Light scattered by Spherical Metal Particles. 475 



until no particles are left behind in suspension. All the 

 particles are then o£ radius greater than ai, and the suspen- 

 sion obtained by mixing these with water is now centrifuged 

 for a time t 2 , less than r 1} by which means particles of radius 

 greater than a 2 are removed. Finally, a suspension is 

 obtained containing only particles having radii between a 1 

 and a 2 . 



In order to obtain strictly uniform suspensions by this 

 method it is necessary that a large quantity of raw material 

 be available. Professor Perrin in some of his experiments 

 used several kilograms of mastic, the centrifuging extending 

 over a period of several months. Such a procedure is im- 

 practicable for the preparation of suspensions of silver, and 

 it is therefore desirable to obtain some idea of the degree of 

 uniformity possessed by suspensions which have been prepared 

 in a less exacting manner. 



The following simple theory, which is strictly applicable 

 only to a hypothetical centrifuge, working at a uniform 

 speed, and which neglects the effect of convection currents 

 in the test-tubes, changes in temperature, and errors due to 

 speeding up and slowing down, shows in more detail the 

 kind of processes that occur during fractional centrifuging. 



Let m=the effective mass of: a particle, 

 a = the radius of a particle, 

 co = the angular velocity of the centrifuge, 



and r = the distance of the particle from the axis of the 

 centrifuge. 



Then by Stokes's law — assuming that the velocity at each 

 position has tlielimiting value corresponding to that position* — 



m co-r =G7T7]av, 



where rj is the viscosity of water and v is the velocity of 



clr 

 the particle. Replacing v by -j , and m by its equivalent 



\ira z (p — p) — p being the density of the particle and p' that 

 of water — we find 



ity C r *dr 



Jo Mp-pVJr, 



whence U?/ . r 



2a-(p-p)a>~ & n 

 and f drj r a ) i 



* This is justifiable as long as ?>7Ti](i/m for the particles dealt with is 

 large compared with w. 



