SynopsisEarlier determinations of density gradient proportionality constants p0, density distributions p ( r ) , and the effect of pressure on density gradients in the analytical ultracentrifuge have been of limited precision and usefulness in the study of proteins and polypeptides. Reasons for these difficulties are that numerous intermediate relationships were required in the calculations, and the density ranges studied were generally above 1.2 g/ml. Relations are derived in the present paper to directly compute $ ( p ) values and @J'(p) values from the original data without any intermediate expansions or approximations. Data are presented for CsCl, CsBr, and Cs2SO4 and compared with literature values. Density distributions are computed for all three salts under a wide variety of experimental conditions of density, column length, and angular velocity. These values of p ( r ) and re are obtained by a numerical iterative technique. Values obtained by this new method are compared with values obtained using closed-form expressions. The effects of pressure on the composition density gradient for the three salts given above are calculated and found to be significant for CszS04 solutions.