I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1380 and
Vol. 43, No. 6
and
y = exp [-0.9874~4
+ 6.714723 1 4 . 1 1 4 4 ~+~ 10.1638~+ 0.46841
y = exp [-1.8750z4
(21)
Both equations produce bimodal distributions, but Equation 20 shows better agreement with the data. An analysis of Equation 8 shows that a four- or five-ordinate method can be applied to a size distribution of the form shown in Figure 5. The data for the experimental curve in this figure are given in Table 11. The left-hand portion of this curve rises steeply; a very rapid drop to the origin from a maximum occurs, but is not indicated in the figure. Such distributions are not uncommon in the study of emulsions. This curve as fitted by the same method as above and by using four selected ordinates. The equation representing the latter form of distribution is y = exp [ -(a323
+ a2z2+ alz+ UO)]
(22)
Two equations calculated from sets of selected ordinates are 3 = exp [-1.5330x3
+ 1 0 . 1 7 2 9 ~-~ 18.81392 + 10.6012] (23)
+ 1 1 . 9 9 5 1 ~-~ 2 3 . 0 9 0 3 ~+ ~ 12.72902 + 2.03321
(24)
These equations are plotted in Figure 5 LITERATURE CITED
(1) Fagerholt, G., Ph.D. thesis, Den Polytekniske Laereanstalt,
Denmark (1944). ( 2 ) Kapteyn, J. C., “Skew Frequency Curves,” P. Noordhoff,
Groningeti, 1903. (3) Lipscomb, W. K.,Rubin, T. R., and Sturdivant, J. H., J . Applied Phus., 18, 72-9 (1947). (4) O’Toole, A. L., Ann. Math. Statistics, 4 , 1-29 (1933). ( 5 ) Ibid., pp. 79-93. (6) Pauling, L., and Wilson, E. B., “Introduction to Quantum Mechanics.” Chap. 1‘. New York, McGraw-Hill Book Co.. 1935. (7) Pearson, Karl, Phil. T ~ a n sRou. . Soc., Ser. A . , 185, Pt. I, 71-110 11894). ( 8 ) Schoenholz, D., and Kimball, C. S., Soap Sanit. Chemicals, 23, No. 8, 131, 133, 135 (1947). RECBIYED January 3, 1951.
END OF SYMPOSIUM Reprints of t h i s symposium, including two papers appearing in the June 1951 issue of Analytical Chemistry (pages 844 t o 853), may be purchased for 50 cents from the Reprint
Department, American Chemical Society, 1155 Sixteenth St., N.W., Washington 6, D. C.
Biosynthesis of Riboflavin, L. bulgaricus Factor, and Other Growth Factors LABORATORY AND PILOT PLANT STUDIES OF BIOSYNTHESIS BY A . GOSSYPII CULTIVATED ON GRAIN STILLAGE MEDIA I
