JUNE 15, 1939
ANALYTICAL EDITION
number of particles having a given diameter.) The parameters 5 and b can be evaluated from a graph such as is shown in Figure 11. Equation 18 shows that when x = E, R = 100/e = 36.79 per cent, so that the value of x can be read directly as that value of x a t which the percentage oversize is 36.79, or at which the percentage undersize is 63.21. This is illustrated in Figure 11 by the intersection of the line for the size distribution with the dot-dash horizontal line a t R = 63.21 per cent, in this case, 1: = 6.25 cm. (2.5 inches). The constant 2: is therefore a measure of the magnitude of the size of t,he particles considered and in this respect is analogous to M and M , in the preceding equations. The value of parameter b is given by the slope of the curve. It is a measure of the dispersion of the distribution, that is, if b is large, the particles are closely grouped in diameter, whereas if b is small, the particles are distributed over a relatively wide range. The constant b is therefore analogous to Q in the preceding equations. The form of Equation 17 makes it difficult to express Green’s average diameters, or the specific surface, in terms of 5 and b. Summary It is desirable for many reasons to be able to plot a cumulative size-distribution curve as a straight line. If this can be done, the number of measurements can be reduced, interpolation becomes easier, extrapolation becomes more reliable, the consistency of the observations can be judged a t a glance, the calculation of average diameters is facilitated, and the frequency distribution curve can be readily obtained. No single method of plotting which is applicable to all materials has been found, nor is it likely that one exists. There are, however, three methods which have proved successful for
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certain classes of substances. The most widely applicable one is to plot particle size on a logarithmic scale and cumulative per cent on an integrated probability scale. It gives satisfactory results for crushed or ground materials such as silica, granite, limestone, clay, sodium carbonate, and alumina. The second is the Rosin-Rammler method which plots size on a log scale and cumulative per cent on a log-log scale; i t has been notably successful with broken coal. The third method, which appears to have only a very limited applicability, is to plot size on a linear scale and cumulative per cent on the integrated probability scale. These methods have a possible application to the determination of whether or not one has a representative sample on a material whose composition varies with size of lump, and can even be extended to distributions other than size, such as the variation with time of the composition of pig iron from a given furnace. Literature Cited (1) Bennett, J. Inst. Fuel, preprint, 1936. (2) Daeves, “Praktische Grosszahl-Forsohung”, VDI Verlag, Berlin, 1933. (3) Drinker, J.Ind. Hyg., 7,305 (1925). (4) Green, J. Franklin Inst., 192,637 (1921). (5)Ibid., 204,713 (1927). (6) Hatch, Ibid., 215, 27 (1933). (7) Hatch and Choate, Ibid., 207,369 (1929). Anal. Ed., 10,45(1938). (8) Jones, IND.ENQ.CHEM., (9) Loveland and Trivelli, J . Franklin Inst.,204, 193,377 (1927). (10) Martin, Bowes, Coleman, and Littlewood, Trans. Ceram. SOC., 25, 240 (1926). (11) Norton and Speil, J. Am. Ceram. SOC.,21,89 (1938). (12) Rosin and Rammler, J . Inst. Fuel, 7,29 (1933). (13) Weber and Moran, IND.ENO.CREM.,Anal. Ed., 10, 180 (1938). (14) Work, Bull. Am. Ceram. SOC.,17, 1 (1938).
Improved Form of Jones Reductor P. NILAKANTAN AND N. JAYARAMAN, Indian Institute of Science, Bangalore, India
I
N T H E course of analytical work which involved the estimation of iron, the authors have found a modified form of Jones reductdr very convenient. I n the usual form (I), shown at right of Figure 1, hydrogen collects just below the zinc column and cannot escape freely. This gives rise to two disadvantages in manipulation: (1) The free and steady flow of the acid solution is impeded. (2) Since in resetting the reductor for a fresh experiment the zinc has to be washed thoroughly and all the accumulated gas displaced by distilled water, and since this cannot be accomplished easily either by passing a swift stream of water through the reductor or even by applying suction, it often becomes necessary to remove the reductor from its support to displace the gas. The improved form obviates both these difficulties. The wide tube is bent round at the bottom, as shown, and the gas which collects below the zinc rises in the narrow tube and is automatically pushed out by the solution. Hence, it cannot accumulate to any undesirable
Amalgamated aino granules Glass wool or asbestos pulp Glass beads d. Perforated porcelain disk a.
b. c.
extent and thereby impede the flow. For washing the apparatus finally and for displacing any remaining gas bubble before commencing a fresh experiment, all that is necessary is to run down water in a brisk stream through the tube with the stopcock fully open. Literature’ Cited FIGUR 1. ~JONES REDUCTOR ’
(1) Treadwell and Hall, “Analytical Chemistry”, Vol. 11, p. 554,New York, John Wiley & Sons, 1935.
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