248 H. K. SCHACHMAN AND R. C. WILLIAMS 



curve of refractive index (or concentration) versus distance, and the condi- 

 tions for interference arise in a much different way. Rather than exploiting 

 interference conditions from pairs of positions within the boundary as in the 

 Gouy method, here interference is estabhshed between each point in the 

 diffusion cell and a conjugate point in a reference cell filled with a homo- 

 geneous liquid like water or buffer. The vertical coordinates of the cell are 

 imaged along the length of the vertical fringes. In the absence of a boundary 

 the fringes are straight because the optical path difference for rays passing 

 through the diffusion cell and the comparison channel is a constant. "When a 

 bomidary is present, the fringes become warped and their course represents 

 the change of refractive index (or concentration) in the diffusing boundary. 

 For optical reasons, a single fringe cannot be traced through the whole 

 bomidary. However, the family of fringes, when taken together, gives a 

 direct measure of the change in refractive index (and therefore of concen- 

 tration) as a function of distance. Measurements are made of the location of 

 each fringe as a function of the vertical distance. From these data and the 

 necessary tables representing the integral of Equation (13), the diffusion 

 coefficient is evaluated (Longsworth, 1952). Fringes can be paired in different 

 ways to calculate the diffusion coefiicients and the lack of variation in the 

 resultant values is good evidence for the homogeneity of the diffusing 

 substance. Unlike the Gouy method, the Rayleigh method as customarily 

 employed does provide an image of the cell, and it therefore is useful in the 

 examination of moving boundaries. Patterns with this system are likely to 

 find wide apphcation in ultracentrifugation and electrophoresis as well as in 

 diffusion. Representative photographs from a diffusion experiment are given 

 in Fig. 2. 



c. Interpretation of Diffusion Coefficients. In general, diffusion coefficients 

 are employed in conjunction with the results of sedimentation velocity 

 experiments for the calculation of molecular weights. Without both results 

 such computations cannot be made with certainty unless the shape, degree 

 of hydration, permeabihty, and flexibility of the macromolecules are known. 

 Rarely, if ever, are these factors available. Despite these uncertainties about 

 the morphology of the macromolecules, no ambiguities accompany the 

 evaluation of molecular weights from the combination of diffusion and 

 sedimentation data. As long as these data are accurate and correspond to 

 infinitely dilute solutions, the molecular weights are reliable. The fact that 

 the diffusion and sedimenting unit in solution contains large quantities of 

 solvent is immaterial. Whether the shape, the permeability, and tlie flexi- 

 bility of the kinetic unit conform to some specific model is unimportant. 

 Values of the molecular weight calculated from the sedimentation and 

 diffusion data correspond to the anhydrous particles. Iii this way they are 

 directly analogous to the results of light-scattering measurements. 



