&
INDUSTRIAL A N D ENGINEERING CHEMISTRY
816
nearly zero and increases toward one with decreasing volatile content. Such a change in the character of the reaction may be due either to the differences in rank of the fuels or to the different temperature levels within which the rates are measurable. I n addition there is a practical difficulty in thermometric procedures. The reactivity indices depend critically upon the determination of that instant at which there is assumed to be no flow of heat to or from the sample. I n a particular case, the assumption that a single thermocouple of the pair used to determine this conditon was in error by 1’ C. resulted in a 10’ difference in a calculated reactivity index. The furnace thermocouple is placed in contact with the outer surface of the tube holding the sample. Since the temperature is rising, there must be a net flow of heat into the wall of the sample tube a t all times. At the instant when the temperatures on the outer surface of the tube and in the middle of the sample are identical, there p u s t be a minimum temperature within the tube wall. This must be true, otherwise the tube wall could not be rising in temperature. Under these conditions a portion of the heat required to heat the sample tube must arise from the heat released from the sample. This is contrary to the original assumption that identity of temperature of sample and furnace thermocouples corresponded to zero heat flow to or from the sample. However, the portion of the heat taken from the sample may be relatively constant. This means that the procedure is in error due to the inclusion of an unknown portion of the heat capacity of the sample tube together with the heat capacity of the sample; the result is an error in absolute scale of reactivity indices. I n spite of these criticisms, the reactivity indices have considerable value. Unlike ignition points which are as much a function of the physical environment as they are of the reactivity
Vol. 36, No. 9
of the sample, the reactivity indices do give a measure of the reactivity of the sample at different sample temperatures. Even for the low-rank coals where there is greatest doubt as to firstorder dependence upon oxygen partial pressure, TISdoes not involve much extrapolation from the experimental points and gives a measure of the reactivity in oxygen. Likewise, T16involves small extrapolations from the experimental points in air, and since the ratio of 75 to 15 is approximately that of the partial pressure;: of oxygen in pure oxygen and air, 2’76 could be interpreted as TI6 measured in air. It is probably for these reasons that such remarkably good correlations are found between the reactivity indices and the volatile contents. The different slopes found for 2’16 and for T76 are indicative of the dependence of the mechanism of reaction upon the rank of the fuel. ACKNOWLEDGMENT
The experimental data presented in this paper were obtained by J. J. S. Sebastian, a member of the staff of the Coal Research Laboratory prior to August, 1942. Grateful acknowledgment is here made to those who supplied the samples and analyses for the work reported in this paper. LITERATURE ClTED
(1) Sebastian, J. J. S.,Div.of Gas and Fuel Chem., A.C.S. meeting,
.
Boston. 1939. .. ~~. (2) Sebastian, J . J . S.,and Mayers, M . 9., IXD. ENG.CHEM.,29, 1118-24 (1937). ( 3 ) Sherman, R . A . , Piloher, J. M ., and Ostborg, H . N . , A m . SOC.
Testing Materials, Bull. 112, 23-34 (1941). in part before the Division of Gas and Fuel Chemistry at the 106th hfeeting of the AMEnICAN CHEXICAL SOCIBTY, Pittsburgh, Pa.
PRESENTED
Solvent Dehydration by Salting Out 0 J
PREDICTION OF MAXIMUM DEGREE OF DEHYDRATION
H. P. MEISSNER AND CHARLES A. STOKES Massachusetts Institute of Technology, Cambridge, Mass.
T
HE problem of removing water from aqueous solutions of
organic solvents is often encountered industrially. Such dehydration is most frequently accomplished by distillation, which may be carried out at, above, or below atmospheric pressure, and with or without the addition of an entraining agent. It is also possible to dehydrate by other methods, such as freezing and filtering out water crystals, reacting the water chemically with materials such as lime, or adsorption of the water on materials such as silica gel. Another dehydration procedure, often mentioned in the literature ( 1 ) and perhaps more frequently used in the laboratory than in industrial plants, is that known as salting out. This involves bringing the wet solvent in contact with some substance, usually an electrolyte, which has the power of withdrawing some of the water present to form a second phase which can then be removed by decantation. The “salting out” of ether by addition of sodium chloride to a solution of water in ether may be cited as an example. The dehydrating substance may be added either as a solid or as a concentrated aqueous solution, this second method being more easily adapted to large-scale continuous countercurrent operations. The addition of such dehydrating substances is advantageous only in those cases
where the possibility of forming a water-rich and a solvent-rich layer exists. Some methods of dehydration may give greater “clean-up” than others. I n industry, that combination of methods is normally chosen which accomplishes the desired result at minimum cost. Dehydration by a salting out process, used either alone or perhaps in combination with a distilling operation, often shows real cost advantages. The object of this paper is to discuss some of the principles of dehydration by salting out and to illustrate them with the system methyl ethyl ketone (MEK), water, and salts. INDUSTRIAL APPLICATION
Dehydration by salting out may be accomplished either in batch or continuous-flow operations. Batch operation might involve agitating the wet solvent either with the dehydrating substance or with an aqueous solution of this substance (hereafter referred to as a “brine”). Similarly, flow operations would involve passing the wet solvent through a bed of the substance (if a solid) or possibly flowing the wet solvent through a tower coun-
September, 1944
I N D U S T R I A L A N D E N G I N E E R I N G CHEMESTRY
“Salting out” is a technique little used i dehydrating organic solvents. This method of removing water involves adding to the wet solvent a dehydrating substance, usually an inorganic salt insoluble in the organic liquid, which will result in the formation of waterr rich and solvent-rich phases. The mi content of the solvent phase is obtained wh phase is saturated with the dehydrating substance. A method is presented for predicting this maxi of dehydration for any given substance. illustrated by data and calculations for dehydration of methyl ethyl ketone by various salts.
0 tercurrent to a brine. Only the batch case will be discussed in this paper. A primary question in designing a salting out operation is the choice of a suitable dehydrating substance. I n addition to having dehydrating power, this substance must meet other requirements. To avoid contamination of the product, it obviously must be insoluble in the solvent being dehydrated. For this reason sodium hydroxide would not be suitable for alcohol dehydration, It must not react with the solvent; therefore sdlfuric acid, for example, could not be used to dehydrate ethyl ajcohol. Similarly, chlorates and nitrates might not be suitable for dehydrating certain solvents due to explosion hazards. I n addition, cost questions, corrosion problems, and other considerations will narrow down the choice in any given case. I n spite of these limitations, dehydration by Baking out is quite generally applicable. Normally it is not difficult to find a suitable dehydrating substance that is insoluble in the particular solvent to be treated. For example, most inorganic salts of the type discussed in this paper are substantially insoluble in the higher esters, ketones, ethers, alcohols, and the like. The degree of dehydration to be expected in all these cases can b e predicted by the technique described here. Hence, i t is not unreasonable t o expect that the salting out method of dehydration may find somewhat wider application in the future, especially in those cases where the solvent forms an azeotrope with water, which prevents separation by ordinary distillation. DEHYDRATION OR SALTING OUT
When a substance such as sodium chloride is added at constant temperature to a solution of water in an organic solvent in which the salt is insoluble, the following occurs: As the dehydrating substance is added in small increments, it progressively withdraws water from the solvent layer and goes into solution, forming a brine layer which is immiscible with the solvent layer. A little of the solvent also tends t o dissolve in this newly formed brine layer. Further additions of salt cause more water t o be withdrawn from the solvent layer, which is thereby progressively dehydrated. Finally, a point is reached where no more salt will dissolve, and further salt additions result in no further change in the composition of the two liquid phases. It is clear that maxi-
TABLE I. EQUILIBRIUM DATA ON THH SYSTEMCALCIUM TEMPERATURE (23.5-26’ C.) CHLORIDE-WATER-MEKAT ROOM Ketone
...
1.96 2.26 3.42 5.11 10.6 16.8 22.4
Water Layer, Wt. % CaClr Hz0 45.0 55.0 43.50 54.5 33.65 64 1 26.10 70.5 20.35 74.5 10.40 79.0 4.12 79.1 77.6 0.0
Ketone Layer, Wt. % Ha0 Ketone 0:705 1.87 4.11 5 22 7.61 12.00 12.60
99:3 98.1 95.9 94.8 92.4 88.0 87.4
817
mum possible dehydration of the solvent layer by the given dehydrating substance at the specific temperature has now been attained. Four phases are now present in equilibrium: the vapor phase, the brine layer, the solvent layer, and the excess dehydrating material. For convenience, this type will be called a “saturated three-component system”. METHYLETHYL KETONE-CALCIUM CHLORIDE-WATER. Since this system will be used to illustrate the points raised, its phase diagram is of interest. Table I lists Stanton’s values (10)for the composition of various equilibrium mixtures. Figure 1 presents these values graphically, together with a conjugate line, B, for interpolation purposes. Triangle mgb represents the three-phase region (although line mb is not drawn into Figure 1 because it falls almost on the edge.of the diagram); the two-phase regions are represented by areas mcb, gfb, and gem. The onephase regions are eufg and line dc. The latter is a line rather than a region because calcium chloride is insoluble in ketone of this low water content. An explanation of the significance of triangular diagrams of,this sort may be found in ahy good text on physical chemistry or in Sherwood’s book on absorption (8). The values presented by Stanton were obtained by the usual experimental techniques, as follows: Appropriate amounts of water, MW, ,and. calcium chloride were shaken together until equilibrium was reached at the temperature in question. The phases were then separated by settling and decantation, and analyzed. Salt in each layer was determined by evaporating a known sample to dryness, and wei hing the residue. Water in the ketone layer was determined(33y the method of Smith, Bryant, and Mitchell (9). The MEK in the brine layer was anal zed by the method of Marasco (6). The water content in the trine layer and the MEK in the solvent layer were determined by difference. The water content of the solvent layer was determined by Hanak (8) and Werby (11) by two additional independent methods: titration of a solvent sample with pure water and judging the end point by the first ap earance of two phases, and comparison of the density of an unlnown solvent layer sample with that of known mixtures of ketone and water. These two methods are applicable only where no salt dissolves in the solvent layer. This system is interesting for several reasons. First, MEK and water are not miscible in all proportions, the composition of the two phases in equilibrium being shown by points d and e of Figure 1. Second, the composition of the vapor inequilibrium with these two layers is practically the same as that of the solvent phase, as the p x diagram of Figure 2 shows. Consequently, further dehydration of an MEK-water mixture containing over
WATCR
*
FIGURE f
-
23 26 *C.
*
818
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 36, No. 9
PREDICTION OF WATER VAPOR PRESSURE
WElGHT.PER CENT M E K /N LIQUID
If the dehydrating substance itself is hydrated as in the c a s of calcium chloride, for which the stable hydrate is CaC12.6HpO a t room temperature, then the water vapor pressure over the saturated three-component systems being considered must be the same as over the solid hydrate. Inasmuch as the literature lists the partial pressure of water over most such hydrated substances or over their saturated aqueous solutions, the prediction of the vapor pressure of water over the solvent layer of the threecomponent systems presents no difficulties. If the dehydrating substance is not hydrated, as in the case of sodium chloride, then the partial pressure of water over the saturated three-component system is not the same as the vapor pressure of water over saturated aqueous solutions of this substance. As a first approximation, however, it may be assumed that the water vapor pressure is the same for these two cases, as demonstrated below. A method for computing the difference between these two vapor pressures is also presented. Since the literature lists the vapor pressure over the saturated aqueous solutions of most substances, the estimation of the desired vapor pressure again presents no difficulties. WE/GHT PER CENT M E K
Figure 2.
/N LIQUID
Vapor and Liquid Composition at One Atmosphere
12.6% by weight of water by simple distillation a t atmospheric pressure is not possible. I n other respects this system i s characteristic of those under discussion, in that the dehydrating agent is insoluble in the solvent but readily soluble in water. For example, consider the case of an MEK-water mixture containing 10% water, as indicated by point h on Figure 1. As salt is added, the over-all composition of the system shifts along dotted line bh. Immediately upon adding a little salt, water is withdrawn from solvent layer and a brine layer forms. When enough salt has been added to reach point j , for example, the composition of the two phases is represented by the terminals of tie line A'. Finally after further salt additions, point k is reached, which marks the limit of salt solubility in the system; from this point on, three condensed phases are prestoo ent-namely, the two liquid phases and the solid eo phase, shown by points m, g, and b. Further 60 additions of salt result in no further change in the composition of these phases. The maximum 1. 4 0 dehydration of the solvent layer, therefore, which can be accomplished by calcium chloride is shown by point m (representing 0.71% water by 20 weight). It is plain that this maximum de2 hydration is obtained when all three condensed 3 phases are present, and that this corresponds 4; v i t h the above described saturated three-com3 io ponent system. 8.0 PREDICTION OF MAXIMUM DEHYDRATION. The 6.0 maximum dehydration attained in a saturated s: 0 three-component system, as described above, Q 4.0 can be predicted in any given case from the 3 fact that the partial pressure of water must be the same over the three condensed phases, since 2.0 they are in equilibrium. The fist problem to be faced, therefore, involves predicting the partial pressure of water over the system. Second, 1.0 a relation between the composition of the solvent layer and the partial pressure of water must be found. It is B simple matter t o oompute the oomposition of the solvent layer if Figure 3. these two relations are known.
At constant temperature and pressure the familiar Gibbs equation can be written for the brine layer of the saturated threacomponent system as follows:
where subscripts S, W , and D refer to the pure solvent, water, and dehydrating subst,ance, respectively. Lewis (4) showed that if substanceSis added in infinitesimal amounts to a saturated solution of D in W , then since d l n f ~= 0, and since a t very low concentrations, fs = lcszs
(2)
it follows that Equation 1reduces to:
5
4
3
$
Vapor Pressures of Saturated Salt Solutions at Various Temperatures
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1944
Similarly, in a solution containing only the two components,
W and S, the Gibbs equation for constant temperature and
pressure is:
(4)
For the case in which minute amounts of S are added to pure W , S must obey an equation of type 2 (even though constant k may be different numerically when component D is also present), and Equation 4 reduces again to Equation 3. I t follows from Equation 3 that the fractional lowering of the fugacity (or vapor pressure) resulting from adding a small given increment of S to, say, one mole of pure TY is the same as the fractional lowering of the vapor pressure of water resulting when this same increment of S is addetl to a saturated solution of D in one mole of W . The solubility of S in a saturated brine is always small for the case under discussion, in which the dehydratin substance is quite insoluble in the pure solvent but readily sol&le in water. Similarly, the amount of solvent in the brine layer in these saturated three-component systems is small enough so that it can be considered an increment to which Equation 2 above applies. The fractional lowering of the vapor pressure of water for this case is never large, due to this small solubility, and may be computed from Equation 3 or neglected as a first approximation. This procedure may be illustrated with the system MEKwater-sodium chloride. It is reported (7) that at room temerature 100 grams of a sodium chloride brine saturated with 10th MEK and salt contain about 2.5 grams of RiEK and 73 grams of water, corresponding to 0.0086 mole of MEK per mole of water. The reduction in the partial vapor pressure of water resulting when 0.0086 mole of MEK is added to 1 mole of pure water at 25' C. is about 0.2 mm., as is evident from extrapolation of Marshall's data (6) to this temperature with the help of the van Laar equation discussed later. This corresponds to only an 0.8% reduction from the vapor pressure of pure water, which at 25" C. is 23.8 mm. The vapor pressure of water over a saturated aqueous sodium chloride solution a t 25" C. is approximately 18 mm., and this must likewise be reduced by 0.8% when saturated with MEK, in accordance with the above reasoning. This reduction is obviously negligible, and so it follows that a t this temperature the vapor pressure of water over a saturated threecomponent system of the type discussed is ractically the same as that over a saturated aqueous solution o?the dehydrating substance in question. I t is clear that this vapor pressure reduction remains negli4ible a t all temperatures for which the solubility of the fiolvent in the saturated aqueous solution of the dehydrating substance is small.
819
of such liquid-vapor composition data to lower or higher temperatures can usually be accomplished with good precision by the use of some integrated form of the Gibbs-Duhem equation, such as the van Laar, Scatchard, Margules equations, etc. These relations were discussed in the recent paper of Carlson and Colburn (a). The van Laar equation, together with the data of Marshall mentioned above, was used to predict the relation between the partial pressure of water and the composition of MEK-water mixtures a t various temperatures as follows. The van Laar equations are usually written: 1
where subscripts W and S refer to water and MEK, respectively. Rearranging Equation 5 , (79
~
On the basis of the foregoing, it is possible t o classify dehydrating substances once and for all with respect to their dehydrating power in a salting out operation. That is, their relative dohydrating power a t any given temperature stands in inverse relation to the vapor pressure over their saturated aqueous solutions. Figure 3 shows the familiar vapor pressure curves of saturated aqueous solutions of several salts numbered in order of increaqing dehydrating power. As demonstrated above, these vapor pressures also apply over the type of saturated three-component systems under discussion. Hence, lithium chloride is the best and magnesium sulfate the poorest of the eight salts plotted in Figure 3, with respect to dehydrating power in a salting out operation of the type discussed.
0.06
0.04
Figure 4. Van Laar Correlation for MEK-Water Solution
Hence the reciprocal of the term dT In y v plotted against zw should give a straight line on rectangular coordinate paper. Figure 4 presents the data of Table I1 plotted in this fashion, and shows that an excellent straight line can be drawn through the first four points. These points were favored rather than the entire spread of points, since the region of low-water concentration is of greatest interest in this case. The values of R and B are now readily determined from the dope and intercept of the dotted line of Figure 4, and are found to be 0.907 and 711, respec' tively. Inserting these values in the van Lnnr equation, it becomes possible topredict thepartial pressures of water over MEKwater mixtures for any temperature. The solid lines of Figure 6 present this information in graphical form. PREDICTING MEK DICHYDRATION
It is now possible to predict the maximum dehydrating power WATER VAPOR PRESSURE OVER SOLVENT LAYER
Granting that the partial vapor pressure of water over the brine layer is known, then the degree of dehydration accomplished in any given saturated three-component system can be predicted if the relation between the partial vapor pressure of water and composition of the solvent-water layer is known. Since water almost never forms an ideal solution with organic solvents, these vapor pressures cannot be predicted by Raoult's law but must be calculated from laboratory data. Experimental data on vapor pressure or vapor compositions over solutions of water and most important organic solvents are available in the literature. Usually, these data are reported for normal boiling temperatures only. For example, Marshall (6) reports the relation between composition and vapor pressure over MEK-water mixtures a t 73.6" C., as shown in the f i s t three columns of Table 11. Extrapolation
of the salts plotted in Figure 3 with respect t o MEK-water mix-
VAPOR PRESSURES OF WATEROVER TABLE 11. PARTIAL WATER-MEK SOLUTIONWHEN1 = 73.6' C. xw 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.4128 0.94798
1.0
PW
0 90.0 146.0 188.0 216.0 238.0 252.4 259.3 262.8 263.6 263.6 273.0
P Tola 619.7 680.0 714.0 735.0 748.0 767.0 760.4 760.9 769.8 759.4 759.4 273.0
YR 6:bQ 5.36 4.59 3.95 3.99 3.08 2.71 2.41 2.34 1.02 1.0
::w 0 0.0526 0.111 0.176 0.250 0.333 0.429 0.539 0.667 0.703 18.2 m
d
1
m
0 : b:?b3 0 0414 0.0436 0,0459 0,0478 0.0505 0.0538 0.0574 0.0582 0.383
....
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
820
Vol. 36, Ho. 9
chloride is capable of the greatest dehydration of the several salts considered. At 20” C., for example, its uze results in an MEK-water mixture containing only about 1.2 mole % (0.3 weight yo)water. The dehydrating power of salts predicted by this method i? compared with the results obtained by experiment in Table3 I11 and IV, which show the values of Stanton (IO),Hanak (S), and Werby (11) for various salts. Agreement is good, particularly in view of the comparatively paor precision of the experimental methods used. CONCLUSIONS
Organic solvents containing dissolved water may be dehydrated by addinq various substances insoluble in these solvent-water mixtures but PARTIAL VAPOR PRESSURE OF W A ~ E RM , M MERCURY soluble in water. A method ii7 preqented by which the maximum dehydrating power of such Figure 5. Partial Vapor Prensure of Water over 3TEK-Watcr Solutions substances may be predicted. This involves a a t Various Coilcentration? and T e m p e r a t u r e s knowledge of -the relation between the partial water v a p x pressure and compocition of solventtures. For example, Figure 3 shows that the vapor pressure over $1 ater mixtures and the vapor pressure over the saturated a q u o a saturated aqueous calcium chloride solution (solid pha-e = ous solution of the dehydrating substance. For the case in CaCL.GH,O) a t 20” C. is 6.1 mm. of mercury. Similarly, \I hich the dehydrating substance forms a stable hydrate, the parFigure 5 shows that an MEK solution containing 3.6 mole % tial pressure of water over the four-phace eysterll will be the same water exhibits a partial pressure of water of 6.1 mm. of mercury as over a saturated aqueous solution of the dehydrtinx material. This is also shown to be nearly true for the ca-e in which the deat 20” C. Hence the maximum dehydration achieved by w e of calcium chloride on MEK-water mixtures a t 20’ C. must rewlt hydrating substance does not form a stable hydrate. in a solvent layer containing 3.6 mole % (0.92 weight %) of water. The dehydrating power of the other salts can be simiACKNOWLEDGMENT larly predicted. Thanks are due to E. J. Stanton for obtaining the data preT o illustrate the effect of temperature on dehydrating power sented in Figure 1 and Table I, and to E. W. Hanak and R. T. of the salts con-idered, the vapor pressure curves of Figure 3 have Werby for the data in Tables I11 and IV. been replotted on Figure 5 as indicated by the dotted lines. The dehydration obtainable with these salts a t any given temNOMENCLATURE perature can be read directly from the intersections of the solid and dotted lines on Figure 5. This chart makes it clear that the R , R = empirical constants dehydrating power of lithium chloride is substantially indef = fugacity pendent of telrperature. On the other hand, the dehydration Y “ activity coefficient = p/nx acromplished by calcium chloride and sodium chloride is somek = Henry’s law constant what affected by temperature. It also shows that the lithium P a partial pressure of given component in a solution vapor pressure of the pure component 7 r = T - temperature, O Kelvin x = mole fraction ‘ TABLE 111. EFFECT OF TEMPERATUR~ ON EQUILIBRIUM WATER z = mole ratio-in a water-ketone mixture, for example, CONTENT OF MEK IN CONTACT WITH SATURATED BRINES zw = xw/x9 % Water by Weight in Solvent Layer I
TzmC, 20 30 40 50 60
TABLE IV.
Calod. 0.29 0.29 0.30 0.30 0.32
LiCl Exptl. 0.38 0.40 0.42 0.43 0.45
KCHaCOi Calod. Exptl. 0.50 0.69 0.55 0.68 0.63 0.67 0.65 0.62
CaClz Calcd. Exptl. 0.92 0.83 0.59 0.70 0.55 0.65 0.50 0.57 0.55 0.62
....
EQUILIBRIUM WATERCONTENT OF MEK IN CONTACT WITH SATURATED BRINES % Water by Weight in Solvent
Compound MgClo
Mgs04
LirSO4 SrCln NaCHsCOn
Tzmz., 29 52 25 49.6 52.5 25 25 51 25 49.5
Calod.
Layer Exptl. by density
0.98 1.0 5.1 4.8 5.0 3.9 2.7 3:o
..
1.3 1.6 6.7
... ... 2.9
5.4 2.3 3.3 3.4
aDetermined by titration with Karl Fisoher reagent.
Exptl, by titration 1.2 1.1 5.3 5.7 5.8 5.1” 2.8 3.6 3.7 3.4
Subscripts D . = dehydrating substance W = water S = ‘solvent being dehydrated LITERATURE CITED
(1) Butler, J. A. V., “Fundamentals of Thermodynamics”, pp.
164-75, London, Macmillan Co., 1934. (2) Carlson, H. C., and Colburn, A. P., IND. ENQ.CHEM., 34, 581 (1942). (3) Hanak, E. W., S.B. thesis, Mass. Inst. Tech., 1941. (4) Lewis, G. N., Proc. Am. Acad., 43,259 (1907). (5) Marasco, M., IND.ENG.CHEM., 18, 701 (1926). (6) Marshall, J . Chem. SOC.,89, 1350 (1906).
(7) Shell Chemical Co., “Methyl Ethyl Ketone”, 1938. (8) Sherwood, T. K., “Absorption and Extraction”, New York. McGraw-Hill Book Co., 1937. (9) Smith, D. M., Bryant, W. M. D., and Mitchell, J., Jr., J . Am. Chem. Soc., 61, 2407 (1939). (10) Stanton, E. J., S.M. thesis, Mass. Inst. Tech.. 1941. (11) Werby, R.T..S.B. thesis, Mass. Inst. Tech., 1941.
’
