November, 1945
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Proof of the previoua paragraph is self-evident. In the upper graph of Figure 1,for example, the viscosity of both benzene and of luretic acid is a straightcline function aa plotted logarithmically against the vapor pressure of water at the me temperature. Hence, the viscosity of benzene (or of any other material which gives a straight line on this graph) would be a straightline tunction of the viscosity of acetic acid taken at the 8&me temperature. The same would hold for a plot of fluidity a t the same temperature against that of a reference substance, or for either viscosity or fluidity against that of a reference substance a t the same reduced temperature. The last mentioned plot is analogous to the plot of vapor pressure for one substance against vapor pressure of another at the same temperature (14)or critical temperature (16). The elopes of the lines on such a plot are the ratio of activation energies of viscosity of the two liquids (or of reduced activation energy). ACKNOWLEDGMENT
Appreciation is expressed to Alfred F.Schmutzler and Allan P. Colburn for interest and suggestions during the course of this study, and to Samuel Josefowitr for drafting the figures.
11 1s
LITERATURE CITED
(1) Andrade, E. N. da C., Nature, 125,582 (1930). (2) Andrade, E. N.da C., Phil. Mag., (7117,497,698 (1934). (3) Andrade, E. N. da C., Proc. Phys. SOC.(London),52,748(1940). (4)Creighton, H.J. M., J. Franklin Inst., 193,647 (1922). (6) Doraey, N. E., "Properties of Ordinary Water Substance". New York, Reinhold Pub. Corp., 1940. (6) Ewell, R.H.,J. C h a . Phys., 5,571,967 (1937). (7)Ewell, R. H., and Eyring, H., Zbid., 5, 726 (1937). (8) Eyring,H.,Ibid., 4,283 (1936). (9) Glasatone, S., Text-bok of Physioal Chemistry, New York. D.Van Nostrand Co., 1940 (10) Gusman, 3. de, Andes soc. eapafl.fls. quCn, 11, 353 (1913). (11) Irany, E.P.,J . Am. Chem. SOC.,60,2106,1938; Phil. Mag.. 33. 685 (1942). (12) Magat, M., Trans. Faraday SOC.,33,81 (1937). (13) Nieaan, Phil. Mag., 32,441 (1941). (14) Othmer. D.F.. IND. ENO.CIIEM.,32,841 (1940). t16j Zbid., 34, 1072 (1942). (16)& I& 36,669(1944). (ln Othmer,D.F., and Gilmont, R., Ibid., 36,858 (1944). Othmer, D.F.,and Sawyer, F. G., Ibid., 35,1289 (1943). (19) O t h e r , D.F., and White, R. E., Ibid., 34,952 (1942). (20) Perry,J. H., and Smith, E. R., Zbid., 25, 195 (1933). (21) Porter, A. W., Phil. Mag., [e] 23, 468 (1912).
.
il6
Hydrolysis and Catalytic Oxidation of Cellulosic Materials DETERMINATION OF STRUCTURAL COMPONENTS OF COTTON LINTERS 'H.I?.NICKERSON2 AND J. A. HABRLE'
......,..,.....,.
A
BOILING aqueous solution containing 2.6 moles of hydrochloric acid and 0.6 mole of ferric chloride per liter evolves carbon dioxide rapidly from glucose a t a nearly constant rate which is proportional to the glucose present in the system (6). This reagent under the same conditions also liberates carbon dioxide from cellulosic materials but a t slow, initial rates which increase as hydrolysis is continued (4, 6). These observations have led to the conclusions that some of the cellulose is hydrolyzed to simple sugars which, by oxidation, yield carbon dioxide, and that the course of the hydrolysis can be determined from instantaneous rates of carbon dioxide evolution (6). The technique and apparatus originally employed in this laboratory were modified and improved by Conrad and Scroggie (9),who verified And extended some of the earlier work. Hydrolysis-time curves obtained by this method for a number of different cellulosic materials have in common a shape that indicates rapid, early disintegration of part of the cellulose and a subsequent slower and more constant breakdown of the remainder. As Badgley and collaborators (1) stated in a recent review, such curves are generally regarded as evidence of a structural heterogeneity. The rapid initial hydrolysis represente the easily accessible or disordered fraction; the slower and more constant, subsequent hydrolysis, the denser less accessible or highly nrdered fraction of the material. However, these two parts of a typical hydrolysis-time curve are not sharply differentiable and, For previous papers in this series, see literature citations 8-8.
* Present addrens, A. C. Lawrence Leather Company, Peabody, Mass. 8
Preaent address. Crescent Heights, New Brighton. Pa.
,
Mellon Institute, Pittsburgh, Pa.
consequently, only a rough approximation of the distribution between ordered and disordered states can be obtained from the
tast. The study described in this paper was undertaken to yield deeper insight into the meaning of hydrolysis-time phenomena and, if possible, t o develop a practical method of resolving the typical curve. Samples of cotton linters were subjected to acid hydrolysis for varying times under controlled conditions, and the resulting insoluble residues were washed and dried. This series of hydrocelluloses waa then investigated by the hydrolysiq-oxidation method. MATERIALS AND METHODS
A well-blended batch of processed, high-viscosity acetategrade cotton linters was used without additional purification as starting material. Hydrocelluloses, representing 0, 0.07,0.2,0.8, 2, 4, and 7 hours of treatment with boiling hydrochloric acidferric chloride rea ent or its equivalent, were isolated for investigation by the metfiods described below. The intact sample (0 hours) was boiled 4 minutes in water; the 0.07-and 0.2-hour samples were digested singly in boiling 2.5 N hydrochloric acid for 4 and 12 minutes, respectively. The rest of the series was prepared by refluxing a suitab!e batch of linters in h drochloric acid-ferric chloride reagent siphomng off portions o r t h e boiling BUS nsion 5-10 minutes short of the times indicated, and, as q u i c k g a s possible, filtering the hot SUIpension on c o m e alundum crucibles. Crucible and residue were then given preliminary washes with cool, dilute hydrochloric acid and water; finally, the crucible containin moist residue was transferred to boiling 2.6 N hydrochloric acid for 5-10 minutes to complete the digestion. A volume of 40 ml. of hydrolyzing solu-
1116 25
20
;r
-
c:
-e::
15
0
-e*
$ IO 0
a
0
a
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 37, No. 11
tubes with short side arms, and two pairs of detachable right-angled, glass extensions for the arms were empioyed in each run. Fitted with a pair of the extensions by means of rubber connections, an absorption tube could be seated over two vertical orifices provided with mercury cups and, so placed, would bridge a gap in the train. At the end of aQrescribed time interval the absorption tube w&s quickly removed and replaced by another absorption tube extension assembly. I n practice the ten tubes were conditioned together overnight in a lar e desiccator and weighed. Nine of the tubes were t%en used to cover a 7-hour hydrolysis-oxidation period. After further overnight conditioning in the desiccator, all ten tubes were reweighed, and the weight increments were corrected for chan es in the blank. The series of tubes was then reafy for a new run.
$ 5
CARBON DIOXIDE EVOLUTION
The assumption that soluble hydrolytic producta derived from cellulose yield carbon dioxide in the I 2 3 4 5 6 7 same manner as glucose receives support from the Time i n Hours data in Table I. Presented on a comparable basis Figure 1. Hydrolysis-Time Curves Calculated for Linters and as cumulative moles of carbon dioxide per mole of Derived Hydrocelluloses glucose. these data indicate that glucose and celloThe times indicate amounts of hydrolytic pretreatment employed i n preparation biose behave the same within exDerimental error. of samples. This basis of presentation was suggested by Scroggie (7). tion per gram of starting material was found to be satisfactory. Table 11 shows the variation of cumulative carbon dioxide The use of ferric chloride reagent for the longer eriods of hyoutput, as moles per mole of anhydroglucose, with time for indrolysis hinders the accretion of undesirable tarEke products, tact linters and for hydrocelluloses derived from them. These while the double digestion is designed to extract occluded iron data on conversion by the method of slopes (6)yield the percentsalt. Directly after receiving the treatment just. outlined e?ch age hydrolyzed-time curves of Figure 1. I n both forms these sample including the intact control, was purified in the follomng observations indicate that prior hydrolysis reduces the yield of way: +he solid was filtered on a coarse alundum crucible, and carbon dioxide, a t first rapidly and then at a decreasing rate to washed in the crucible with hot water, with several floodings of practical constancy in about one hour. I n fact, this result might warm 5% ammonia, and then successively with boiling water, acetone, and benzene. It was removed from the crucible and airalmost have been anticipated from the relative densities of intact dried. linters and of the various hydrocelluloses prepared for use in the Approximately. 2 grams of the hydrocelluloses were placed in runs. Figure 2 also suggests that constancy of a sort is attained tared weighing bottles, dried at 105" C., and weighed accurately in about an hour of hydrolysis. before use. Time-carbon dioxide evolution data covering a 7hour period were then determined for each preparation by a At the end of each 7-hour hydrolysis-oxidation run, the inmethod similar to that used previously (6, 6). The apparatus soluble cellulosic residue in the digestion flask was filtered off, however, was modified so that weighing bottle and. Sam 1: could washed, dried, and weighed. From the known starting weights of be dropped into the boiling hydrochloric acid-ferric chgnde reeach sample, the percentages of unhydrolyaed matter were readily agent through a port in the digestion flask. Time for the hydrolysis-oxidation reactions was reckoned from the entrance of the calculated. I n Figure 3 these percentages are plotted against the sample into the boiling liquid. In previously reported experihours of hydrolysis the samples received prior to the actual ments i t was necessary t o introduce the sample and assemble runs. The amounts of recoverable residue, represented by the the apparatus before the digestion mixture was heated and to solid line, rise sharply and then level off after the first hour. count time from the onset of boiling. The change in technique was designed to eliminate Similarly, t h e estimated any spurious effects the quantities of cellulose hywarming-up period might drolyzed during the 'I-hour have caused. runs taken from Figure 1 A further modification of Glucose, cellobiose, cotton linters, and a series of derived the a p aratus was made in and shown by a dotted line hydrocelluloseswere examined by the hydrolysis-oxidation the sufkitution of an asdecrease rapidly with hymethod for the purpose of obtaining more information on carite-gravimetric absorpdrolytic pretreatment, and linters structure and on the method itself. Carbon tion system for the aqueous become more or less conbarium hydroxide-ti trimedioxide evolution data for these materials and for a tric system used earlier for stant after an hour. Incidextrose-hydrocellulose mixture that simulates intact carbon dioxide determinadentally, the sums of the linters are reported. Other variables investigated include tion. T h e g r a v i m e t r i c corresponding values on moisture adsorption and insoluble matter recoverable method proved to be simpler the solid and dotted curve8 after hydrolysis-oxidation runs. The linters starting and less time consuming are approximately 100 in than the titrimetric and material appears to contain, as distinguishable parts, fully as accurate. Since most cases and tend to highly disordered, highly ordered, and transitional comsuitable absorption trains confirm the validity of the ponents in amounts by weight of approximately 3,94, and have been adequately decalculations. 3%, respectively. The highly disordered component is scribed by Whistler, Martin, I n sum these observations readily differentiated by its hygroscopic nature and hydroand Harris (8) and by indicate that the linters Conrad and Scroggie (8), lytic susceptibility, the crystalline or ordered component, only the novel feature of starting material is strucby its uniformly low hydrolytic reactivity. A single that used in the present inturally heterogeneous and hydrolysis-oxidation run is probably insufficient to vestigation needs mention that virtually c o m p l e t e characterize a sample, but the differential approach may here. homogeneity is produced by be used advantageously. Ten similar a s c a r i t e about an hour of hydrolysis filled, U-shaped absorption 0
XNDUSTRIAL A N D ENGINEERXNG CHEMISTRY
November, 1945
under the oonditions of the experiments. The evidence suggeste that the major change occurring in the first hour of hydrolysis and resulting in homogeneity is the removal of part of the structure. Further informstion on this change can be obtained from the data in Table I1 by utilization of differences. For example, subtraction of d u e s in column B from those for corresponding times in column A gives a series of differences which indicate how the ability of linters to yield carbon dioxide is reduced by 0.07 hour of hydmlytio pretrestment. If, as might be expected, these dieerenoes represent the loss of mme essily hydrolyzed snhydroglucose from intaot linters, it should be possible to express them in terms of glucose by use of the data in Tsble I. However, while column A values m e yielded by one equivalent of intaet linters, column B data are based upon one equivalent of bydrocellulose, whish must neoessasily represent more than one equiv5 lent of starting materiaL In other words, it is B59umed that the carbon dioxide values for intsct linters are sums of carbon dioxide derived from B fraction that behaves like column B and a fraction that behaves like gluoose. This s u m p t i o n may be expressed by the equation,
1117
- - 0
oar
0.2
0.8
2.0
7.0
LO
Figure 2. Appsaranoe ofDry‘, 1-Gram Samples of Linters and Derived H y d m l l u l o s e a N m m h indiuto h-
of h7d.DIJflo di-tlon
rrrsired
-.oh
..mp1-.
a t about 0.03 mole. as can be confirmed qualitatively by Table 111. Thus, preparation. representing longer pretreatment thao 0.07 hour respond to hydrolysipo?ddstion as if they differ from intact linters by 0.033 mole of immediately hydrolyzed snhydroAe-(l--z)Bg+zG~ (1) glucose and, in addition, some gradudly svsilable cellulosic material. Column B - D,corresponding to the 0.07 0.8 hour where z is the mole fraction of glucoselike msterial; A, E, and 0 pair, shows how the gradually hydrolyzed cellulosic material me carbon dioxide values at time t far corresponding items in aecumulates and indicates that the maximum of it present in inoolumm A and E of Table 11, and for glucose in Table I, respaotact linters is about 3.0 mole %. This estimate sgrees fairly well t i d y . Solution of thi3 equation for z gives with the vertical spacing of the 0.07- and 0.8-hour curves in Figure 1, after they have been adjusted for the concentration d e e t mentioned nbove. The foregoing calculations yield the result that the tinters starting material contain8 s p p r o h s t e l y 3.3% of resdily hya more convenient form for cslculation. drolyzed anhydmgluoose, 3% of a gradually hydrolyzed fraction, The results obtained hy applying Equation 2 to several pairs and, consequently, between 93 and 94% of slowly hydrolyzed, of columns in Table I1 are shown in Table 111. Despite cansidresistant cellulose. Support, 03peoislly for the latter estimate, erable experimental error, the data, especially those derived from is provided by the data of Figure 3; they suggest not only that the0 - 0.07-hour p&ir,indioate clearly that intact tintersreaponds resistant material of uniform behavior ia produced by an hour as if it contained 0.033 mole of glucose or, as is more Wraly, 0.033 or mom of hydrolysis under the oonditions, but alw that sbout mole of easily hydrolyzed anhydrogluwse. Other pairs, euch 88 84% of this material is rowversble st the end of a 7-hour by0 0.2-hour and 0 O.&hour’oolumns, yield not constants but drolysisdxidation run. The 84% rewvery value holds over an series of inoreasing values which, plotted sgsinst the elapsed appreciable range of pretreatment times and may be wumed times of Table 111, give essentially strsight lines. In each case to hold for intect linters. Thus, the 77.2% recovery for intact where intact linters (column A) is the minuend, extrspolation of linters may represent about 84% of the total resistant cellulose the stmight line so obtained to zero time‘ produoes an intercept of this stsrting material. The ratio of these two quantities yields an eatimste for total resistant oellulase in intact linters of 92% which sgreea very well with the independent value derived hy the other method. Tasm I. C-ON DIOXIDE EVOLVED BY GLUCWE w n CELLOThe sbove dieeerential analysis suggests that intact linters beBIOSB IN H ~ ~ C X L O ACID-FE~IC R~C CEW-E RBAQENT haves like the sum of glucose and 0.07-hour hydrocellulose fracMol- COdMals Clvtions during hydrolyskxidstion. This surmise was eonlimed E l w e d Time. Hr. Glvooss Cellobime experimentally. A mixture of crystalline glucose (resgent dex0.047 0.8 0 86 0.045 trose) and this hydrooellulose preparation, in the calculated pro1.3 0.124 0.118 0.95 1.8 0.211 0.210 1.04 portions of 0.033 to 0.967 mole, w~ subjected to hydrolysis. 2.6 1.04 0.310 0,322 oxidation. Carhon dioxidetime data yielded by this mixture 0.414 3.1 1.03 0.428
-
-
-
4.0 6.0
8.0 7.0
0.682 0.711 0.865 0.878
0.588 0.710
0.846
0.887
101
100 0.89
0.88
TABLE 11. CUBON DIOXIDE EvoLunoN OF ~ N T E B . w n Dw ~ Y E D HYDROOELLUWSE~ IN Hmmcxwruc ACE-FE-C CXWBIDEREAQ-
0.8 1.3 1.8
2.5 3.1 4.0
6.0
6.0
7.0
0.0031 0.0015 0.0015 0.0013 0.0088 0.0062 0.0.0041 0.0185 0.0117 0 . W 8 0.0089 0.0277 0.0198 0.0163 0.0151 0.0412 0.0284 0.0246 0.0225 0.0835 0.0458 0.0387 0.0361 0.0900 0.0876 0.0572 0.0531 0.1190 0 . m o . o m 0.0716 0.1498 0.1180 0.0886 O.oQ1S
0.0015 0.0037 0.0078 0.0131
0.0013 O.MH2
0.0011
0.W39 0,0101 0 . W g l 0.0147 0.0138
0.0206 0.0222 0.0204 0.0338 0.0370 0.0344 0.0506 0.0531 0.M84 0.0887 0 . w ~o . 0 ~ 0,0888 0.0891 0.0876
f0W.
hr 0.8 1.3 1.9 C O . . ~ ~ l ~ / m . l ~ . . h y d ~ ~ ~mix$. l ~ - i0.0031 ~ 0.0088 0.0188 Tima 3.1 4.0 5.0 8.0 cos 0.0441 0.0640 0.0801 0.1180
Ti-
2.6
0.0288 7.0 0.143
These data compare favorsbly with those for intact linters in Table XI and indicate that the behwior of the starting material can be simulated almost perfectly by this me-. The variation of moistweadsorbing capacity of oertain unaubstituted cellulosio materials with amount of hydrolysis has already been demonstrated (6). These observations show thst B 6 Owioa to a l o r initial rata of carbon dioxide svolvtion from %la(a). .napparent lag see- to LWEYI hetraaon additiom of slvooaa and a p m w d carbon dioridr For thi. -a MIO time for the sltrapolstion ir at sp~mdnuta4r0.4 hour.
AND ENGINEERING CHEMISTRY
INDUSTRIAL
1118
TABLE 111. CALCULATED GLUCOSEEQUIVALENTS OF CARBON DIOXIDEDIFFERENCES PRODUCED BY PRIORHYDROLYSIS Moles of Glucose Eqdvalent to Column Differences (from Table 11) A-B A - C A-D B-D 0.035 0.e36 0.039 0,004 0.029 0.035 0.038 0.009 0.034 0.043 0,048 0.014 0.027 0.039 0.043 0.016 0.033 0.043 0.048 0.015 0.034 0.047 0.052 0.018 0.035 0.050 0.056 0.021 0.034 0.053 0.061 0.02? 0.037 0.057 0,065 0.028
Elspaed
Time,Hr. 0.8 1.3 1.9 2.6 3.1 4.0 5.0 6.0
7.0
rapid initial fall in regain capacity is followed by a continual, slow rise. Moisture vapor sorption determinations were also made on the present series of preparations. The dry samples were simultaneously exposed a t 70"F. and 65% relative humidity until weights became constant. The data obtained follow: Time hydrolyied hr. 0 Re aln of reaidue' #e? oent 7.66 Moles wster/moIe anhydroglucose
0.07
0.2
0.8
2
4
7
6.26
6.43
6.77
7.14
7.71
8.17
0.689 0.563 0.579 0.609 0.643 0.694 0.735
In addition to confirming the previously reported variation of hygroscopic behavior with progress of hfdrolysis, these data may be ueed in the calculation of an interesting result: Since intact linters appears to be composed of 0.033 mole of a glucm-analogous cellulose and 0.967 mole of 0.07-hour hydrocellulose, the preceding table shows that 0.145 mole of water are associated with the 0.033 mole of quickly hydrolyzed cellulose [from 0.689 (0.967) (0.563),since intact linters is considered to contain only 96.7% of 0.07-hour hydrocellulose]. This represents about 4.4 molecules of water per anhydroglucose unit or about 1.5 molecultx of water per hydroxyl group for this part of the structure. Unreported observations indicate that the 0.07-hour hydrocellulose shows about one third less adsorption-desorption hysteresis than intact linters; presumably, therefore, a part of this moisture may be condensed in capillaries which the hydrolysis destroys. Even so it is evident that there must be a high percentage of free hydroxyls, each having one molecule of water, in the easily hydrolyzed regions of intact linters.
-
STRUCTURAL COMPONENTS
The evidence presented can leave little doubt that the intact linters starting material is structurally heterogeneous. I n fact, examination of the data suggests that the structure is composed of three different pasts or, more specifically, of three distinguishable degrees of association of the anhydroglucose chains. For want of more descriptive terms, these three parts are designated as crystalline, amorphous, and mesomorphous components. The crystalline component comprising the bulk of the linters
Vol. 37, No. 11
is characterized by its low hydrolytic susceptibility. The data in Table I1 and the curves in Figures 1 and 3 show that hydrolysis for about an hour under the conditions produces a residue which is remarkably uniform in its behavior towards further hydrolysis. It is reasonable to assume that this residue represents the highly organized or crystalline regions of the linterb whose low reactivity per unit weight is caused by their relative impermeability and inaccessibility. It is estimated that thb component constitutes about 94% of the starting material. The amorphous component, on the other hand, is characterized by its complete accessibility. It quickly hydrolyzes to glucose or soluble glucoselike products which can be separated from the rest of the structure, In addition to exhibiting the greatest hydrolytic susceptibility, this component is the most hygroscopic, it apparently has a t least one molecule of water per hydroxyl group at standard textile testing conditions. These results suggest that the amorphous component consists of extremely random or disordered portions of anhydroglucose chains. The data indicate that inta'ct linters contains about 3.3% by weight of thir component. The role of this disorganized part of the linten structure is very important for, as Figure 2 shows, its removal reduces the linters to a coarse powder. The mesomorphous component is intermediate in hydroly tie susceptibility. It appears to be less accessible than the amorphous and more accessible than the crystalline component Furthermore, its behavior suggests that i t is less homogeneoup in itself than either of the other components since it exhibits all degrees of hydrolytic susceptibility between those of the amorphous and crystalline components. In short, it acts precisely as if it were the transitional state of matter between two extremes of structural organization. It seems to be rather sharply differentiable from the amorphous component but not from the crystalline. The mesomorphous material is estimated to constitute about 3% by weight of the intaet linters. The photographic evidence suggests that further powdering of the lintem occurs when this component i s removed. From these results it is apparent that a single hydrolysisoxidation run may not be sufficient to characterize a sample oompletely. The amorphous component, set free at the start, falls in the range where measurements are least accurate. Furthermore, extrapolation as a means of estimating the total noncrystalline cellulose presents an uncertainty in that the point of transition from mesomorphous to Crystalline is, at best, obscure. However, it seems reasonable to expect that a differential method of the type employed in this investigation will overcome both of these difficulties. Present results should facilitate the application of the differential method to other materials. For example, it is conceivable that the amorphous component of other cellulosic materials would hydrolyze completely under roughly the' same time and concentration conditions as were observed for linters. I n support of this suggestion is the fact that similar hydrolyzing conditions produce moisture regain minima in about the same time for a variety of natural and modified cellulosic materials (5). HOWever, it should be noted that more precise methods than that employed may be adapted for glucose determinations, and that somewhat milder hydrolyzing conditions requiring a longer time than 0.07 hour may also be desirable for greater accuracy. Some work along these lines has already been completed. LITERATURE CITED
:I,, 4
,,
76
I
I
,
,
2 3 4 5 Hour8 of prior hydrolysis
6
,
I
,
{,*j
Figure 3. Effect of Hydrolytic Pretreatment of Linters
on Yield of Insoluble Residue and on Amount of Cellulow Hydrolyzed during Hydrolysis-Ofidation Runs
(1) Badgley, W., Frilette, V. J., and Mark, H., IND. ENG.CHBM., 37, 226 (1945).
Conrad, C.C.,and Scroggie, A. G., Zbdd., 37, 692 (1945). (3) Nickerson, R.F., Ibid.,33, 1022 (1941). (4)Ibid., 34,85 (1942). (5) Ibicl., 34, 1480 (1942). (6) Nickerson, R.F., IND.ENG.CHEM.,ANAL.ED.,13,423 (1941). (7) Bcroggie, A. G., private communication. (8) Whistler, R. L., Martin, A. R., and Harris, M., J. Reseurch Nntl. Bur. Standards,24,13(1940),
(2)
