PEINCIPIA. 



have just been considering, the resistances vary as the 

 square of the velocity, the square of the diameter, and the 

 density of the fluid. 



If we have two fluids whose particles when at a distance 

 do not act with any force on each other, such fluids come 

 under the description of the similar systems just considered. 

 Let the particles of the two fluids be equal, then the 

 resistances to equal similar bodies moving in them are 

 accurately as the squares of the velocities of the bodies and 

 the densities of the fluids. Next, suppose the bodies not 

 equal. Because the motion of the fluid varies continu 

 ously from point to point, and because the force of collision 

 due to two equal particles moving in the same manner is 

 equal to that of one particle of double size, the forces of 

 collision will be the same if we divided the fluid into 

 elements, and considered them as particles. Let the equal 

 fluids be divided into elements, which are proportional 

 to the volumes of the similar bodies moving in them. 

 Then the resistances will vary as the square of the diameter, 

 the square of the velocity of the body, and the density of 

 the fluid. 



But how far are we justified in applying these conclusions 

 to the fluids we meet with in nature? The forces to 

 which collision and reflexion are due, are those which are 

 sensible only at distances which are indefinitely small com 

 pared with the average distances between the particles. 

 Are these the only forces which exist between the par 

 ticles of a fluid? Incompressible fluids are the nearest 

 approach to such a state of things. In elastic fluids the 

 particles have a tendency to recede from each other, and 

 our previous reasoning cannot therefore apply to them. 



Let there be three fluids A, B, C ; let them consist of 

 similar and equal particles regularly disposed at equal dis 

 tances, and let the parts of A and B have a tendency to 



