256 THE CHEMICAL CONTROL OF THE DAIEY. 



serum less tte weight of the globule, or 



e = k.ii7zr^ .(ds- df) . g, 



where i is a constant varying with the units adopted for r, dg and d/. 

 Tz is the ratio of the circumference of a circ'e to its diameter, 

 r is the radius of the globule, and 

 g is the acceleration due to gravitation. 

 d) and d/ are the specific gravities of the serum and fat. 



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

 globules move the resistance is \'ery nearly proportional to the square of 

 the velocity. 



We may then write the equation : — 



Total force at any moment impelling the globule to rise is — 



■^^ = k .t Ttr" .(ds — df)g — cv^ 



by equating k Itt . (dg — dj) g . tob^, leaving only the variables, we may 

 write this — 



-^ J2 ^3 _ (.^2_ 



at 

 Integrating this, we get — 



^ 6?-" ■ (e«' - 1) 

 " ~ c (1 + e»') ' 

 where a = 2br'-. 



For large values of t the expression =-— — jj wiU approach very nearly to 



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



this by substituting the value of h, we get — 



^^ ^^fc . ix {d, -dj)g. )-3 _ 

 c 



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

 will be after a short time established 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 mUlc 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 -rrsTjT;- 

 must be substituted for g. o,bUU 



V = velocity in revolutions per minute, 

 b = 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 — 



Solving this equation and integrating between the limits b and b^, we get — 



