ANALYTICAL CHEMISTRY
1562 mechanism was able to cope with scan rates up to 5 A. per second. At faster scan rates, the slit did not attain the maximum and minimum values obtained a t 1 A. per second but fell off as much as 20% at 20 A. per second. The detailed results given in Table VI11 are sometimes reported only to two significant figures in cases where rapid change made the value very difficult to read with certainty. I t has been pointed out ( 1 ) that higher slitcontrol settings will tend to minimize the lag in the slit response. In conclusion, it should be noted in connection with reproducibility of the log-absorbance spectrum that it is essential for the zero setting to be correct. It may be readily shown that the logabsorbance spectrum is independent of the concentration only if
the absorbance is exactly zero for equal energy transmission of the sample and the reference solution. ACKNOWLEDGMENT
The authors are indebted to the iltomic Energy Commission for partial support of this work. LITERATURE CITED
(1) Cary, H., private communication. RECEIVEDMarch 30, 1953. Accepted J u n e 26, 1963. Presented a t the Symposium on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, P a . , March 1953.
Use of Tangent Intercept to Determine an Average Speed of Sedimentation WALTER P. REID U . S. Naval Ordnance Test Station, China Luke, Calif. HE
theory behind the intercept method for getting particle
T size determinations is given, and it is shown that the time intercept of the tangent line to a sedimentation curve may be
used to obtain an average settling speed. The method for getting particle size distributions from ordinate intercepts of tangent lines to a sedimentation curve is well known (1-3). However, the use of the time intercepts of the same tangent lines for obtaining average settling speeds does not seem t o have been employed. This may reflect a lack of general interest in average sizes, and hence in average settling speeds. Neve-theless, average sizes are sometimes of interest. A method for getting an average settling speed will be given in this paper. This may be used to obtain an average radius by assuming Stokes’ law of settling, although the theory in this paper assumes simply a constant speed of settling for each particle. Consider an assortment of particles of the same material in a liquid with which they do not react chemically, and in which they do not dissolve. Suppose the particles all to be small enough so that each will settle with a constant speed in the liquid. Assume that the particles are initially distributed uniformly throughout the liquid with no two of them sticking together, and with no air adhering to any of the particles. The concentration of particles should be small enough so that the particles will not appreciably influence each other’s speeds of settling. Assume that each particle begins settling immediately 6 t h a constant speed characteristic of its size (the larger particles falling faster). Define a function F ( v ) such that the area under the F ( v ) curve between any two values of v will be equal to the mass of particles per unit volume of the original mixture which settle a t speeds lying between those v values. After time t, the particles whose dv will have settled approxisettling speeds lie between v and v mately a distance vt if dv is sufficiently small. There will then be none of them in the layer of depth V I a t the top of the fluid. Consider a plane, B C, which is a distance H below the surface of the liquid. Those particles above this plane whose centers lie under area A of the surface of the liquid will lie within a region of volume A(H-ut), for vt
