March, 1052
INTERATOMIC
DISTANCES I N O X Y G E N ACIDSAND RELATED SUBSTANCES
36 I
INTERATOMIC DISTANCES AND BOND CHARACTER IN THE OXYGEN ACIDS AND RELATED SUBSTANCES BY LINUSPAULING Contribution No. 1647 from the Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California Received January 8, 1069
In a complex such as the sulfate ion the sulfur-oxygen bond assumes multiple-bond character through resonance involving one sigma bond and two pi bonds. An empirical equation has been formulated connecting interatomic distances and bond number for resonance of this sort. On application of this equation it is found that in many complexes the amounts of multiplebond character are such as to cause all atoms to conform rather closely to the principle of electroneutrality.
A number of years ago there was developed in our laboratories’ an interpretation of observed interatomic distances in the oxygen acids and related substances in terms of the partial doublebond character of the bonds. For example, the Si-0 distance 1.60 A. observed in the silicate group in silica and many silicate crystals, which is 0.23 8. less than the sum of the single-bond radii, was interpreted as indicating that the silicon atom forms with each of the four adjacent oxygen atoms a bond that is essentially a double bond, making use to some extent of the 3d orbitals of silicon, as well as the 3s and 3 p orbitals. This interpretation is not completely satisfactory, in that bonds of this sort, even with a reasonable amount of ionic character for the u bond (about 4001,),would correspond to a negative charge on the’ silicon atom, which however would be expected to have a positive charge. Schomaker and Stevenson2 have introduced a revised set of single-bond covalent radii for the first-row elements, and an equation by means of which the effect of partial ionic character of a bond on the interatomic distance may be computed; the use of their system leads to a smaller difference between the observed interatomic distances and those calculated for single bonds with the normal amount of ionic character, as given by the difference in electronegativities of the bonded atoms. Pitzera has recently stated that he does not believe that these bonds have any multiple-bond character whatever; he suggested that the observed short distances are due entirely to the SchomakerStevenson shortening plus a bond-lengthening effect that operates in bonds between second-row atoms (such as the Si-Si bond) because of a great repulsion of inner shells. The question of the nature of the bonds has been discussed also by Wells4 and Moffitt.b A few years ago6J I proposed an electroneutrality principle-the postulate that the electron distribution in stable molecules and crystals is such that the electrical charge that is associated with each atom is close to zero, and in all cases less than *l, in electronic units. In a molecule involving single bonds we expect a transfer of charge from atom to (1) See L. Pauling. “The Nature of the Chemical Bond,” Cornell University Press, Ithaca, N. Y.,1939, Chap. 7. (2) V. Schomaker and D. P. Stevenson, J. Am. Cham. Soc., 63, 37
(1941). (3) K.9. Pitzer, ibid.. 10, 2140 (1948). (4) A. F. Wells, J . Cham. Soc., 1949, 55. (5) W. E. Moffitt, Proc. Roy. SOC. (London), M O O , 409 (1960)
(6) L. Pauling, Victor Renri Memorial Volume, Li&ge, Maieon Desser, 1948. (7) L. Pauling, J . Chsm. Soc., 1401 (1948).
atom as a result of the partial ionic character of the bonds. For the Si-0 bond, for example, the difference in electronegativity of the two atoms corresponds to a partial ionic character of the u bond amounting to roughly 5070, as found by use of the empirical function based on dipole-moment data? The partial ionic character of four Si-0 single bonds would thus confer on the silicon atom a charge of approximately +2, which is incompatible with the electroneutrality principle. A reasonable way to neutralize this large positive charge is through the formation of ?r bonds between oxygen and silicon, with use of the extra outer electron pairs of the oxygen atom. If each Si-0 bond were to have about 50% r-bond character enough negative charge would be transferred to the silicon atom to give it the resultant charge zero, and thus to cause silica and the silicates to satisfy the electroneutrality principle. I have found that the assumption that in molecules and crystals in which there are atoms with extra electron pairs the bonds have somewhat less ?r-bond character than necessary to neutralize the charges on the atoms due to the u bonds, as calculated from differences in electronegativity of the bonded atoms, leads to calculated interatomic distances, electric dipole moments, and bond angles in good general agreement with experiment. Use is made in this calculation of a new equation that is proposed for representing the shortening effect of ?r-bond character when two pairs of r electrons are involved, and also of a revised relation between the partial ionic character and the electronegativity difference. Interatomic Distances for 8-Bond Resonance In calculating the interatomic distance with use of the amount of 8-bond character we need an equation different from the original equation representing resonance between single bonds and double bonds. The original equation9
-
-
+
R = RI (RI R,) 3n’/(2n’ 1) (1) in which n’ is the amount of double-bond,character, leads with Rt - R2 given the value 0.21 A. to satisfactory agreement with the observed carbon-carbon interatomic distances for graphite and benzene in relation to those of ethane and ethylene. The curve corresponding to this equation is shown in Fig. 1. It falls below the curve R = Rt - 0.706 log n, in which n is the bond number, by about (8) Reference 1, S o . 12. (9) Refewnoe 1, Chap. 5.
362
LINUSPAULING
Vol. 56
A. for R1 - Ra,and by takin the values of
0.00
Correction of interatomic distance for ~ j T. , resonance ry alone \‘
and a3 as, (1 - anw)*, nw( 1 - : n j , and ;1n / , corresponding t o independent resonance of the rYand wl electron pairs, b the result 0.63nr 0.195nZr R=Ri(31 1 1 2% anar
+
+
oil, “2,
+
Here na is the total amount of w-bond character. The curve corresponding to this equation is also shown in Fig. 1. It is seen that it lies below the curve representing resonance between a single bond and a wU (or w s ) double bond by the amount 0.026 b. at n,,! = 0.5, and by 0.045 A. a t the point for a pure double bond, ns = 1.0, these differences re resenting the effect of. the extra resonance stabilization wfen two w electron pairs are involved. Values corresponding to the curve are given in Table I.
-0.21 at n=l
-0.2 I’
ThBLE
1
BONDSHORTENING BY T-BONDRESONANCE lZRa
-0.34
3
2
I
Fig. 1.-Curves representing the dependence of interatomic distance on amount of *-bond character for resonance with a single w electron pair, and with two w electron pairs. The uppermost curve represents the function R = RI - 0.706 log n, in which n is the bond number; it corresponds to the dependence of interatomic distance on bond number without correction for resonance shortening. The numbers 1, 2, 3 as abscissas are bond numbers, which are 1 greater than nz.
0.03 A. in the neighborhood of 50% double-bond oharacter, because of the stabilizing effect of resonance.1° I n case that two pairs of ?F electrons, corresponding to the wave functions p , and p , (with the x axis taken in the direction of the bond), are involved, a larger amount of resonance energy would be expected for the same amount of n character than in case that only one pair of ?r electrons is involved. It is found by solution of the appropriate secular equation that the resonance energy for 50% n-bond character when equally divided between ?ry and 1~~ is about twice as great as the resonance energy for 50% ?r-bond character of a single type; we would accordingly predict thgt the interatomic distance would be about 0.03 A. less for the former case than for the latter case. I n the following discussion use is made of an equation that has been formulated by the method given earlier in a discussion of the equation for resonance between a single bond and a double bond11 and of the interatomic distances in the carbon monoxide molecule and carbon dioxide molecule .l2 The potential function for the bond is assumed to have the form 1 1 V ( R ) = 2 aiki(R - RI)* 2 c~zkz(R- R2)Z 51 a&(R Rs)’ (2)
+
+ -
in which al, 012, 013 represent the extents to which the singlebond structure, the double-bond structure, involving either the wU or the ?r, electron pair, and the triple-bond structure, involving both of these electron pairs, contribute to the state of the molecule, the k’s are their force constants, and the R’s their interatomic distances. For single, double, and triple bonds the k’s may be taken in the ratio 1:3:6. ?e e uilibrium value of R is found by equating the derivative d%/dR t o zero and solving for R, which leads, with introduction of the empirical values 0.21 A. for R1 - RZand 0.34
-
(10)L. Pauling, J . Ana. Chem. SOC.,69, 542 (1947). (11) Reference 1, Rect. 22. (12) Reference 1, Sect. 25.
- AR
- AR
nr
0.0 0.000 0.8 0.227 .1 .054 0.9 .241 .2 .095 1 .o .255 .3 .127 1.2 ,276 .4 .154 1.4 .294 .5 .176 1.6 ,310 .6 .195 1.8 ,325 .7 212 2.0 .340 a Here nn is the amount of w character (the sum of wal and R., which are equal), and AR is the bond shortening, 111 b.
-
For calculating the interatomic distance for a single bond,
El, involving an atom of nitrogen, oxygen, or fluorine (or
two such atoms), we use the equation of Schomaker and Stevenson; namely R1 = RA RB - o.og\xA - ZBI (4) The radii 0.74 A. for nitrogen, 0.74 A. for oxygen, and 0.72 A. for fluorine are to be used with this equation. The question may be raised ,as t o the extent to which the Schomaker-St6venson correction includes recognition of the double-bond effect. Equation 4 applies to trimethylamine and dimethyl ether, in which there is no double-bond formation expected because the more electropositive atom in the C-N and C-0 bonds, the carbon atom, is given a negative charge by the partial ionic character of its bonds to hydrogen that is larger in magnitude than the positive charge conferred on i t by the C-N or C-0 bond, and hence does not have a free ?r orbital to accept an elect.ron from the nitrogen or oxygen atom. We conclude that separate consideration must be given to the effect of the formation of ?r bonds by atoms of second-row elements with use of 3d orbitals. The correction for this effect is made by application of Equation 1 or Equation 3.
+
The Partial Ionic Character of
Bonds A number of years ago an equation was proposedla for calculating the partial ionic character of a u bond between two atoms A and B from their electronegativity difference X A - X B partial ionic character = 1 - e - o ( z A - z B ) P (5) This equation, with a = 0.25, was based on the observed electric dipole moments of HC1, HBr, and HI. Since then the value of the dipole moment of HF has been determined; it is 1.98 D, which corresponds to 47% ionic character, whereas Equation 5 with a = 0.25 gives 59%. It seems justified to formulate an empirical function, based on the values 5, 11, 17, and 47% for the hydrogen halides HI, HBr, HC1, and HF, as calculated from their (13) Reference 1, Chap. 2.
u
March, 1952
INTERATOMIC DISTANCES IN OXYGENACIDS A N D RELATED SUBSTANCES
electric dipole moments and internuclear distances. The values given in Table I1 were obtained by making uniform slight adjustments, by not over h0.03, in the curve of Equation 5 with a = 0.18, so as t o conform to the values for the hydrogen halides. Several authors have pointed out that other structural features (unshared electron pairs, asymmetry of electron distribution for pure covalent bond between unlike atoms) contribute to the dipole moment, but lack of knowledge of the magnitude of their contributions prevents us from making corrections to the values given in Table 11. TABLEI1 PARTIAL IONlC CHARACTER OF BONDSIN RELATIONTO ELECTRONEGATIV~TY DIFFERENCE Axa
la
Ax
I
Ax
I
0.0 .1 .2 .3 .4 .5 .6
0 0.9 17 1.8 44 1.0 20 1.9 47 1 2 1.1 23 2.0 51 26 2.2 58 3 1.2 29 2.4 64 5 1.3 32 2.6 70 7 1.4 1.5 35 2.8 75 9 38 3.0 80 .7 11 1.6 .s 14 1.7 41 3.2 83 a I is the per cent. partial ionic character, and Ax is t,he electronegativity difference ZA - XB.
The Extent of n-Bond Formation In a molecule such as SiF4,in which the central atom forms several bonds with a large amount of ionic character (58y0), it is to be expected that a compensatory mechanism, the formation of ?r bonds, would operate to reduce the charge on this atom; but it also seems likely that this mech-' anism would not reduce the charge to zero, but rather would leave it at an intermediate value. An experimental determination of the charge distribution for this molecule is not easily made. The consideration of values of electric dipole moments and interatomic distances for many substances has indicated that the extent to which ?r bonds are formed is dependent on the row-numbers of the atoms involved and on the number of bonds formed by the central atom. Let us consider a molecule MX,, in which each atom X is attached to the central atom M by a u bond and n,n bonds. Let the electronegativity difference of M and X be such as to transfer the charge e from each X to M. The charge distribution is then M,(a-na) X-(e-nr). We assume that the energy E of the molecule contains a quadratic term in the charge 1 of each atom: - k ( e - YL,)~for each atom X and 2 1 - kn2(E - n1,)2for M. This term represents the 2 electroneutrality principle : it operates t o minimize the charges on the atoms. The value of k depends, of course, on the nature of the atom; for simplicity, we shall neglect this dependence. We also assume 1 that E contains a similar term - k'na2 for each 2 bond, representing the resistance of the ?r electron pairs of X to being drawn into ?r bonds. The expression for E is thus
363
The energy has a minimum value relative to the structural parameters. Hence we place hE/&nr =
- k(n2 + n)(E - n r ) + k'nnr
=0
(7)
which leads to
_nr E
- k'/k
n + l
+n + I
(8)
This equation gives the calculated extent of neutralization of the charge due to the u bonds through rr-bond formation, as a function of the number of X atoms in the molecule, n, and the ratio k'lk of the two force constants, the electroneutrality constant k and the 7-electron constant k'. With k'/k = 1.5, for example, the values 0.77 for n = 4 and 0.57 for n = 1are obtained. Dipole-moment and interatomic-distance data indicate that Equation 8 can be used generally for compounds MX, by giving k'/k the values 0.0555 X 3 ( a + b ) , in which a and b are the rownumbers of atoms M and X, respectively: 1 for 0 and F, 2 for Si, P, S, C1, and so on. Table I11 contains values of n/t, calculated in this way. TABLEI11 OF NEUTRALIZATION OF BONDMOMENT BY PERCENTAGE T-BONDFORMATION FOR MOLECULES MX, a + b =
3
4
5
6
7
n = l
57 67 73 77
31 40 47 53
13 18 23 27
5 7 9 11
2 2 3 4
2 3 4
Sulfur Dioxide and Other Oxides For sulfur dioxide, with resonating Lewis structure
1 a charge - - is placed on each oxygen atom and 2 +l on the sulfur'atom. I n addition, the electronegativity difference 1.0 leads to 2Oy0 ionic character for each u bond. The charge distribution without rr-bond formation would be S +1.4002-0.70. From Table I11 (a b = 3, n = 2) we obtain 67% as the amount of neutralization of charge through ?r-bond formation, which gives yia = 0.47 and the charge distribution S+o.4602-o.23. This charge distribution, with the known structural parameter^'^ S-0 = 1.433 A. and L 0-5-0 = 119.5",leads to 1.61 D as the calculated value of the dipole moment. This value agrees exactly with the experimental value. For S-0 the single-bond distance is 1.69 A., and the ?r-bond correction (for n, = 0.97, the sum of the ?r-bond character given by the Lewis structure, 0.50, and tha$ induced by the charge distribution, 0.47) is Ob25A. Hence the predicted S-0 distance is 1.44 A., in satisfactory agreement with the experimental value 1.433 8.
+
(14) B. P. Dailey, 6. Golden, and 871 (1947).
E. B. Wilson, Jr., Phvs. Rea., 73,
LINUSPAULING
3G4
Vol. 5G
For sulfur trioxide, with resonating Lewis structure
charge placed on the central atom, per bond, by the single-bond formula; that is, it is equal to the oxid* tion number of the central atom diminished by 4 and divided by 4. The sum of these two quantities, given in the following row, is the amount of charge placed on the central atom by one bond of the single-bond structure. This number multiplied and 0.20 ionic character of the u bonds, the charge by 0.77, from Table 111,in the next row, represents distribution before n-bond neutralization is S+2.s0 the, amount of n-bond character. The following Q3-0.87. Table 111gives 73% neutralization, which row gives the change in interatomic distance correleads to n, = 0.97 (including 0.33 for the Lewis sponding to this amount of ?r-bond character, as double bond). The predicted S-0 distance is calculated with Equation 3, and the row below it hence 1.44 8., which agrees fatisfactorily with the predicted interatomic distance, according to our the observed value, 1.43 f 0.02 A. assumptions. Finally, in the last row there are For dimethyl sulfone, (CHa)2S02,the predicted given values of the observed interatomic distances amount of r-bond character is 0.67 X 1.10 = 0.80, in crystals of salts of these acids. It is seen that which leads to S-O = 1.46 A., slightly lgrger than the agreement with experiment is good. The charges on the oxygen atoms due to partial the experimental value, 1.43 f 0.02 A. In dimethyl sulfoxide, (CH3)2S0,the predicted value of nr ionic character of the bonds to the metal atoms in is 0.57 Xo1.20 = 0.68, and the predicted value of the silicates and other salts should be taken into S-0, 1.48A., agrees with the observed value, 1.47 A. consideration in making this calculation. These An interesting example is provided by the trimer charges lead to further decreases in the Si-0, P-0, of sulfur trioxide. In this molecule the three sulfur S-0, and C1-0 distances, of amount depending atoms are joined together into a six-membered ring on the nature of the metal and the structure of the by bridging oxygen atoms, and each sulfur atom crystals. Because of uncertainties in the system also has attached to it two unshared oxygen atoms, of equations used in this paper, this refinement in in addition to the two bridging oxygen atoms, the the calculation has not been carried out. It is interesting that the amount of n-bond charfour oxygen atoms being arranged tetrahedral8 about it. The sulfur-oxygen distance is0 1.60 A. acter in these oxygen complexes varies from about for the bridging oxygen atoms, and 1.40 A. for the l/s to about 2/a, and that for the sulfate ion it correothers. The Lewis structure, with 20% ionic char- sponds closely to the resonance formula acter of u bonds, gives the charge distribution S+2.8003-0~400~-1.20. We make use of the value for .. =0: , etc. --:On = 4 of Table 111, 77%, which leads to 0.15 and .. 0.92 for %, and hence to 1.61 8. and 1.44 A. for 0: the two kinds of S-0 bonds, in reasonably good agreement with experiment. in which the central atom is shown with zero formal Molecules of the oxides of phosphorus P~OS charge. and P4OI0 also contain bridging oxygen atoms. TABLE IV The predicted amounts of n-bond character, 0.73 INTERATOMIC DISTANCES IN SALTS OF OXYQEN ACIDS X 0.32 = 0.23 and 0.77 X 0.32 = 0.25, respecPerSalt Silicate Phosphate Sulfate chlorate tively, lead with use of the single-bond distance 1.71 A. and Equation 1 to theopredicted value 1.61 Electronegativity difference 1.7 1.4 1.0 0.5 A. for P-0 in P406 and 1.60 4. in P4Ol0. The ob- Sum of radii 1.91 1.84 1.78 1.73 served values, 1.65 f 0.02 A. in P40a and 1.62 -0.091~~ - ZBI -0.15 -0.13 -0.09 -0.05 0.02 A.in P4Ol0,are slightly larger. For the oxygen atoms in P4OI0that are bonded t o Single-bond distance 1.76. 1.71 1.69 1.68 only one phosphorus atom the predicted amount of n-bond character, 1.02, leads t,o 1.45 8. for the Ionic character of u bond 0.41 0.32 0.20 0.07 P=O distance. This is in only rough agreement Formal charge per with the observed distance, 1.39 i 0.02 A.
[ ;;I. 1
i
+
.
Salts of Oxygen Acids
The discussion of interatomic distances in salts of oxygen acids of the second-row elements is presented in Table IV. In the first row of this table, below the names of the salts, there are given values of the electronegativity difference X A XB, in the second row the sum of the single-bond radii, in the third row the SchomakerStevenson correction, and in the fourth row the single-bond interatomic distance. The next row contains the fractional amount of ionic character of the u bond, as given by the electronegativity difference with use of Table 11. The next row contains the amount of positive
-
bond 00 Sum .41 Amount of u-bond character .32 Correction for Tbond -0.13
.25 .57
.50 .70
-75 .82
.44
.54
.63
-0.16
-0.18
-0.20
Predicted dis1.63 1.55 1.61 1.48 tance Observed distance 1.62" 1.55' 1 . 50e 1 .4gd Average of reported values for zircon, andalusite, sillimanite, staurolite, topaz, titanite, thortveitite, muscovite, apo hyllite, hardystonite, analcite, carnegieite! sodalite, danKurite, scapolite, and cristobalite; mean deviation 0.02 A. * Average for BP04 \1.64 A.) and KHS0&(1.56 A.). For K&304and other sul ates. For Mg(C104)-6H*0.
March, 1952
BONDLENGTHCALCULATION IN CONJUGATED MOLECULES
It may be emphasized that bonds corresponding to a completed sp3 octet for the second-row atom are to be distinguished from those involving orbitals beyond the octet. It is the octet bonds-the Lewis structures-that are of primary importance in determining the bond angles and general configuration of the complex, with the additional R bonds, involving d orbitals, effective mainly in changing the interatomic distances and the charge distribution. It might be possible to formulate an empirical system of quadratic energy terms, like those in Equation 6, that would reproduce many properties of molecules in a satisfactory may. Efforts ,to this
365
end have not yet been successful; even the simple treatment of Equation 6 fails when it is applied to molecules in which atoms of two or more kinds are attached to a central atom, and a similar treatment of the charge distribution (electric dipole moment) in molecules in which polar bonds interact with one another through induction has been found to be only partially satisfactory. The practical difficulties attending the quantum-mechanical treatment of the electronic structure of molecules are so great that the main hope for future progress in the treatment of molecular structure may, well lie in the development of a quantitative empirical theory of this sort.
BOND LENGTH CALCULATION IN CONJUGATED MOLECULES BY 0. CHALVETAND R. DAUDEL University of Paris, Paris, France Received January 6,196s
Hartmann has recently introduced the notion of bond type. The bond type in a purely conjugated hydrocarbon is determined by the number of the adjacent C-C bonds. Vroelant and Daudel, using the spin states method, have shown that to a rather good approximation Penney’s bond order for such a bond depends only on the types of the adjacent C-C bonds. A given bond is designated by a notation based upon the types of adjacent bonds. It is possible to show that there is for each notation a good relation between its exact Penney’s bond order and the Pauling double bond character taking account of only the Kekule formulas. I n this manner the evaluation of the Penney bond orders reguires only the calculation of the Pauling double bond characters which are very easy to obtain. Following an idea of Pauling and work by P. and R. Daudel, A. Laforgue has established an empirical self consistent method of evaluating the bond orders and the atomic charges in a conjugated molecule. This method uses the relations between interatomic distances, bond orders and the B integrals, and the relations between charges, electronegativities and the CY integrals. This method has been applied to the evaluation of t,he interatomic distances in some molecules like Ni04. The large N-N bond length found experimentally in this molecule is accounted for.
Introduction This paper is devoted to the description of some methods useful in the calculation of interatomic distances in conjugated molecules. In the first part we are concerned with a very simple method of estimating bond lengths in purely aromatic hydrocarbons. I n the second part we describe a possible way of evaluating with a rather good accuracy the bond lengths in some more complicated molecules.
A Very Rapid Method of Estimating Bond Lengths in Purely Aromatic Hydrocarbons The simplest method of estimating the bond lengths in aromatic hydrocarbons is to determine the “double bond character” using only the Kekule formulas as Pauling suggests.’ It is now well known,2 that the calculation of the bond orders using the molecular orbital method, or the valence bond treatment lead to better results. Evidently such a process is very laborious for large and non-symmetrical molecules, such as benzanthracene, for example. Here, we describe a method as simple as Pauling’s process but giving about the same accuracy as the molecular orbital treatment. It is applicable to the estimation of bond lengths in such polyaromatic (1) Pauling, “The Nature of the Chemical Bond,” Cornell Univ. Press, Itliaca, N. Y. (2) See for example Corilsou, 1)sudel sild Robertson, Proc. Rou. SOC. ( L o n d u n ) , i n the pmns.
compounds as naphthalene, aiithracene, pyrene, coronene, ovalene, and so on. Hartmann3 has recently introduced the notion of bond type. The bond type in a purely conjugated hydrocarbon is determined by the number of the adjacent C-C bonds. As an example the a-0 bond in naphthalene is designated as bond type 2 and the central bond as type 4. . Vroelant and Daude14 using the spin method, have shown that with a rather good approximation the bond order of such a bond depends u p o n only the types of the adjacent C-C bonds. A particular bond is more fully described by means of a notation in terms of the bond types of adjacent C-C bonds. The following diagram s h o w the types of the bonds in naphthalene. As an
2c(): 2
2
3 9 0 1 2
3 3
2
example of the notation the a-/3 bond is dcsignatedl2v3the 6-p bond (2,2), and the central b o d (3,3,3,3): Now it follows from the Vroelant and Daudel approximation that the bond order of a bond is related to the above notation. As there is a relation between bond order and length we are able t o construct Table I giving for (3) IIartnisnn, 2. Nalurhrschuny, A, IPeb., 1947. (4) Vroelaut and h i i d e l , Bull. 8or. ckim. France, 16, 36, 277 (1949).
