OPTICAL DENSITY WITHIN ROTATING ULTR-4CENTRIFUGE CELLS 1305 rect value of a is the one which will give a set of log K A -D-' points for systems 1 4 which will lie on the extrapolation of the line through the points for systems 5-7. The four points a t the left in Fig. 5 are those obtained using 6 = 9.0 in (8). Within the validity of the various approximations made, this is in satisfactory agreement with the value if. = 8.5 found from the slope of Fig. 4. The points obtained using J (5.0) and J ('7.0) in (8) lie below any reasonable extrapolation of the line approximating the points for systems 5-7. Now J ( a ) represents the change in mobility due to the higher terms in the conductance equation, while KA(a) of course describes the ion-pair equilibrium. The agreement between the values of a from J and from K A shows that charge-charge interaction suffices to describe the behavior of BudN.BPh4 in the solvent system CH3CN-CC14. From the viscosity coefficient F, the value of the hydrodynamic radius was found3to be 5.4 h., assuming the two ions to be of equal size. Center-to-center distance a t contact, based on viscosity data, then would be 10.8. This is in fair agreement with the electrostatic parameter, 6 = 9, considering the completely different physical processes underlying the two results. Molecular models show that the nearest one can possibly bring the borqn and nitrogen atoms of BulIV.BPh, is about 7 A. ; this must represent the lowest possible bound for 8. The two ions are, of course, not spheres; the boron-nitrogen distance averaged over random orientations of the two ions a t contact must certainly be larger than this minimum figure, as we found above from the conductance (and viscosity) data. Finally, we consider the Walden products shown [CONTRIBUTIOS The design and applications of an exponential aperture for analytical ultracentrifuge rotors are described, Images of the Photometry of these photorotating aperture and ultracentrifuge cell are recorded side by side on absorption photographs. graphs provides the necessary data for accurate evaluation of optical density within the rotating cell, The photographic determination of optical density within a cell during the operation of the analytical ultracentrifuge is of importance in many experiments.' It is convenient in such work to employ the film within the linear range of its characteristic response to exposure and to measure its optical density with a photometer possessing linear response to film optical density. These two conditions are expressed by the relation /3 log exposure = Pen Deflection + f i (1) where , R and "f1, are constants characteristic of the film specimen and the photometer.(1) T. Svedberg and K. 0. Pederson, "The Ultracentrifuge," The Clarendon Press, Oxford, 1940, pp. 240-253. Because film characteristics vary with emulsion and conditions of exposure and development, a verification of film linearity must be made whenever accurate work is to be done.A convenient method for calibrating the response of the film and photometer has been...