September 1950
INDUSTRIAL A N D ENGINEERING CHEMISTRY
At the outset it was thought that wheat grit mashes might supply all the nutrients required by Isctobacilli and thus be suitable without supplement for studying the effects of controlled pH on the lactic acid fermentation. However, analyses of the early runs showed considerable and variable amounts of residual sugar. If the fermentations had been complete, all the residual sugar values should have been low and similar. Because they were not, it appeared that the medium was deficient in some constituent. So when run 19 stopped, 1 gram of solid potassium dihydrogen phosphate was added. Within an hour fermentation revived; within 3 hours normal activity probeeded in this s u p posedly exhausted mash. Based upon this observation, nutrient salts were added to the mashes, but even the addition of minerals did not appreciably lower the minimum residual sugar value. So when run 26 appeared nearly complete, 3 grams of Difco dehydrated yeast extract were added. Within a few minutes the fermentation rate increased and then continued to rise for several hours; previously the reaction rate had decreased rapidlyat this stage of the fermentation. The activity of yeast’ extract indicated the need for organic nutrient supplements in the mash at this pH. The experimental technique just described should demonstrate whether or not other fermentation mashes have a sufficient quantity of growth factors. Large amounts of growth factors are required in present commercial lactic acid fermentations where calcium carbonate is used to neutralize the acid as i t forms. Some of the materials used for the preparation of these commercial mashes originally contain sufficient growth factors. Where they do not, nutrients must be added in the form of malt sprouts, corn steep liquor, etc. The reason for using large amounts of accessorygrowth factors in commercial lactic acid fermentations is apparent from a study of Figures 4 and 7. In plain wheat grit mashes the optimum lactic acid yield occurs a t pH 6.0 but amounts to only 10% at pH 4.5. Likewise, the average fermentation rate at pH 0.0 is about five times more rapid than a t pH 4.5. However, when yeast and nutrient salts are added, the maximum yield occurs
1857
at pH 4.6 and then drops slowly as the pH is raised to 6.0. The average rate of fermentation is increased by the addition of nutrients to the extent that the rate at pH 5.6 in the supplemented mash is equal to that of the plain mash at pH 6.0. Because calcium carbonate usually buffers p H in the range 4.5 to 5.0, i t is apparent that both the yield and rate of lactic acid production are considerably improved in this range when large amounts of growth factors are present. It is also evident that equivalent yields and rates of fermentations can be obtained from plain, unsupplemented mashes when the pH is controlled at their optimum value. ACKNOWLEDGMENT
This study was made possible by a grant of funds from the Graduate School of the University of Minnesota and by equipment obtained from surplus property of the United States Government. The senior author was the recipient of a fellowship from the Standard Oil Company of Indiana during one year of the research. LITERATURE CITED
(1) Berge:
D. H.,“Bergey’s Manual of Determinative Bacteriology, 6th ed., p. 359, Baltimore, Williams and Wilkins Co.,
1948. (2) Freeman, G. G.,and Morrison, R. I., Analyst, 71,511 (1946). (3) Friedemann, T. E., and Graeser, J. B., J . Biol. C h a . , 100,291 (1933). ENQ. (4) Leonard, R. H.,Peterson, W. H., and Johnson, M. J., IND. CHEM.,40,67 (1948). (5) Long, Louis, Jr., “Sugar and Sugar By-Products in the Plastics Industry,” p. 18, New York, Sugar Research Foundation, 1949. _. -.
(6)
Longsworth, L. G., and MacInnes, D. A,, J.Bact., 29, 595 (1935); 31,287 (1936);32,567 (1936).
(7) Pan, S. C., Peterson, W. H., and Johnson, M. J.. IND.ENQ. CHEM.,32,709 (1940). (8) Shaffer, P. A., and Somogyi, M., J. Biol. Chem., 100,695 (1933). R~PCEIVSD June 18,1948. Presented before the Division of Agrioultural and Food Chemistry, Fermentation Section, at the 113th Meeting of the AMSBICAN CHEIIICAL SOCIETY, Chiaago, Ill.
Lactic Acid Fermentation Rate EFFECT OF CONTINUOUSLY CONTROLLED pH R. K. FIN”, H. 0. HALVORSON’,AND EDGAR L. PIRET University of Minnesota, Minneapolis, Minn.
The rate of fermentation of dextrose solutions to lactic acid by Lactobacillus delbruckii has been studied at various pH levels from pH 3.5 to 6.0. The pH was held constant by automatic controls throughout each fermentation, and equipment was devised to continuously record the rate at which acid was produced. The maximum rate of acid production during a fermentation cycle was increased as much as fourfold by raising the pH only 0.5 units. At all levels of pH relatively high concentrations of accessory nutrients were necessary for the rapid production of acid. Increasing the concentration of yeast extract in the medium from 0.3 to 3.0% stimulated the rate of acid production, but higher concentrations did not provide further increases in rate. The rate of fermentation appeared to be independent of the sugar content of the medium in the range of concentrations from 5 to 10%. The effects of pH on the yield of lactic acid and on the residirul swgar content of the broth confirmed earlier work in ’ Present sddreaa, University of Tllinoih. Yrhana, Ill.
which a wheat-grit mash was used. At the pH corresponding to highest yield, the maximum rate of acid production was about 0.13 gram per hour per 100 ml. of broth, and this value was substantially independent of the composition of the mediums tested.
I
T HAS been pointed out (9) that the large scale production of lactic acid by the fermentation of blackstrap molasses is commercially attractive owing to a market for high grade acid in the plastics industry. New methods for the recovery and purification have been proposed ( 1 ) which may make it more economical to use ammonia instead of calcium carbonate to neutralize the acid formed during fermentation. Such a change would necessitate the careful control of p H through the fermentation, and accordingly a study of the proper environmental conditions was undertaken. A previous paper from this laboratory (4) reported the effects of controlled pH on the yield and conversion attained in the fermentation of wheabgrit mashes. Using a variety of lactic acid
INDUSTRIAL AND ENGINEERING CHEMISTRY
1858
bacteria, itl was shown that for a maximum yield of acid, the pH must be neither too high nor too low; the exact value of the optimum pH varied from 4.7 to 6.0 depending on the extent to which the mash had been fortified with accessory nutrients. There were also noted in this earlier vork significant variations in the time required for complete fermentation; the average rate of fermentation increased rapidly as the pH was raised.
I I
A
f
/
A Figure 1. Diagram of Equipment for Fermentation and pH Control A
B C D E
Fermentation crock protected by paper shield and located inside incubator room (stirrer, vapor-type thermometer, electrode assembly inlets for earbonate solution, and esrbon dioxide) = gH meter and pH recorder-controller eservoir for carbonate solution s s Pump for earbonate solution = Recording thermometer =
Vol. 42, No. 9
and was supported across the pulley by a small brass counterweight. Modification of the Hydrograph consisted simply in the attachment of a larger pulley and a different system of gears. The purpose was to speed movement of the pen across the chart and to increase the sensitivity to small changes in liquid-level. As modified, the pen traversed the rhart once in 24 hours and withdrawals of as little as 2 to 3 nil. of carbonate solution from the liter graduate were recorded. Figure 3 shows the Hydrograph chart from a typical experiment; the volume of solution is recorded in the vertical direction, and time is recorded in the horizontal direction. According to calibration tests, each small division on the chart corresponded to 15.0 minutes and 17.7 ml. of earbonate solution. The slope of the line on the (-hart is a measure of the rate of acid production. Figure 3 shows that the rate increased rapidly a t first, then attained a constant value, and finally decreased to zero a t the end of the fermentation. These periods correspond roughly to the'phases in the familiar growth cycle of bacteria, in which there is a logarithmic growth of population followed by a stationary phase, and finally acrelerated death of the cells (IO). The phase of increasing arid production was not studied in this work because it is influenced by variables which were not controlled (6). The phase during which acid was produced at a maximum rate was characterized by a constant slope of the line on the Hydrograph chart. This slope, measured directly on the chart with the aid of a straight edge, was readily converted to grams of arid ralculated R S ltwtic which were formed per hour.
I n the work reported here attention was directed to a study of the maximum rate of acid production which persisted during the middle portion of each fermentation cycle. Instead of a wheatgrit mash the fermentation medium consisted of dextrose and mineral salts fortified with various amounts of yeast extract. The use of this easily reproducible substrate permitted the rapid estimation of cell populations and also served to extend t h t a seope of previous studies. APPARATUS AND METHODS
Although a new method for measuring rate was used in this investigation, the equipment for fermentation and p H control was essentially the same as described earlier (4). A diagram of the fermentation equipment is shown in Figure 1. I t was found to be important for dextrose solutions that the fermenting broth be protected from atmospheric oxygen, although strictly anaerobic conditions were unnecessary (7). Sufficient protection was provided by continuously bleeding onto the surface of the broth a small stream of carbon dioxide. To prevent air currents from striking the surface, a paper jacket extending 7 inches above the surface of the broth was placed around the fermentor. I n order to estimate the rate of arid formation it was convenient to measure the rate of addition of neutralizing solution, since a t constant pH the amount of acid formed by the bacteria is equivalent to the amount of alkali used for neutralization. It was desirable also to make continuous measurements throughout the course of fermentation so that the period of maximum rate could be singled out for study. A Type F Stevens Hydrograph, commonly used in sewage control work, was modified to serve this purpose. It provided a continuous record of the time and liquid level in the 1-liter graduated cylinder which served as a reservoir for the neutralizing solution. A photograph of this liquid-level recorder is shown in Figure 2. The float shown in Figure 2 was made from an ordinary 25m1. pipet by sealing off the bulbed portion and weighting it with a small amount of mercury. The float was suspended by a length of silk fishing line which fit into the grooved face of the pulley
Figure 2.
Hydrograph Liquid-Level Recorder
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
September 1950
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added along with the inoculum. The basal medium also contained the mineral salts Stock solutions of mineral salts used: described in the footnote to B A Table I. Sodium acetate, 60 grain@ M 804 lOHnO 40 granis Hexametaphosphate 60 gram8 Fe%O,.?HnO,i grama Various modifications of this Make up to 400 ml.; ;so, 20 ml.for 2800 mi. MnS04 lHnO 2 gram6 basal medium were used. In Make ;p to io0 ml.; use, 7.5 ml.for 2800 ml. one the concentration of yeast Final sugar Lacti0 Yeast 1niti~1 Final Bug= Lactia ConverApid Residual Final Extract extract waa reduced from 3 to Acid, don, Yield, Sugar, Volume, Sugar, sugar Used Used, Run Granu M1. Gram; NO. G r a d Grams % % % 0.3%, and in order to supply PH % 124 76 2410 49 50 102 80 3 38 3.50" additional nitrogen there were 124 40 37 2580 78 74 94 3 4.00 30 a d d e d 16 grams of B a c t o 11 124 110 94 14 "I 3 2715 88 4.30 9.4 124 12 2870 112 103 92 3 28 4.40 p e p t o n e , which h a d been 1.3 1.8 98 124 2820 122 117 3 29 4.90 117 96 122 1.4 1.7 124 2880 3 25 5.00 treated with sodium hydrox107 87 1.5 1.8 124 2890 122 3 28 5.40 ide, f o r removing g r o w t h 113 92 124 122 1.8 1.5 3025 3 24 5.80 1.7 104 88 124 122 1.7 3120 3 34 6.00 factors as recommended by 2820 124 31 93 25 49 4.10 6 Snell et al. (19). 31 4.90 0.3 2480 124 50 74 89 66 40 I n another modification it 35 4.90 0.3 3120 124 44 94 61 36 80 76 37 5.20 0.3 2790 114 108 9b 87 8.2 was desired to increase the 32 5.60 0.3 3100 124 124 'T.1 123 124 101 100 0.9 concentration of dextrose from 33 6.86 0.3 2590 124 1.1 123 120 98 97 0.9 5 to 10%. In this case, howNo pH control used; this was niiniiiiuni pH of fermentation. ever, the entire medium was made double strength so as to e l i m i n a t e a n y complications from insufficient amounts of growth factors. The neutralizing solution was 2.6 N sodium carbonate containing 5 grams per liter of sodium hexametaphosphate. In run 26 guanidine carbonate was substituted for sodium carbonate without apparent effect on the fermentation. TABLE
OF 6% GLUCOSE I. LACTICACIDYIELD AND SUGAR CONWRSION FOR FERMENTATION MEDIUMFORTIFIED WITH YEASTE X T ~ C AND T MINERALSALTS
...
...
. I .
@
80
Figure 3.
Hydrograph Chart
A11 fermentations were conducted a t 45' C. using Lactobacillus delbriiclcii NRRL:B-445, a homofermentative organism. The particular strain was one of those used previously in this laboratory and was obtained from the United States Department of Agriculture. The fermentation procedure was essentially the same as that used in the earlier studies. The basal medium for a fermentation batch consisted of 2500 ml. of tap water containing 5% U.S.P. dextrose and 3% Difco d e hydrated yeast extract. These materials were separately sterilized and in their preparation allowance was made for the quantities
4.0
5.0 I
6.0
PH
Figure 4. Yields of Lactic Acid from Fermentations of 5% Dextrose Broths at Controlled pH Levels A l s o shown is ourve for fortified wheat-grit mashem obtained
earlier ( 4 )
4.0
5.0
6.0
PH
Figure 5. Residual Sugar in 5% Dextrose Broths Fermented at Controlled pH Values Data from previous work with fortified wheat-grit mashes is also shown 0 = 3.0% yeaet extract 0 6.0% yeast extract
-
It n-aadesirable to measure the total number of bacteria producing lactic acid during the portion of the fermentation cycle when the rate was at a maximum. Since both viable and nonviable cells may continue to form acid, a total count was desired rather than a plate count. This total count was estimated from optical density measurements made with a Coleman Universal spectrophotometer using light with a wave length of 575 mp. Samples of fermenting broth were taken near the end of the maximum rate period and, before measurement, were diluted until the optical density was less than 0.5, the observed upper limit for the validity of Beer's law. Optical density measurements were calibrated by comparisons with plate counts following the recommendations of Longsworth (6),who has shown that during the logarithmic growth phase or early stationary period of the g r o F h cycle, there is a constant ratio between the plate counts and optical density measurements. For three determinations the ratio averaged 3.2 X 108, and this value was used to calculate the cell counts shown in Table 11.
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
1860
4.7 but also the minimum p I f of 3.5, as shown in Table I, agrees with the value for minimum oH obtained in the
OPTICALDENSITYMEASUREMENTS, AND TABLE 11. RATESOF ACID PRODUCTION, CALCULATED CELLCOUNTS FOR FERMENTATIONS AT CONTROLLED pH (Dextrose mediums fortified with yoavt estract and mineral saltso; Lactobacillus delbfickii a t 45' C.)
-
-
.
._ 3 3 3
wheat-grit mash c o n t a i n et1 11% nonfermentable sugar, and as a consequence the calculated percentage yields werc based on an initial sugar content which wm, in part, UIIavailable. This explains tho lower yields obtained throughout the previous work. The curves in Figures 4 and 5 for mediums containing only 0.3% yeast extract are similar in shape to the curves for more complete mediums, but the pH of maximum yield was higher. A similar effect was observed for wheat-grit mashes when yeast extract or mineral salts were omitted from the medium. The low yields of lactic acid a t pH values below the optimum were caused almost entirely by incomplete utilization of sugar. This is evident from Figures 4 and 5 and from Table I, which also shows that in this range of pH the conversion of sugsr to lactic acid was practically complete. The incomplete utilization of sugar a t low pH can be caused by inadequate concentrations of growth factors. Figure 5 shows that at a pH of 5.0, for example, an increase in yeast extract concentration from 0.3 to 3.0% resulted in a more complete utilization of the sugar. As the pH was lowered below the optimum pH for high yields, the lactobacilli required higher concentrations of growth factors than could be supplied by the 0,3y0yeast extract, a concentration which would ordinarily be considered sufficient. There is, of course, a limit to the protection against acidity which growth fact.orswill provide. Thus, in run 49 at pH 4.1, increasing the concentration of yeast extract to 6% did not further improve the fermentation. The rate of acid production, as shown in Figure 6, increased rapidly as the pH was raised, and this trend continued over the entire range from pH 4.0 to 6.0. The change in rate with pH was greater for the more strongly acid fermentations where a change in pH of 0.5 unit produced a fourfold change in rate. Low rates were observed for mediums containing only 0.3% yeast es-
2410 0.548 1:lO 1.76 4.2 1:20 2.44 6 8 0.381 2580 o:Oi2 8.0 0.229 1:40 2.04 0.12 2715 0.432 2670 0.041 1:20 2.76 7.2 3 2620 0.430 1:40 5.50 11.4 0.21 3 2860 0.25 0,407 1:40 5,21 14 !I 3 2890 0.43 0.445 1:40 5.70 16.4 3 5 3025 0.42 ... ,.. 3 0.62 5 3045 o:340 f:40 4.35 13.? 3 13.0 4.29 0.335 1:40 0.68 3030 5 3 13.5 4.30 0.338 1:40 6.00 3 5 3120 0.52 10 3120 0.03 n.319 i:20 2.04 6.3 4.40 6 10 3100 0.13 0.353 1:40 4.50 14.0 41 4.70 6 23.7 3435 0.38 0.539 1:40 6.90 43 5.30 6 lo 10 3515 0.76 0.327 1:80 8.38 20.4 40 5.70 6 5 3075 0.72 0.360 1:40 4.61 14.1 45 5.70 6 0.268 1:20 1.72 4.5 49 4.10 6 5 2620 0.032 2480 0.018 0,292 1:lO 0.94 2.3 31 4.90 0.3 5 0.280 1:lO 0.90 2.5 0.018 5 3120 35 4.90 0.3 4.4 0.421 1:lO 1.35 0,086 5 2790 37 5.20 0.3 7.9 5 3100 0.309 0,399 1:20 2.56 32 5.50 0.3 33 5.85 0.3 5 2590 0.15 0.862 1:20 2.30 6.0 0 Mineral salts solutiona same as shown in Table I ; double quantities were used for runs 40 -43, inclusive. b Nominal. No pH control used. The value 3.50 was the minimum pH of fermentation.
38 30 21 28 29 25 26 24 46 48 34 42
3.50b 4.00 4.30 4.40 4.90 5.00 5.40 5.60 5.70 5.70
5 5 5 5 5 5 5
Vol. 42, No. 9
The analytical procedures fordetermining lactic acid and sugar were those used in the earlier studies (4). The reported yields of lwtic acid are based both on the initial sugar content of the broth and on the quantity of sugar actually used up in the fermentation. The yields based on the sugar consumed are reported as percentage of sugar conversion in Table I. 1 .oo
.CO .60 .
.40
2 .OP ' .01 4.0
5.0
6.0
RH
Figure 6. Maximum Rates of Aoid Production in Fermentation of Dextrose Broths at Controlled pH Levels
8
dextrose 0.3 %yeast extract 5%dextrose,'3.0% yeast extract 5% dextrose, 6.0% yeast extract A = 10 % dextrose, 6.0 % yeast extract 0
5
RESULTS
The data on yield and residual sugar presented in Table I and Figures 4 and 5 show that the fermentation characteristics of the basal medium containing 3.0% yeast extract were comparable with the characteristics of the fortified wheatrgrit medium used earlier. For both types of mediums, the maximum yield of lactic at about 4,7 pH and at this pH the mediums became acid exhausted of fermentable sugars. Not only the optimum pH of
TABLE 111. YIELD OF LACTIC .\CHI PER CELL FOR FERMENTATIONS IN 5% DEXTROSE FORTIFIED WITH YEASTEXTRACT AND MINER.4L S.4LTS"
Total Yield of Lactic Total Yield of Lactic .4cid. Cells, Aoid/Average No. PH Grams X 10-1s Cell, Grams X 1011 4.2 11.8 38 3.50s 50 6.3 9.5 30 4.00 74 8.0 11.8 21 4.30 94 7.2 14.3 28 4.40 103 14.4 8.2 29 4.90 117 14.9 7.9 25 6.00 117 16.5 6.5 26 6.40 107 34 6.00 104 13.5 7.8 81 4.90 74 2.3 29.8 80 2.5 29.6 114 4.4 24.8 183 7.9 15.6 32 33 5.50 5.85 0.3 123 6.0 20.0 Mineral salts solutions salne as shown in Table 1. b No pH control used: 3.50 was the minimum pH of fermentation.
Run
:!
::::
Yeast Extract, % 3 3 3 3 3 3 3 3 0.3
::!
INDUSTRIAL AND ENGINEERING CHEMISTRY
Septemlmr 1950
4.0
5.0
6.0
DH
Figure 7.
Cell Counts in Dextrose Broths Fermented at Controlled p H Levels
tract, but the curve describing the change in rate with pH is similar in shape to the curve for mediuma containing 3.0% yeaat extract. Figure 6 shows that for medium with 0.3% yeast extract, the rate dropped off rapidly below pH 5.0. This fact may be of practical importance in fermentations buffered with calcium carbonate where the pH may fall as low as 4.7. The rate and yield curves in Figures 4 and 6 disclose that a particular value of the rate waa associated with a particular value of the yield, independently of the composition of the medium. Thus, at the pH of maximum yield, the rate of acid production was between 0.12 and 0.14 gram per hour per 100 ml. for both the 0.3 and the 3.0% yeaet extract mediums.
I
I
I
1
I
I
I
I
4.0
5.0
6.0
OH Figure 8. Yields of Lactic Acid per Average Cell in Fermentations of 5% Dextrose Broths at Controlled pH Levels
Longsworth and MacInnes (7)in their study of Laotobclcillwr ucidophilua at pH 6.0 were able to correlate changes in rate with changes in the concentration of undissociated lactic acid. This explanation does not account for the behavior of Lactobacillus d e l b w k i i in these experimentg since Figure 6 shows that the same rates were attained in both single-strength and double-strength mediums even though the double-strength medium contained a higher concentration of undissociated acid. Throughout the experimental work it was observed that for fermentations in which there was a considerable amount of residual sugar, the maximum rate period waa of short duration, and a gradual decline in rate continued until the end of fermentation.
1861
Such a rate curve resembles those observed by Longsworth and MacInnes ( 6 ) who found a maximum rate but no appreciable conetant rate period. These workers reported only 80% utilisation of the sugar; this suggests that their galactose-peptoniaed milk medium may have contained insufficient nutrilitee even a t the relatively high pH of 6.0. Figure 7, which shows the variation in cell count with pH, indicates that an insufficient supply of growth factors severely limited the population in dextrose broth. In completely enriched mediums the acidity of the medium was limiting below pH 5, but a t higher pH values the sugar concentration became limiting. The further significance of these data is shown in Figure 8, where the yield of lactic acid per single average cell is plotted against pH. Deficient mediums showed consistentlyhigher yieldg of lactic acid per cell than mediums which contained adequate amounts of gmwth factors. This observation supports other evidence (3,8) that a deficiency of nutrilites interferes with cell production to a greater extent than it interferes with fermentation. The high rates of fermentation observed in these studies make more attractive the possibilities of continuous fermentation. By proper control of both pH and accessory nutrients it should be possible completely to ferment a 10% sugar solution in 15 to 20 hours. Moreover the variable efficiencies reported in previous studies of continuous fermentation (11)could no doubt be eliminated by application of the principles presented here. ACKNOWLEDGMENT
The assistance provided by a fellowship grant from the Minnesota Mining & Manufacturing Company is gratefully acknowl-
edged. This work was also supported in part, by funds from the Graduate School of the University of Minnesota. BIB LIOGR APEY (1) Filachione, E. M., and Fisher, C. A,, U. 8. Patent 2,420,234 (1947). (2) Hinshelwood, C. N., “Chemical Kinetics of the Bacterial Cell,” p. 64,London, Oxford University Press, 1946. (3) Isbell, H., Proc. 800.Exptl. Biol. Med., 60,311 (1946). (4) Kempe, Lloyd L., Halvormn, H.O., and Piret, Edgar L., IND. ENO.CHEY.,42,1862 (1960). (6) Longsworth, Lewir G., J . Bact., 32, 307-28 (1936). (6)Longsworth, Lewis 0..and MacInnes, D. A., Ibid., 29, 595-607 (1936). (7) Ibid., 32,667-86 (1936). (8) Muedeking, M. R.,Ph.D. thesis, Dept. of Bacteriology, Univ. of Minn. (1946). (9) Needle, Hsskell C., and Aries, Robert S., Sugar, 44, No.12, 32-6 (1949). (10) R a h , Otto, “Physiology of Baoteria,” pp. 104-7, Philadelphia, P. Blakiston’s Son & Co., 1932. (11) Rogers, L.A., and Whittier, E O., J . B a t . , 20, 127-37 (1930). (12) Snell, E. E., Strong, I?. M., and Peterson, W. H., Biochem. J . , 31. 1789-97 (1937). RBCEIVED nfarah iti, 1850.
Liquid-Gas Interfacial Area on Packed Columns-Corsec tion Since publication of the article on “Liquid-Gas Interfacial Area ENO.CHEM.,42,1099 (1950)l the folon Packed Columns” [IND. lowing errors have come to the attention of the authow: In the fifth line of the abstract, page 1099, the word “by” should be “into.” Table I, page 1101, the word (‘copper” should be “brass” (in five places). Equation 24, page 1103,the coefficientshould be (1.93/18) = 0.107.
JOEL WEISMAN CHARLES F. BONILLA
