76 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



RTjM, from which M can be calculated. Pressure measurements are 

 therefore made over a range of low concentrations and the curve 

 extrapolated to zero concentration so that 



P RT 

 Lt — = 



c->o c M 



It is particularly to be noted here that osmotic pressure determinations, 

 depending as they do on the number of particles in solution, give a 

 number average molecular weight, i.e. 



where «,• is the number of gm. moles of molecular weight M,- and the 

 summation is taken over all values of /. 



{b) A second method for the determination of high molecular weights 

 and one which was, in fact, devised precisely for that purpose, involves 

 the ultracentrifuge of Svedberg. Actually there are two distinct methods, 

 the method of sedimentation equilibrium which again has a sound 

 thermodynamic basis, and that of sedimentation velocity. This latter, 

 in view of the fact that it does not involve equilibria, has naturally no 

 thermodynamic basis but the theory underlying the method is now 

 unquestioned. These may be considered briefly in turn. 



(1) Sedimentation equilibrium 



(b) The principle of this method can perhaps best be grasped by 

 considering the equilibrium attained in a column of air under the earth's 

 gravitational field. The molecules of gas will tend to separate out and 

 are prevented from doing so only by the thermal agitation of the mole- 

 cules. This leads to a variation in the properties of the atmosphere with 

 which everyone is familiar. Thus, considering unit cross-section, the 

 decrease in pressure dp, for a small increase in height dh, is given by 



—dp=gQdh, 



where q is the mean density of the gases at height h. Assuming the gases 

 to be perfect, then 



Q==MplRT, 



whence 



-dplp=(MIRT)g.dh, 



which integrates to 



\n{p^lp^)={MglRT){h^-hd, . .(1) 



where /7i is the pressure at height /ij, and/?2 that at height h^. 



