258 H. K. SCHACHMAN AND R, C. WILLIAMS 



of its mass and the volume of liquid of known density which is displaced 

 upon the addition of the particle to a large volume of solution. Alternatively 

 tliis force can be expressed, without resort to a mechanistic point of view, 

 by application of thermodynamics of irreversible processes. In this treatment 

 the force is wTitten as the gradient of the total potential. Under the 

 influence of the centrifugal field the particles quickly attain a limiting 

 velocity at which the frictional force (which is proportional to the velocity) 

 is equal to the driving force. Each of the different theoretical treatments 

 gives the result 



This equation, it should be noted, is limited to two component systems, 

 i.e., those solutions containing a macromolecule and the solvent. When 

 other components are present, such as buffer salts, an additional term is 

 required. Generally the evaluation of this term is difficult, and it is tacitly 

 assumed that it can be neglected as long as the salt concentration is low. 

 Omission of the salt, though desirable from a theoretical point of view (in 

 terms of Equation 22), would cause a greater error owing to the electro- 

 static effects discussed previously. When large amounts of a third component 

 like urea, sucrose, or inorganic salts are present, the use of Equation 22 is 

 likely to lead to serious errors (Schachman and Lauffer, 1950). 



For dilute solutions of the macromolecules, the frictional coefficient in 

 sedimentation is considered to be the same as that encountered in diffusion; 

 therefore Equations 14 and 22 can be combined to give the famihar Svedberg 

 relation 



M=-?^ (23) 



D(l ~ Vp) 



where R is the gas constant, 8.314 X 10' ergs/mole/degree. No assumptions 

 as to the shape or degree of hydration of the sedimenting molecules are 

 involved. Despite the fact that the molecules may be extensively hydrated 

 in solution, correct values of the molecular weight are obtained through the 

 use of Equation 22; moreover, the calculated molecular weight corresponds 

 to the anhydrous molecule. In this respect the sedimentation-diffusion 

 method is analogous to that of light scattering. 



Treatments of the frictional coefficient similar to those already presented 

 for diffusion are applicable to sedimentation as well, and the shape or hydra- 

 tion are calculated readily from Equations 22 and 23. In the absence of 

 knov.dedge of either the shape or hydration, the sedimentation coefficient 

 and molecular weight are combined with the intrinsic viscosity, according 



