NOVEMBER, 1938
INDUSTRIAL ANI) ENGINEERING CHEMISTRY
demonstrate the applicability of the process a t higher temperatures and with the use of 95 per cent alcohol as solvent. The relations which exist between the temperature of extraction, the concentration of alcohol in the solvent, the time of extraction, the quantity of solvent, and the yields and properties of lactose and protein powder resulting from the process require further investigation. The work of Ferry, Cohn, and Newman (6) on the influence of salts on the solubility of egg albumen in 25 per cent alcohol a t - 5 " C. indicates that the critical concentration of 70.7 per cent alcohol a t room temperature reported in this paper may vary with temperature. Incomplete data obtained in this laboratory tend to indicate that a t lower temperatures the advantages which accrue to the use of 95 per cent alcohol a t higher temperatures may be obtained with 70.7 per cent alcohol. It is unnecessary for the purpose of this paper to account theoretically for the effect of alcohol concentration on the solubility of the alcohol-precipitated whey proteins. Alcohol precipitation of lactalbumin from a practically salt-free solution gives a product readily soluble in water, and precipitation from a solution containing salts in considerable quantity gives a relatively insoluble albumin. On this basis, then, the solubility in water of alcohol-precipitated whey lactalbumin may depend on the solubility in alcohol of the soluble whey salts which, in turn, may depend on the concentration of alcohol. The whey protein powder produced may be made to contain approximately 50 per cent protein. The pretreatment of whey to remove insoluble materials (casein and insoluble calcium salts) results in a considerable improvement in the final products- lactose and protein powder. As a result the quantity of insoluble or coarsely dispersed material associated with these products becomes insignificant. However, the process is limited a t present to the preparation of a powder
1311
containing not more than 50 per cent protein. This powder contains in the neighborhood of 15 per cent ash; consequently about 35 per cent of the powder is lost in the ashing process. Presumably, therefore, the salts contained in the powder consist in part of the insoluble and soluble citrates and lactates originally present in whey. To obtain a further increase in the protein content of the powder, it would evidently be necessary to treat the original whey for the removal of calcium citrate and calcium lactate. However satisfactory the results have been on a laboratory scale, the process has not been projected on a plant or pilotplant scale extensively enough to warrant any statement as to the possibilities of its commercial exploitation. The simplicity of the steps involved leads to the opinion that no particular difficulty should be encountered in the application of the process to a plant scale. The qualities and useful properties of the products obtained indicate that it has great potential value.
Literature Cited (1) Assoc. Official Agr. Chem., Methods of Analysis, 3rd ed., p. 216 (1932). (2) Ibid., 3rd ed., p. 365 (1932). (3) Bell, R. W., Peter, P. N., and Johnson, W. T., Jr., J . Dairy Sci., 11, 163 (1928). (4) Evelyn, K.A., S.Biol. Chem., 115, 63 (1936). ( 5 ) Ferry, R. M., Cohn, E . J., and Newman, E. S., J. Am. Chem. SOC.,58, 2370 (1936). ( 6 ) Herrington, B. L., J. Dairy Sci., 17, 805 (1934). ( 7 ) Leviton, Abraham, U. S. patents pending. (8) Osborne, T. B., and Wakeman, A. J., J. Biol. Chem., 33, 243 (1918). (9) Troy, H. C., and Sharpe, P. F., J . Dairy Sci., 13, 140 (1930). (10) Tuckey, S. L., Ruehe, H. A., and Clark, G. L., Ibid., 17, 587 (1934). (11) W7atson,P.D.,IND.ENG.CHEM.,26, 640 (1934). RBCEIVED May 24, 1938.
SEPARATION PROCESSES Correlation between the y us. x and the Molal Heat Content us. Mole Fraction Diagrams MERLE RANDALL AND BRUCE LONGTIN University of California, Berkeley, Calif.
P
REVIOUS papers (3, 4) have indicated the general validity of the molal property us. mole fraction diagrams as a representation of the behavior of separation processes. While they are valid, they are not always convenient. They will become most useful when we can transfer their implications to the simpler 21 us. z diagrams. This can be readily accomplished when we recognize a fundamental correspondence between geometrical elements of the diagrams. Contact Transformations The y 08. 5 diagram may be obtained from the molal property vs. mole fraction diagram by what is known mathe-
I n the McCabe and Thiele diagram for the design of fractionating columns and in similar diagrams, various simplifying assumptions are usually made. This paper indicates methods of transferring various operations which can be represented with no simplifying assumptions in a mole property V S . mole fraction diagram to diagrams of the McCabe and Thiele type. Thus a pair of liquids each with a different heat of vaporization is shown to give a curved instead of straight operating line in the McCabe and Thiele diagram. matically as a contact transformation ( 2 ) . Through each point (z, y) in the X Y plane there is an infinite number of line elements; each has a different slope, p . By the equations
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INDUSTRIAL AND ENGINEERING CHEMISTRY
1312
we define a line element in new coordinates whose position is (x’,y’) and whose slope is p’. Each line element in the X Y plane completely defines a t least one line element in the X’ Y‘ plane. This is a transformation of lineal elements, by which a line element in one set of codrdinates is transformcd into a line element in another set of coordinates. I n general, the position of a transformed line element depends not only on the position of the original element but also on its slope (Equations l and 2). If we consider the line elements t h a t make up a curve (to which they are tangent), it is not generally true that they will remain tangent to the curve after the transformation. A contact transformation is defined as the most general transformation of lineal elements that will transform elements tangent t o the same curve into corresponding elements tangent to the corresponding curve. I n general, an element which lies on a curve need not be tangent to it. If the slope of the curve is d y l d x , p is not necessarily equal to d y / d x , and hence ( d y - pdx) is not zero. But if the element is tangent t o the curve, ( d y - pdx) must vanish. If the transformed element is to be tangcnt to the transformed curve, then a t the same time (dy’ - p ’ d d ) must vanish. The necessary condition for a contact translormation is that (dY‘
- P’dZ‘)
3 P(Z,
!t,
P)(&
-P
W
(4)
where pis any nonvanishing function.
Transformation H us.
N t o y os.
x Coordinates
I n the y vs. x diagram the compositions of two streams are represented by a point. I n the H us. N diagram both the compositions and the relative amounts of the two streams are represented by the positions of three points on a straight line ( A ,B , and D of a previous paper, 3). I n the y us. x diagram we can give this additional information by drawing a short stroke (i: e., l i n e c l e m e n t ) through the point ( 2 , y) whose slope is the ratio, R, of the number of moles of liquid to the number of moles of vapor in countercurrent flow (in concurrent processes R becomes negative). By this dcvice we are able to represent the relative amounts and the c o m p o s i t i o n s of t w o streams in the y us. x diagram by a single line element, whereas in the H us. N diagram me need a line segment with three points on i t for thc same purpose (Figure 1). If we consider only liquids and vapors a t their boiling points, points A and B must lie on the liquid and vapor equilibrium N=O curves, respectively. I n FIGURE 1. PROJECTION OF DIFthis case it is sufficient to FERENCE BETWEEN TWO PHASES specify the position of IN H vs. N DIAQRAM TO y us. x REPRESENTATION point D and the slope of
-
line BAD. Tlicn points A and 13 are determined by the intersections of the ray through D with the equilibrium curves. A liquid and vapor stream a t their boiling points (not necessarily a t equilibrium) may be represented by n lineal element located at D, with its slope, p , that of line BAD. We may gencralixe this last consideration. Point D alone (Figure 1) represents a liquid not at its boiling point. When we draw a lineal element through it, we imply the existence of a saturated vapor, B, which, added to liquid D,will produce a boiling liquid, A . We may think of the “cool” liquid, D, as the difference between an arbitrary boiling liquid, A , and the vapor which mould have t o be condenscd in order to convert D into this liquid. Similarly we may think of a superlieated vapor as the difference of an arbitrary saturated vapor and the liquid which would have to be vaporized in order to convert the superheated into saturated vapor. I n terms of lineal elements, the nonboiling liquid or vapor is represented by the whole bundle of lineal elements tlirough the point which represents the liquid or vapor. ll the point should happen to lie betwecn the two equilil~Iiumcurvcs, the bundle of elements implies an arbitrary mixture or sum (rather than differencc) ol liquid and vapor (not necessarily a t cquilibrium) which has a given gross composition and molal heat content. Corresponding to the lineal element ( H D , N D , P D ) which represcnts a boiling liquid and saturated vapor in tile H us. N diagram, there is a lineal elemcnt (r,u, R ) in the 3 us. x diagram. Its coiirdinates, x and y, are the mole fractions, NA and N e , of light component in the boiling liquid and saturated vapor. Geometrically the point (x,y) may be located by projections as indicated in Figure 1. By such a projection the correct y us. x construction corresponding to any 13 us. N rectification diagram may be obtained. The dope of the lineal element of slope R through this point is detcrmincd by the ratio into which point D divides line HAD. This slope may be constructed graphically as shown in Figure 1. We have here a graphical transformation of the lineal elemcnt (HD, N D , PD) into a lineal elemcnt ( 2 ,y, R). The geometrical construction is sufficient to detcrniine any y us. x diagram from its corresponding H JS. N diagram, and vice versa. However we can obtain much more powerful methods by examining the more formal aspects of the trnnsformation. Although we have obviously a transformation of lineal elements, this does not ensure that it is a contact transformation. We can easily set up the equations of the transformation from the equations of the material and heat balanccs (3) and the geometry of the construction. The equilibrium curves determine the molal heat content of the liquid as a function, H=,of mole fraction x , and that of the vapor as a function, H ~of, mole fraction y, The equations of the transformation are
Examination of the equations shows that (dHD - p~ dND) is not proportional to (dy - R d x ) , and hence this is not a contact transformation. However, the properties of the diagram unmistakably indicate the existence of a contact transformation. The paradox lies in the choice of the lineal element in the y US. x diagram Although the element of slope R does not give a contact transformation, there is another element through point ( x , y) which does give a contact transformation. If me inquire what the slope, R’, of such an elemcnt must be, in order to give ( ~ I I D - p~ ~ N D )proportional to (dy R‘dx), we find t h a t it must. be E’ = R[(H’.s
- PD)/(H’v
- PD)]
(8)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
where H’, and H ’ ~ are the derivatives of H, and H~ with respect to x and y, r e s p e c t i v e l y . If we define the lineal Y e l e m e n t as o n e whose coordinates are x and 1~ (as previously) and whose slope is R’, we obC X tain a contact transform a tion whose e q u a t i o n s may be obtained by eliminating R H between Equations 5 , 6 , 7 , and 8. The significance of slope R’ becomes s i m p l e w h e n me study Figure 1. If we allow the elemcnt a t D to rotate w i t 11 o u t slii f t i ng, point (2, y) moves I p 3 along a curve whose N=O N slope is not necessarily R. If ratio FIGURE 2. COXTACTTRANSFORMATION O F ELEMENTS IN THE H us. N R were constant (as DIAGRAM T O ELEMENTS IN THE y US. Z is assumed in the DIAQRAM hlcCabe and Thiele construction, 2 ) the material balance would require that dy/dx be equal to R, and point ( 2 , ~would ) move along element (x,y, R). The characteristic property of a contact transformation is that it transforins elements tangent to a curve into elements tangent to the new curve. I n certain singular cases, however, it transforms them into elements bound together in a point. The converse is also true. If in Equation 4 we let p vary without changing x or y (i. e., let the element rotate about its fixed position) the right member vanishes and hence the left must also vanish. This requires that elements (d, y’, p’) which correspond to any set of elements bound to a point must all be tangent to the curve along which they lie. As we allow the element at D to rotate, the transformed element whose slope is R‘, being obtained by a contact transformation, must be tangent to the curve traced out by (2, y). Slope R’ is the value of dy/dx along the curve representing the changes which the liquid and vapor stream may undergo while remaining a t the boiling point. Slope R is the value of dy/dx along the curve representing the changes which could occur when the relative amounts of liquid and vapor remain constant. I
/
Properties of the Transformation Let us examine the way these elements behave in the diagrams. I n the H us. N diagram we have only t o watch the element (HD,ND, p ~ as) it moves about. I n the y us. x diag a m element (3, y, R) is of particular interest, but it is to element (2, y, R’) that we must look for correspondences between the diagrams. I n Figure 2 is shown the same set of lineal elements represented in the y us. x diagram as (x,y, R‘), and in the H us. N diagram as (LID, ND, PO). For any fixed point in the y us. x diagram the coefficient of R in Equation 8 is constant, and R’ is proportional to R. At any fixed point in the y x diagram the elements (2, y, R ) and (2, y, R’) will therefore bear the 11s.
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relation shown in Figure 3, in which the slopes are in constant ploportion. The value of R’ is equal t o that of 12 at zero and infinite slope (i. e., element horizontal or vertical) and either leads or follow it all the way around the point between these two positions. If the liquid curve in the H us. N diagram is parallel to the vapor curve so that its slope, H’=, is equal to the slope, H ’ ~ , of tlie vapor curve, then 12’ mill be equal to R for all ff f d c R.gencrally I n no other true. case It 8 ”., 1, / ,I c mill thisofbe values
ii:y
may happen that for a par‘.,‘!, / / ,,’ ticular x and y the values A’* and H ’ are ~ the same, but this is a singular cape. To any single point in the 1~ us. x diagram there corrcsponds one line A B in the R FS. N diagram (as may readily be secn FIGURE 3. RELATION OF from Figure 1). \%‘hen R is ELEMENTS (ZI Y, AND (2,y, R’) IN THE y US. 2 zero, there is no liquid stream, DIAGRAM WIiE,rE T~~ and D lies on the vapor curve. SLOPES ARE IN coNsTANT As the amount of liquid inPRoPORTlON creases, D moves upward along A B away from the vapor curve, and R increases. As element (HD, ND, PD) moves along itself upward from the vapor curve, clement (2, y, R ) rotates countcrclockwise about fixed point (x,y) while element (2, y, R’) follows it as in Figure 3. In Figure 2 this behavior is exeniplificd by elements 1 t o 7 associated with point P in the y us. x diagram, which in the H us. N diagram lie directed along line PP and move along it as indicated, and by the elements associated with points Q and S . It is apparent that any point in the y us. x dial gram corresponds to a straight line in the H us. N diagram, and conversely, any straight line in Y thc H us. N diagram corresponds t o a point in the y cs. x diagmm. It is not true that any point in the H (IS. N diagram corresponds to a straight 0 0 X I line in the y us. x diaFIGURE 4. LINEAL ELEMENTS gram. THROVUH A POINT(t, y) ON In general, because of THE EQUILIBRIUM CURVEIN A the contact transformaus. x DIAGRAM tion, element (r, y, R’) will trace out a curve to which i t is tangent, while element (HD,ND, p ~ rotates ) about a fixed point. Hence a point in the H us. N diagram corresponds to a curve in the y 2‘s. x diagram. Only if R’ is constant will the curve be straight. If R is zero or infinite, the D point lies on either the liquid or vapor curve, and a. rotation of the line K D does not alter R. At the same time it leaves R’ constant. Hcnce the curves corresponding t o points on the eqnililrium curvcs are straight lines which are either horizontal ( R = 0, all vapor) or vertical ( R = a,all liquid). This is shown in Figlire 2 by elements 5 , 8 , and 9 associated with point V , and dements 1, 7, 10, and 13 associated with point L. This result is obvious, since in one diagram the point L, on the liquid curve, represents a liquid whose composition in the y us. x diagram is represented by the vertical line whose x coordinate gives the liquid composition. Counterclockwise rotation about a
1314
INDUSTRIAL AND ENGINEERING CHEMISTRY
point on the liquid curve in the H us. N diagram corresponds to upward motion in the y us. x diagram, and counterclockwise rotation about a point on the vapor curve corresponds to motion from right to left. If the liquid and vapor curves are parallel straight lines, which will be exactly true only for solutions of identical substances, then H’,__ and H ’ are ~ constant and equal. At the same time the line BAD which passes through a fixed point, D, will be cut in a constant proportion, no matter where D is located. I n this case R and also R’ are constant for all elements (HD,ND, P D ) belonging to the same D point. When the liquid and vapor curves are parallel straight lines, and in no other case, all points in the H vs. N diagram are represented by straight lines in the y us. x diagram. And in only this case is R’ always equal to R. I n all other cases the points in the H us. N diagram, except for certain singular points, correspond to curves in the y us. x diagram.
Equilibrium Diagram Consider the equilibrium curve in the y us. x diagram. Any lineal element on this curve represents the compositions and relative amounts of a liquid and a vapor which are a t equilibrium. I n the H vs. N diagram the corresponding element must lie along an -extended equilibrium tie line. Each of the elements which makes up the tie line corresponds G to an element through the I point on the y us. x equilibrium curve, and one of them corresponds to the element which is tangent to the curve (Figure 4). The elements tangent to the y us. x equilibrium curve must correspond to elements tangent to a curve. Hence every extended tie line is a t some N=O N=I FIGURE 5 . CAUSTIC CURVE point tangent to a particular OF TIE LINESIN CONJUcurve; the tie lines possess GATE PHASES an envelope or caustic curve. This caustic curve of the tie lines (Figure 5 ) has already been discussed (4). Examples are found in the diagrams of Savarit (6). I n general, when in the y us. x diagram a set of points has a curve in common (e. g., the equilibrium curve), the corresponding straight lines in the H’VS. N diagram will be tangent to the same curve (have an envelope) or all pass through the same point. Conversely, when a continuous series of lines in the H us. N diagram have a point in common, the corresponding points in the y us. x diagram lie on a curve. And when any number of points lie on a straight line in the H us. N diagram, the y us. x curves which correspond to these points will intersect a t the point which corresponds to the common straight line.
Transformation of Rectification Diagrams I n the H us. N diagram for the simple column section the essential feature is the fixed D point in which several lineal elements are bound together. I n the y us. x diagram this point is transformed into a curve. The straight lines through D are transformed into points which lie on this curve (Figure 6). The lines through the D point represent the liquid and vapor streams a t the same interplate level. In the y us. x diagram they are represented by points on the operating line.
I n this case the curve corresponding to D is the operating or reflux curve, and the points on it, corresponding to the lines through D,are the corners of the stepwise construction of McCabe and Thiele ( 2 ) . Only when the liquid and vapor curves in the H vs. N diagram are p a r a l l e l a n d straight will this reflux line be straight. And in general in any other case the slope of the reflux line is not equal to the reflux ratio a t that point in the column, but is (HI,
-
PD)/(H’y
-
VOL. 30, NO. 11
X
I
I
PD)
times the reflux ratio. I Often (in the case of distillation at least) the equilibrium curves in the molal property vs. mole fraction diagram I N= I are sufficiently close to FIGURE6. CONTACT TRANSp n r a l l e l so t h a t t h e FORMATION OF A RECTIFICATION corresponding curvature DIAGRAM FOR A SIMPLECOLUMN of the reflux line is negSECTION ligible. H o w e v e r , a s was pointed out by Thiele (6) in the case of distillations in the critical region, the curvature may become sufficiently great to make the y vs. x diagram almost useless.
Method of Correspondence By making use of the known correspondences between points, lines, and curves in the two diagrams, and remembering that contacts in one diagram remain contacts in the other, we may translate the description of one diagram into a description of the corresponding diagram. These correspondences are as follows: H vs. N Diagram
a. Straight line
y vs.
x Diagram
6
Curve Clockwise rotation
1 a. Point b. Point on y = x c . Equilibrium curve point 2 Vertical straight line , 3 Horizontal line 4 a. Curve (straight line if the equilibrium curves in H 9s. N diagram are parallel) b. Reflux curve 5 Curve or straight line 6 Upward motion not parallel to
7
Upward motion
7
1
b. Vertical straight line c. Tie line 2 Point on liquid curve 3 Point on vapor curve 4 a. General point b. D point 5
u = x
Counterclockwise rotation
I n order to translate from the H vs. N diagram we substitute for the words in the first column the corresponding words in the second column. As an example, for a simple enriching column with total condenser we start the construction in the y vs. x diagram by fixing the reflux curve, as determined by the values R, x, and y a t the top of the column. Then we join the point of the reflux curve which lies on y = x with a point on the equilib-
NOVEMBER, 1938
FIGU.RE 7. CONTACT TRANSFORMATION OF DIAQRAM FOR FEEDUNIT WITH FEED NOT AT BOILING POINT
INDUSTRIAL AND ENGINEERING CHEMISTRY rium curve by a horizontal line. Then join this equilibrium point t o a point on the reflux line by a vertical line. Join this last point to the equilibrium point by a horizontal line, and so on. Translated, this reads : Start the construction in the H us. N diagram by fixing the D point as determined by the values of R, x, and y a t the top of the column. Then join the vertical line through D to a tie line by a point on the vapor curve. Join this equilibrium tie line to a line through D by a point on t h e liquid curve. Join this line through D to an equilibrium tie line by a p o i n t on t h e v a p o r curve, and so on. This is the construction described in a previous paper for the H us. N diagram (4).
Feed Not at Boiling Point As a final example of the application of these correspondences, we may consider the problem of representing a feed which i s not a t the boiling point. The representation in the H vs. N diagram is relatively simple and was discussed in a previous paper (4). The D points for the sections above and below the feed do not coincide but lie on the same straight line with a point representing the feed. I n the 9 vs. x diagram, therefore, the reflux curves for the sections above and below the feed are not tangent but intersect in the same point with a curve representing the feed. This is precisely the construction described by McCabe and Thiele (2) in their first article on the y vs. x diagram, except for the use of curved instead of straight lines. However, the present method allows a somewhat fuller insight into the meaning of the feed curve, F (Figure 7). As the feed is gradually heated, point F in the H us. N diagram must rise, and the elements which go to make up curve F must rotate counterclockwise; the curve itself rotates counterclockwise as the feed is heated. When the feed is just boiling, the feed curve becomes a vertical straight line. When the feed has been partially vaporized, the feed curve lies in the second quadrant, and when totally vaporized, the curve lies horizontal. A superheated vapor feed is represented by a feed curve whose slope is positive and less than 1. A liquid feed below the boiling point is represented by a feed curve whose slope is positive and greater than 1. As the intersection of the reflux curves in the y us. x diagram moves vertically, the line D$Dt must rotate clockwise. When intersection P reaches the equilibrium curve, line DbFDt, which corresponds to P , will have rotated into coincidence with a tie line. The position of minimum reflux ratio in the H us. N diagram occurs when line DbFDt coincides with a tie line.
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Design Units for y us. x Diagrams If the y vs. x diagram is to be used for the design of other types of equipment than the ordinary continuous fractionating column, it is important to recognize the existence of separate design units. From these design units the design diagram of any complicated process may be built up. Each of the design units which have been discussed in connection with the H vs. N diagram may also be used in connection with the y us. x diagram. The appropriate design patterns are obtained by applying the contact transformation to the corresponding H us. N design pattern. In particular it is to be emphasized that the design pattern for a simple column section-i. e., considered independent of any end equipment-consists of an unrestricted stepwise construction between a reflux curve and the equilibrium curve. This is apparent if we consider the usual design diagram of an absorption tower. In such a diagram the steps are not required to start from or end on the diagonal, y = 2. This requirement, always found in the McCabe and Thiele diagram for a fractionation tower, is not inherent in the column itself. Rather, it is a restriction imposed by the end equipment-i. e., reboiler or condenser. As such it represents the design unit appropriate to a reboiler or condenser, and is not part of the design pattern of a simple column section. Similarly the requirement that two operating (or reflux) lines intersect on a feed line is a property of the feed unit, and not of the column section itself.
Summary The manner has been shown in which correspondences are to be found between the McCabe and Thiele and Ponchon type diagrams and in general between any y us. x diagram and the corresponding molal property US. mole fraction diagram. The correspondences are due to the existence of a contact transformation between the two types of diagrams. They consist essentially in a geometrical dualism between points and lines, and between direction and position. With the help of correspondences, a construction which is easily visualized in terms of one diagram may be translated to the other diagram where it was less readily apprehended. In general, properties of a diagram which have to deal with positions of points are more easily apprehended than those which have to do with directions of lines. Since the direction of a line in one diagram appears as the position of a point in the other diagram, the two types may be used to supplement each other nicely. I n a subsequent paper these principles will be used to discuss further correspondences between the two types of diagrams.
Acknowledgment Clerical assistance by the Works Progress Administration is gratefully acknowledged.
Literature Cited 1) Lie, Sophus, “Beruhrungs Transformationen,” Vol. I, Leipzig, B. G. Teubner, 1896; Cohen, A., “Introduction to the Lie Theory of Continuous Groups,” pp. 178-96, Boston, D. C. Heath and Co., 1911. (2) McCabe and Thiele, IND.ENQ.CHEM.,17, 605 (1925). 13) Randall and Lonatin, Ibid., 30, 1063 (1938). (4)Ibid., 30, 1188 (1938). (5) Savarit, Arts et mdtiers, Aug., 1922, p. 241. (6) Thiele, IND.ENQ.CHEM.,27, 392 (1935). RECEIVED March 25, 1938.
