On the Nature of Alumino-silicate and Iron-silicate Precipitates Formed

On the Nature of Alumino-silicate and Iron-silicate Precipitates Formed by the Mutual Coagulation of Silicic Acid and Alumina and Iron Hydroxide Sols...
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ALUMISO-SILICATES .4ND IROS-SILIC.1TES

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121) IASGMUIR, I.: J. Am. Chem. Soc. 39, 1848 11917). (22) LISSER, E. R., ASD GORTSER, It. -1.: J . Ph;vs. Chem. 39, 35 (1935). (23) hICB.4IS, J. W.:The Sorptc'o~i(?/'Gaseshi/ ,'oli.Is. p . 5 . G . Routledge sild Sons, L t c l . , London (1832;. (24) Reference 2 3 , p . 13 et seq. ( 2 5 ) Reference 23, p . 1"s et seq. (28) MICHAELIS, L.,.\si)R0s.i. 13.: 13iociieiii. % . 15, 1% '190f). 127) PROSAD, IC.: S a t t i r e 127. Yo. 319.4. 90 (1931). (28) RICHARDSOX! J. R . : ,J. .Im.C'lieni. Soc. 39, 1842 i 1 9 1 i J . (29) RICH.4RDSOS, H. L . , .\XI)n O B E R ' r S O \ - i , 1'. \v.: J . Cheni. L?(>C. 127,553 (1925). (30) SCHAEFFER, v. J . : PliV.9. RtV. 62, 4% 11942). (31) SCHMIDT, G. C'.: Z . physii;. Clieni. 15, 56 i1894't. (32) SCHWAB, G . 3 3 . . A X D P m r s c a , E . : %. pliysik. C'htni. B1, 385 (1929). (33) SCHWAB, G.-11.. ASD SCHMIDT, 11.: Z.p h y s i k . C'lieni. B3, 3 3 i 11929). (34) SJfEK.IL, h.: %. Elektrorlieni. 35, 567 ! 1 9 2 9 i , (35) TITOFF, .I.:%. physik. Ctieni. 75, 611 (19101. (38) WILKER. J . , .%SI) . ~ P P L E Y . I R D , R . : ,J. C'hem. SOC.69, 1334 (1898). ( 3 i ) Z s I G l I o s D Y . I t . : Z . anorg. Cheni. 71, 3.56 11911).

ISI'RODL~C"~IG\~

I t is well kn0n.n that on mixing: t w o hydrophobic sols of opposite signs of charge, mutual adsorption of the oppositely chargecl prticles takes place with the lon-ering of the {-potential of the mixed particles (cf. Freundlich ( 5 ) ;Keiuer :md con-orkers (16-1 8)). IYeiser and con-orker.: have shon-n that the precipitating power of a positive sol for an oppositely charged colloid is determined by ( a ) the magnitude of the i--potential in the t\vo eok. ( h ) mutual adsorption of oppoeitely charged particles, (c) the presence of precipitating ions as impurities in the sol, and ( d ) the interaction hetn-een staliilizing ions in the sols. It appears, however, that there is no definite information in the literature regarding the chemical composition of the mut>ualcoagulum. Thus the precipitating colloids may lie side by side or definite chemical compounds may be formed. These alternative points of vien. have important hearings on the formation of clay complexes. The alumino-silicates of rocks are broken up by hydrolysis mostly into oxides of aluminum, silica, and other oxides which, when first formed, are present in the colloidal state. The colloidal sesquiosides are positively charged, ivhilst colloidal silica is negatively charged; mutual coagulat,ion takes place between

.

454

S. P. RAYCHAUDHURI AKD KHONDKAR AMIR HASSN

these oppositely charged colloids, leading to the forniation of clay minerals. According to this picture of the forniation of clay minerals, the clay complex ic; a composite body, the ultimate constituents of TI hich are alumino-silicate minerals, silica, and osides of alumiiiuni and iron lying side by side. X a t t w n ( 7 ) , hoivever, thinks that the clay minerals n hich are ioriiied by mutual coagulation are compounds of alumino-silicates of indefinite composition and are foriiixl bv the interaction betn een the oppositely charged alumina acd silicic acid sols. The evidence of x-ray diagianis shon in% definite cij-stallinc patterns proves that Uattson’s theory. as such, cannot he true. It non- held that part of the clay complex consists of crystalline materials and payt of silica and o\idez 01 aluminum and iron. It n as accordingly con4dered interesting to determine the percentages of free silica and free oxides of aluminum and iron in the precipitates formed by mixing negatively charged colloidal silica \i ith positively charged colloidal osides of aluminum and iroa Triiog tf 01. (15) have determined esperinientally the total amounts of free silica and oi free alumina and iron oxide in the clay conTpleves (cf. also Droidoff and Truog (4)). It TT deqirable that this methotl should be applied to the determination of the percentages of free constituents in the coagulum formed hy mivinq oppositely charged colloidal silica and alumina and iron o.;itle- The niethotl ha. & ~ i o u s limitations, since it has 1 m n shonn by 7’ruo: et 01. iloc. cit.) themselves that from nontronite, an iron silicate mineral, iron n as estensil ely released (12 GO per cent Fe203)by this method; in other nordq, the method doe> not prope:ly distinguish betiyeen free and combined iron oxides. I n qpite oi these limitation< it n as felt that the method should give an approximate measurc of the content. of free silica and free s e s q u i o d e s in the precipitates. Generalizations d r a w i froni such data should therefore be recognized to be approximately applicable. Raychaudhuri and Qudrat Gliani (12) have 4ionn that the uptilre of base is highest n i t h alumino-silicate gel having EL SiO2:-lI2O3 ratio of 8.0. -1150.Raychaudhuri and Hussain Miah (11) have shown that freshly prepared aluniinosilicate gels possess much less buffer capacity than aged ones, and that the buffer capacity of freshIy prepared materials passes through a maximum value with increasing Si02:.41203ratios, whilst with aged ones the buffer capacity continuously increases as the Si02:81203 ratios of the precipitates increase, attaining a masimuni T alue n ith pure silica gel. The maximum value of buffer capacity a t a certain SiOo:Xl2O3ratio of the ireshly prepared gels is in agreement nitli the findings of Mattson (6, 7) and Wiegner (19). Chatterjee and Sen ( 3 ) , worhing n i t h synthetic mixtures of colloidal solutions of dicic acid and aluminum hydroxide. have given evidence of a don- interaction betv:een colloidal silicic acid and aluminum hydroxide. Raychaudhuri and D a t t a (10) have determined the propertie> ot aluminoQilicates formed undei difierent contiition. of mutual coagulation. These authors have mixed silicic acid and aluniinum hydroxide sols in three niolar ratios (SiO2:-2I2O3= 2 , 3 , and 4) in the folloning ways, and have studied the physicochemical properties of the precipitates : (1) silicic acid sol u as a d e d d o ~ l yat the rate oi about 120 drops per minute to an aluminum hydroxide

.IL~MIiTO-SILIC.ITES AND IROS-SILIC-ITES

455

so1 in a beaker n i t h continuous stirring; (2) aluminum hydroside sol was added slo~vly,a t a rate of about 120 drops per n inute, to a silicic acid sol in a beaker, with continuous stirring; (3) silicic acid sol and aluminum hydrouide sols rvere taken in tn-o bottles and n-ere allowed t o come in contact ~ i i t heach other drop b y drop. It mas found that on heating in steam autoclaves, the precipitated alurrino-silicates tent1 to acquire more and more the properties of clay minerals. It n as therefore felt desirable t o investigate in greater detail the physicochemical properties of the mutual coagulum formed under different conditions, especially the percentages of free silica and f i ee scsquiouide components (as determined by the method of Truog et al.) .i\-hichmaybe present in the precipitates. It as also felt desirxhle to determine the distribution of sizes of particles in the precipitateq The electrobsmotic charges end the SiOz:hl2O3ratios have been determined. S e s t t o alumina, iron oxide is the most important constituent of the clay fraction; hence it IT as also felt decirable to obtain precipitates by mising oppositely charged colloidal solutions of silicic acid and ferric hydroxide and to determine the important physicochen3cal properties of these precipitates. EXPERIMESTAL

Prcparatzoiz of sols u,nd precipitates

Silicic acid sol: Silicic acid sol n-as prepared by adding a 10 per cent solution of sodium silicate (Merck) t o an excess of dilute hydrochloric acid, and n-as dialyzed in 8 parclinient 1:ag in running distilled w t e r for 3 days. a41i!viinzm Izydroricic sol: -hi-,monium hydroxide as added drop by drop t o an 8 per cent solution of aluminurn chloride. The precipitate was filtered through a Biichner funnel and was n-ell n-adied n-ith hot n-xter. This precipitate as then transferred to a flask containing miter, the actual proportion being 1 liter of n-ater for every 3 g. of &O3. The whole v a s then heated and kept hydrochloric acid was added i r o n a buret'. After each boiling. and 0.05 addition. water was added t o replace that boiled off. -In opalescent liquid t h a t could be filtered unchanged was obtained. The colloidal solution of aluminum hydroxide, thus prepared, i ~ a then s subjected t o dialysis in a parchment bag for several days, till almost all the chloride was removed. Ferric hyrlroxide sol: X 10 per cent ferric chloride solution was prepared. Of this 40 cc. \\-as added to 2 liters of boiling ~vatei,,whereupon colloidal iron hydroxide n-as formed. The sol v a s then dialyzed in parchment bags. The dialysis was continued for wveral days in riiiinicg dis!illed water, till almost all the chloiide ivas removed. 9 I i i ? ~ ' ~ ! ~ - s i b ' c prccipiintcs: ate The silicic acid and rtluniinuni hyd roside sols were mixed (in proportions wch that the mixture would contain silica and aluniina in the ratios 2 , 3 , and 4) in diffewnt ~ay.:,siich m : (i) ,Uuminum hydroxide sol \\-as added to silicic acid sol a t t h rate of GO drops per minute. (ii) Silicic acid sol :vas added to alurninuni hydroxide sol at the rate of GO drops per minute. (iii) The sols \T-ere mixed drop iiy drop with each other, and the rate of addition 01 drops n-as from 100 ti? 120 drops per minute. S i n e precipi-

tates having Si0?:-Al2O3ratiop of 2 , 3 , znd 4 \\-ere prepared in these three different ways. Iron-szlicate prccipztates: The silicic acid and terric hydroxide sols were mixed in the proportion SiOz:Fe20a= 2 and in three different ways, as in the case ot the alumino-silicates The precipitates appeared only after dialysis for 12 to 24 hr. Purification of the prccipztatts. Both the alumino-silicate and the iron-silicate precipitates formed were first n ashed by ordinary dialysis in parchment bags and subsequently by electrodialysis in a three-compsrtment apparatuq. until there was no change in the conductivity oi the wash water. Determinataon of total szlzca, a l u m i n a , ancl zron oxide: The procedure followed was essentially that given in reference 1. Determinataon of the electrical charge b y electroosmoszs: The electroosmotic experiments with the precipitates were carried out by the modified method ot Briggs, Bennett, and Pierson ( 2 ) , as recommended by Mukherjee (8). Determanatzon of J’we a l u m i n a , free silica, and f r e e i r o n oxides: The percentages of free alumina, iron oxides, and silica were determined by following the method of Truog et al. (15). Determznation oJ’ saticratzon capacity: The saturation capacity was determined at p H 7.0, b y the barium acetate and ammonium chloride method of Parker (9). Determznatzon of bu$el. cumes: The buffer curves of the precipitates were obtained by the procedure adopted by Schofield (14). RESCLTS

A . Physzcochcrnical propcI.tzes o j alicmzno-silzcates

In the iollm ing tables, the symbols AI, A*, ancl A, denote alumino-silicate precipitates, silicic acid sol being added from buret to alumina sol in the beaker: B1,Bz, and 13, stand for precipitates obtained by adcling alumina sol drop by drop to silicic acid sol; C,, C2, and C3 \\-ere obtained by mixing silicic acid and alumina sols in drops. Table 1 shows the Si02:;1-1203mixing ratios and the percentages of moisture contents of the various precipitates. Table 2 gives the data for the SiOz:Xl~Oacomposition ratios of the different alumino-silicate precipitates, together n-ith the electroosmotic charges. Table 3 shows the percentages of free alumina and free silica of the aluminosilicate precipitates. R. Physacocheinzcal properties of won-silzcate precipitates Tables 4 to 6 give the data on the physicochemical properties of the iron-silicates. The mixing ratio Si02:Fe20a of the sols vas 2.0 in each case. The folloning notations werc used: (2) D1 stands for the precipitate obtained by adding silicic acid so! dropn-ise LO ferric hydroxide sol; (zz) E1 stands for the piecipitate obtained by adding ferric hydroiide sol dropwise to silicic acid sol;

SLUMISO-SILIC.iTES

457

A K D IRON-SILIC-LTES

and (iii) Fl stands for the precipitate obtained by mixing silicic acid and iron hydroxide sols drop by drop.

...........................

.1?. . . . . . . . . . . . . . . . . . . . . . . . . . . Bz . . . . . . . . . . . . . . . . . . . . . . . . .

c*. . . . . . . . . . . . . . . . . . . . . .

A3 . . . . . . . . . . . . . . . . . . . . . . . . . . B, . . . . . . . . . . . . . . . . . . . . . . . . . c 3

1

3.0 3.0 3.0 4.0 4.0 4.0

..........................

94 91 92 91 91 90

I

TABLE 2

1

PRECIPITATE NO.

I

...........................

1.6

Bi . . . . . . . ..,. c1. . . . . . . . . . . . . . . . . . . . . . . . . . .

1.0

...........................

1,s 2.6 2.5 3.5 3.5 2.1

1. .

?. -

.........................

A3, . . . . . . . . . . . . . . . . . . Bs . . . . . . . . . . . . . . . . . . . . . . . . . . .

cs. . . . . . . . . . . . . . . . . . . . . . . . . . .

cm

I

.

-2.2 -0.7 -2.4 -2.3 -3.2 -3.4 -3.6 -3.2 -3.7 -5.9 f2.5

I I

1.S

B?

ELECTROOSMOTIC YOVEMEh-P OF I B E BUBBLE P E R 5 MIN.

I

I

Silicic acid gel .Ilumina g e l . . . . . . . . . . . . . . . . .

TABLE 3 P B E C P I T A T E NO.

F R E E Ai203

-

FREE

-1

p e r cant

per cent

A1 . . . . . . . . . . . . . . . . . . . .

e,.. . . . . . . . . . . . . . . I c, . . . . . . . . . . . . . . . . . . . . , d2. . . . . . . . . . . . . . . . . . . .

Bz . . . . . . . . . . . . . . . . . . . . C? . . . . . . . . . . . . . . . . . . . . -13... . . . . . . . . . . . . . . I. B,. . . . . . . . . . . . . . . . . .i Ca. . . . . . . . . . . . . . . . I ~

10.7 8.3 14.5 s.9 6.0 4.0 9.9 4.0 4.6

slog

I

I

I I

I

I

23 13 19 21 27 33 37 43 44

F R E E A1203

I I

I I I

I

+

FREE

SI02

per cent

33.7 21.3 33.5 29.9 33.0 37.0 46.9 47.0 48.6

Table -1 shows the percentages of hygroscopic moisture, the chemical compositions (Si02:Fe203),and the electroosmotic charges of the precipitates.

458

S. 1'. IL.?YCH.\UEHUXI

.\SD KHOXDIZAE AMIR H.IS.19

Table 5 sE,on s the pelcentape< of free S O L and free FeLOsin the iron-silicates. TaLle G gives the data on the uptake r3f haw in milliequivalents per 100 g . of oven-dry rrnteiipl at ciiffic'ieot pH d u e - . The coiresponding data Trith SiOz and Fez03gels are also inclu2,ccl -___

TABLE 4

___

PRECIPITATE NO.

'

HYGROSCOPIC UOISTURE

-__

COUPOSITIOx R i T I O

(SiOz:Fe203)

~~

E L E C ~ R O G S X O T I CY O ~ M E N T OF T H E B U B B L E PER 5 MIX.

~

per cenl

D1.. ................... El.. . . . . . . . . . . . . . . . I F,. . . . . . . . . . . . . . . . ., I

i

cm.

,

84.7 83.9 83.1

Silicic acid g e l , . . . . . . . Fe?Os g e l . . . . . . . . . . . . .

I

1.57 1.86 1.81

-0.2 -0.9 -0.3 -5.2 +2.6

I ~

!

I

I

TABLE 5 PRECIPITATE NO.

i

FREE

Di.. . . . . . . . . . . . . . . . . . ~

E, . . . . . . . . . . . . . . . . . . .

Fi.. . . . . . . . . . . . . . . . .. I

1

Si02

FREE

1

Fez08

FREE

Si02 f

FREE

per cent

per cenf

p e r cent

34.05 36.00 36.20

66.04 64.00 63.81

100.09 100.00 100.01

Fer02

TABLE 6 I

UPTAKE OF BASE IN MILLIEQUI\'ALENTS P E R 100 G. OF OVEN-DRY MATERIAL

~

-

PRECIPITATE S O .

pH

= 1.3

____

D l .. . ..................... El.. ..................... F,.. . . . . . . . . . . . . . . . . . . . . . . . .

I -48.0

i

-39.6 -47.5

Si02 gel. . . . . . . . . . . . . . . . . . . . . . I f 2 . 0 Fe20s gel . . . . . . . . . . . . . . . . 1. -96.7

' '

. ~

pH

= 2.9

1 pH

~~

-25.6 -28.5 -25.9 +2.0

-100.9

pH

= 4.6

I-,-

-10.6 +40.8 -10.8 ' +39.3 -15.0 f38.8 +6.9 f12.7 -30.8 +2T.1 ~

, ~

~

= 7.1

. I .

1 I .

I ~

1

pH = 9.5

1 pH = 12.5 -1

+I50 f160 +1iO

+1Oi +86

I

1 1 ~

~

+422 f4i3 +5ll +149

+160

A . ll"orlLon alzinizrio-szlrcafes Table 1 shons that t h r xoisture contenti of the precipitates are xery high, approximately (30 per ccnt. Thls lsrqe amount of moisture qhould not h a r e nfliected the results, since t h e tinta hai e lieen e\pies.e 1 on an oven-dry basis. Table 2 shons that the compuiition ratios oi the piecipitate+ are lezc than the rrixing ratios Similar ieqult.: ha\ P lieen obtained by Raychaudhuri and Qudrat G h n i (12). Talile 2 a!-o qhoxv that 11 hen silicic noid -01 from the buret is s(1c:cd t o alulninm-i; h;r-c?io~ic!csc,l in the beaker, the SiO?:-Il2Odratios are 1.6, 1 8 . and 3 5 , t h e nii\inL r d m - liein; 2 . 3, an:! 4, re-pectively It is thereIore noticeaide that thc highest amount of d i c a i b retained by the precivtates nhen the solq are nli-.ed in the ratio Yi02:A11203 = 4.0. The same fact is noticeable with precipitates U1, 13?. and B3, in that the composition ratio

459

AiLUMIXO-SILICAiTESA S D IROX-SILIC.LTES

(Si02:A1203)is highest ( 3 . 5 ) when the sol3 are miueJ in the ratio SiO?:A1303= 4.0. 145th precipitates C1,C?, and C3, hoir ever, the precipitate haring the miuing ratio Si02:-11203= 3.0 has the highest conlpoqition iatio. Table 2 also shon s that the electroosniotic charges of all the al~aiiiiio-hilicdtesare neAative, except that of Xl20, gel 11 hich is positively chmgeci I t i q iouncl that the higher the composition ratio (SiO?:.ll103). the higher i h the elnctrcJo*motic charge This corroborates the findincs of Mattson (G), i:ho 11nq shonn that the baseexchange properties of alun ino-silicate pitxipita tee, increasr ith the increase in the ratio of bilica to alumina. The data in talde 2 i h o r i that the eleclroosniotic charge depends on the mode of formation of the precipitates. For the same mixing ratio, the precipitate formed by niiuing the sols dropwise possesses the highest electroosmotic charge. Table 3 shons that the higher the mixing ratio {!

UPT:lE;E OF B I S E I S AI, EQ. PER 100 C . OVES-DRT _\IhTERIAL FIG.1. Buffer cui-vcs

(SiOn:A1503)of the precipitates, the higher is the percentage of free silica. On the whole, it appears that in the mutual coagulation of oppositely charged aluminuni hydroxide and silicic acid sols, the greater portion of silica and alumina remains in the combined state, as is evidencd 11)- the stmi of the percentages of free alurrina and free silica (cide ttzhle 3).l This may he due to the strong chemical affinity between silica and nluminn.

H . Tl'ork on iron-silicutes Table 3 shows that the moisture coiitents of alJ the iron-silicate precipitates is nearly 83 to 83 per cent. Table 1 also shows that the composition ratios 1 In view of the limitations of tile i:iethutl of Truog e t (11. for the determination of free silica and free sesquiosides. a.3 pointed out above, this fact of itself does not preclude compound formation.

460

S. P. RAYCHAUDHURI .iND XHOXDKAR AMIR HASAN

(Si02:Fe203) of all the precipitates are less than the mixing ratios (2.0). The electroosmotic charge is always negative and increases as the composition ratios (Si02:Fe20,) increase. Table 3 shows the percentages of free silica and free iron oxide components in the iron-silicate precipitates. It is interesting to note that the sum of the percentages of free silica and free iron oxide components add u p to 100 nith all three precipitates.' It appears likely, therefore, that in the coagulum, D1, El, and F1, silicic acid and iron hydroxide have remained generally side by side. The fact that mineral formation has not taken place to a considerable extent is also evidenced by the lon- base-combining capacity of the coagulum (table 6). Table 6 gives the data on the uptake of base, at different p H values. The corresponding buffer curves are shon-n in figure 1. It ]Till be seen from the curves that up t o p H 7.0 the buffer curves are steep, indicating that the buffer capacities of these material. are w r y lo\\- up t o this pH. -lfter p H 7.0, however, the buffer curves are flatter. The buffer curves of the freshlv precipitated ferric oxide gel and of the silicic acid gel are steeper throughout than those of the iron-silicate precipitates. indicating that they poswss less Iiuffer capacitie.. throughout the p H range. These ohsen ations *tiagest, therefore, that combination between silicic acid and irrrir oxide sols takes place more effectix-elv above pH 7.0, n-liilst helou- p1-I 7.0 the precipitates contain iron oxide and silica more in the free state. That these constituents of the precipitates are generally in the uncombined state, under ordinary conditions of precipitation, has been shonn in connection n-ith the studies on the free iron oxide and free silica contents of the precipitates (table 3 ) .

dlumino-silicate gels have heen prepared by mixing alumina and silicic acid sols in the ratios Si01:A1?03 = 2, 3, and 4 in three different \my$. Iron-silicate gels have also been prepared by mixing iron hydroxide and silicic acid sols in the ratio Si02:Fe20s= 2 in the same three wags. The precipitates h a w been purified hy electrodialysis. and the follou ing propertit.2 of the purified precipitates and of electrodialyzed silica, dumina, and iron oxide gels liaw heen studied : ( a ) chemical coniposition (SOz:-41L03 iatio) ; ( b ) electrooqmotic charge; (c) percentages of free silica, free alumina. and free iron oxides; i d ) -atination capacity; and ( e ) buffer curve'.. The alumino-silicate and iron-qilicate precipitates are negatively charged. and the negative charger bear fair correlation irith the composition ratios (Si02:111203 or Si02 :FenOs). I n the alurnino-silicates the greater part of the silica and alumina remains in the combined state, and the extent of combination depends on the pH. In the iron-silicate precipitates below p H 7.0, silicic acid and iron hydroxide remain generally in the free state.

r.

\ - . I L \ - I ~.I. , c;. J.ASSSE;S~, .lsl)11. 3r.utri

Polytechnic Inslitute of B ~ o o k l y i i ,Hrookl!lri. ,Yew 1-01.k Recrii3ed 3Iny 15, 1945

Experiments on the influence of tlirinylbenzene on the polymerization of styrene \\ere carried out seI-eral years ago liy Stautlinger ct 01. (4, 5 ) :tnd siniilar studies \\-ere recently puhlished by C'h. JValling ( 7 ) . The principal result if: that copolymers containing only a fen- per cent of tlie cross-linking agent nrc illsoluble in Iwnzene, toluene, ethyl methyl ketone. etc., lint do sn-ell in such liquids. The purpose of this article is to investigate the moleculur-sizr tlisti4iution of copolymers of styrene and &vinyl deri\.atii-rs.. Divinyllienzene is difficult to olitain and prespiw in the purc 1noiio111c1'd a t e 1 Wliytc. ~Ia~infac.tulillgi~iiig ('oiiipaiiy I~i~lristriiil E'cllo\\- :it tlie I'olytcc*liiiic Iiistituto of 13r~J(JkI~Il, 1 ~ 1 . I ) I J k l ! - l I , IC\\ ~ -1lI'k. ? This palwr is :i part of a tlic iihniittecl Iiy .~\. G.. J : i i i ~ q r i i t o the f;rc.ulillgilry r ~ ft l i c x l'iilytrrhiii(>Institiit(, of 13rooklyii i i i partial fulfllinent of tlle d r ~ g r e rof A I a s t r v of Science. Jiiiic. 1045. I t s iiiaiii content \\->is prcsrntril at tlir 108th IIccxting of t h r .hiirrii*:iri ('Iicaiiiiczrl Society, S e i \ - Yot.1; ( ' i r y %Septeiiilwr, 1944. a r i i l :it t l i i x iincc>tiiigr i f tlic, l