THE STRUCTURAL FEATURES 6F CELLULOSE 77 



Equilibrium in the ultracentrifuge is precisely analogous to this. The 

 centrifugal field takes the place of gravity and is very high (about 

 10,000g) in order to bring measurable effects within small compass. 

 At equilibrium, in which a balance is obtained between sedimentation 

 and diffusion, there is a particular distribution of concentration which 

 can be treated in a way quite analogous to the above treatment of gase- 

 ous pressure. Experimentally, the solution is held in a cell with trans- 

 parent windows and is spun at speeds up to about 15,000 r.p.m. The 

 contents of the cell are examined optically by methods described else- 

 where (28), and the spinning continued until the distribution of con- 

 centration remains constant. Then, corresponding to equation (1) 

 above, 



dclc=M(\ -vq)co^x . dxIRT, . . (2) 



where x is the distance of the point of observation from the centre of 

 rotation (=h in equation (1)), w^x is the angual acceleration (=g) and 

 M{1—vq), where q is the density of the solvent and v is the partial 

 volume of the solute (or M(^soiute— ^solvent)), replaces M. On integration 

 M^2RT\n {cjci)l{l -VQ)a)%xi-xl). 



This equation again, as in the osmotic case, applies only to low con- 

 centration. 



(2) Sedimentation velocity 



(b) In this method, the centrifugal field is made so large that opposing 

 diffusion is negligibly slow and no equilibrium is reached. Normally 

 fields of 100,000 to 300,000g suffice, though Svedberg has used fields 

 up to 500,000^. In principle, the theory is very simple. If a molecule 

 of weight M is moving with velocity dxidt under a centrifugal accelera- 

 tion co-x, then equating the forces causing and opposing motion, we 

 have 



M(l -vq)oj^x=F. dxIdt, 



where F is the frictional constant per mole, or, defining a sedimentation 

 constant, s 



s=^(dxldt)lco^x, 



M=FsI{\-vq). ..(3) 



For spherical particles, the frictional constant was given by Stokes as 



FQ—dnNrir, 



N being Avogadro's number, ri the viscosity of the solvent (see below) 

 and r the radius of the particles. This cannot, however, normally be 



