III. CENTRIFUGATION 85 



in which r is the number of grams of the medium combining with one 

 gram of the sohite. 



An idea of the effect of particle shape on the frictional coefficient 

 can be obtained from the following expressions (84) '• 



For oblong ellipsoids (k < 1): 



/ (1 - k'Y^' 



^ " .VMog L+ ^^ - ^^)" 



(10) 



k 

 For oblate ellipsoids (k > 1) : 



/ (k' - 1)'/^ 



/o /v'/' arctan (k^ - 1)'^ 



(11) 



In these formulas k equals the ratio between the equatorial radius 

 and half the length of the axis of rotation, the particle volume being 

 the same for / and /o. Also, random orientation of the particles is as- 

 sumed. 



3. Molecular Weight and Particle Size 



When conditions are such that fs = fo, it is possible to equate 

 expressions (6) and (7) and derive the Svedberg formula (1) for molec- 

 ular weight: 



M = RTs/Dil - Vp) (12) 



The diameter, d, of spherical particles in dilute preparations may 

 be computed from the following expression, which is obtained by equat- 

 ing the net motivating force and the frictional coefficient as given by 

 equation (8) : 



d2 = l877sF/(l - Vp) (13) 



For the equilibrium condition, equating expressions for the trans- 

 port of material by sedimentation and diffusion leads to the following 

 equation (/) for molecular weight in the case of a monodisperse sys- 

 tem: 



^ 2RT log (c,AO 

 (1 - Vp),^\xl ~ x\) 



where Ci and C2 are the concentrations at radial distances Xi and Xi. 



