332 ANDREWS 



ART. I 



long enough to bring about equilibrium. In calculating their 

 distribution in the ultra-centrifuge where forces 5000 times 

 that of gravity are encountered, one cannot consider the force 

 as constant but must take into account the variation of force 

 with distance from the axis of rotation. Using concentration 

 c instead of pressure, the distance x from the axis of rota- 

 tion instead of height, and the force due to the difference in 

 density between particle and solvent instead of gy, equation 

 [233] becomes 



N 

 dc = — r— i irr^ (pp — ps) co^c xdx, (7) 



where co represents the angular velocity. 



If we wish to get the concentration at different points in a tube 

 such as might be placed in the ultra-centrifuge, we may let x^ 

 represent the end of the tube furthest from the axis, i.e., the 

 bottom of the cell. Then on integrating we obtain 



,. = ,,, -S I '■<—>-(^) (8) 



Figure 1 shows the distribution for various particle sizes as 

 calculated by Svedberg from this equation, letting x^ = 5.2 

 cm. and co = IQOtt per sec. 

 We may write equation (7) also in the form 



— = - ^ — ^ ^2 x dx, (9) 



where V is the partial specific volume of the solute. Integrat- 

 ing and solving for M, we get 



2 RT In (ci/c2) . ^, 



CO-'il — Vps) {Xi — X2) 



In this way the measurements of concentration at equihbrium 

 may serve as a means of calculating the molecular weight of 

 the particles. 



Svedberg and Fahraeus'" made observations of this sort 

 on hemoglobin. The solution of hemoglobin was placed in the 



