300 NEWTON S PRINCIPIA. 



If the fluid be homogeneous, this condition requires that 



_ * 2 

 r 



should increase with r. Hence its differential coefficient 

 must be always positive ; that is, 



on substituting for a and (B their values, this gives 



&quot; &amp;gt; l fl i- M 

 =; &quot;2 ( l ^rj 



If there be added or taken away from the fluid and 

 cylinders any constant quantity of angular velocity, the 

 mutual attraction of the particles of fluid will not be 

 changed, and therefore the relative motion will remain 

 the same as before. If we impress on the whole system 

 such a velocity as to make /3 = 0, we get 



a 



**-/&amp;gt; 



and this is the case considered by Newton. Unless the 

 fluid be heterogeneous, this state of motion is unstable. 

 Each particle of fluid has a greater tendency to fly from 

 the centre than those beyond it, and hence if any circum 

 stance occurs to alter the symmetry of the motion, the 

 particles of those strata which have too great a centrifugal 

 force will immediately fly from the centre, and the whole 

 motion will be changed. This state of motion is like the 

 case of a stratum of a heavy fluid resting on the surface of 

 a lighter one. 



