RISING OF FAT GLOBULES. 409 



The globule does not, however, rise freely ; at the velocity at which the 

 globules move the resistance is very nearly proportional to the square of 

 the velocity. 



We maj 7 then write the equation : 



Total force at any moment impelling the globule to rise is 



by equating k n- . (d s df) g . to 6 2 , leaving only the variables, we may 

 write thus 



~dl = 

 Integrating this, we get 



br* . (e at 1 ) 



V = rt\~~> 



3 



where a = 2br?. 



For large values of t the expression - will approach very nearly to 



1, and the equation becomes very nearly equal to , or, expanding 

 this by substituting the value of 6. we get 



Vk . ITT (d, - d f }q . r*. 



c is the coefficient of viscosity of the serum. It is evident that equilibrium 

 will be established after a short time when the resisting force is equal 

 to the impelling force, and if the latter be constant the motion will be 

 uniform. 



The time taken by a globule to pass through a given layer of milk is, 

 therefore, inversely proportional to the square root of the cube of the radius. 



If the globule is acted on by centrifugal force, the expression -^nTT 

 must be substituted for g. 6 ' w 



V = velocity in revolutions per minute, 

 & = distance of globule from the centre of revolution. 



If submitted to centrifugal force, it is evident that the speed of a globule 

 cannot be constant, as the centrifugal force tending to move it varies with 

 the distance of the fat globule from the centre of revolution, and the equation 

 for the motion of globules under these conditions is 



d z s 



Solving this equation and integrating between the limits 6 and b v we get 



30 



