298 NEWTON S PRINCIPIA. 



describe two indefinitely near cylinders with this straight 

 line as their common axis. The fluid between these two 

 cylinders will evidently revolve unchanged whatever 

 be its velocity, and however different from that of the 

 neighbouring fluid, the normal pressure being sufficient 

 to counteract the centrifugal force. There is, however, 

 no perfect fluid in nature : if a stream of one fluid be made 

 to pass through another, it will carry the particles of the 

 second along with it. A true theory of vortices must 

 take account of this &quot; internal friction&quot; of the fluid. 

 Newton starts with the hypothesis that &quot; The resistance 

 arising from the want of lubricity in the parts of a fluid is, 

 caeteris paribus, proportional to the velocity with which the 

 parts of the fluid are separated from each other.&quot; 



This hypothesis, as Newton himself remarks, is probably 

 not altogether correct, but, nevertheless, there can be no 

 doubt that it will give us a general idea of the motion. 

 The first problem to which we shall apply it will be 

 the following: 



Two infinite cylinders &quot;having a common axis revolve in 

 any uniform manner about that axis. Fluid is placed be 

 tween them, and soon acquires a rotatory motion; it is required 

 to determine what that motion will be after it has become 

 settled or steady. 



Divide the whole fluid by concentric cylinders whose 

 radii continually differ by 8r. Then we may suppose the 

 fluid between any two of these to solidify, and the circum 

 stances of the case will not be in the least altered, provided 

 we at the same time make 8 r diminish without limit. Let 

 us then consider the friction between any two of these 

 solidified cylindrical elements. Let GO and ca + 8 w be the 

 angular velocities of two consecutive cylinders, and let the 

 radius of the surface of junction be r. It is manifest that 

 the relative velocity of the two cylinders is 



