10 



C. L. SADRON 



5 hl_ or yhfOfcoil) 

 6 

 Fig. 2. F(9) functions for a few simple-shaped particles. 



P(e) = i-^ 2 f- 



(20) 



where R" is the mean square value of the radius of gyration of the par- 

 ticle. 6 ' 1 



It is very important to note that Eq. (20) is quite general and independ- 

 ent of the model chosen to give a representation of the particle. 



As a conclusion, we see from Eq. (12) that 



(i). 



d (20 



(A 



h + 2Be 



(21) 



and from Eqs. (12) and (20) that 



4K?) 



With the use of two proper extrapolations giving (c/K) c=0 it is possible 

 to measure M (intercept of the curve with the ordinate) and R 2 (initial 

 slope of the curve) whatever the shape and dimensions of the particle. 



Very often these two operations are made according to a process due to 

 Zimm : the values of c/K are taken as ordinates and the values of sin 9/2 + 

 nc as abscissa where n is an arbitrary numeric factor whose magnitude is 

 chosen according to the commodity of the graphic representation. 



6a The radius of gyration of an assembly of N points Ai with the same weight m is 

 R 2 = ~LiTi 2 /N where r, is the distance of Ai to the center of masses of the assem- 

 bly: for a sphere (radius L), R 2 = 6L 2 /10; for arod (length 2L), R 2 = L 2 /3; for a 

 Gaussian chain, R 2 = LV6; for a zigzag chain, R 2 = 6 2 /6 (JV - 1 + 1/2JV). 



