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Determination of Ao for Axially Symmetric Molecules Part III . CH3I
JOURNAL OF MOLECULAR SPECTROSCOPY
23,302-306 (1967)
Determination of A0 for Axially Symmetric Molecules Part III . CH31t THOMAS L. BARNETT AND T. H. EDWARDS
Department of Physics, Michigan State University, East Lansing, Michigan 48823 A value of A0 = 5.134 -4- 0.003 cm-1 was obtained for methyl iodide from a least squares simultaneous analysis of ~4with band origin at 3060.057 cm-I and 2~ with perpendicular component band origin at 6101.89 cm-1 and parallel component band origin at 6052.04 cm-1. Values of other molecular parameters which proved significant in the fit are also reported. INTRODUCTION Our method of obtaining an accurate value of A0 for axially symmetric molecules, b y means of a simultaneous analysis of two suitably related bands, was outlined in Paper I of this series (1). [A0 = h/(8~r2CIoA), where I0 ~ is the principal m o m e n t of inertia of the molecule about its s y m m e t r y axis in its ground vibrational state.] I n Paper I I (2) the method was applied to determine Ac for CH3Br. I n this paper a value of A0 for CH3I is determined from a simultaneous analysis of the ~4 and 2~'4 bands. EXPERIMENTAL PROCEDURE Spectra of ~4 and 2~4 of CH~I were obtained using a high resolution v a c u u m recording spectrometer employing an f/5 L i t t r o w - P f u n d monochromator of focal length 1 meter, in both single-pass and double-pass configurations. The experimental procedure used to obtain the frequencies of the observed lines is outlined in the book by Rao, Humphreys, and R a n k (3). Frequencies for the lines of ~4 and 2~4 were obtained by calibrating t h e m with bands of simple molecules measured by R a n k et al. (4), viz., HC1 (1-0) and H C N (0, 0, 1) for ~4, and N20 (3, 0, 1) and H C N (0, 0, 2) for 2,4. The standard deviations of the calibration fits were 0.004 cm -1 for p4 and 0.006 cm -1 for 2~4. The resolution limits in the spectra were ~ 0 . 0 4 cm -1 for ~4 and ~ 0 . 0 6 cm -1 for 2~'4. Survey spectra of ~4 and 2~4 of CH3I are shown in Fig. 1. Except for the perpendicular Q-branches, the rotational fine structure is clearly resolved in both This work was supported by a grant from the National Science Foundation. 3O2
303
D E T E R M I N A T I O N OF Ao FOR CH~I PQ3
v4
RQ0
RQ3
PQ6
RQ6
3000 C~n-I
3050
j
RQ9
3100
i
3150
t
PQ3
RQ 0
2v 4 I
I
RQ 3
RQ6
RQ9
6050 cm -I i
6100 I
6150 !
6200 |
FIG. l. Absorption spectra of CH3I (a) ~4 (pressure: 6 mm Hg, path length: 6.4 m); (b) 2 ~4 (pressure: 10 mm Hg, path length: 9.6 m). bands. Note, in particular, the anomalous intensity of the RQ6(J) Q-branch ill ~4, and the split RQs(J) Q-branch in both bands. To the right of the Q-branches in the perpendicular bands one m a y observe what we believe to be the Q-branches of hot bands. ANALYSIS The Nielsen-Amat generalized frequency expression representing a v i b r a t i o n rotation absorption transition from the ground vibrational state to any upper vibrational state is given in Table I I of P a p e r I. The energy expression from
304
BARNETT
AND EDWARDS
which this expression was obtained is listed through third order and partially through fourth order in a thesis by Blass (5) and will also be given, with a few more terms in('.luded, in a forthcoming thesis by one of us (T. L. B.). When the two bands to be analyzed simultaneously show evidence of perturbations, the most productive course of action is usually to begin by analyzing the bands individually, and then to combine t h e m in a simultaneous analysis only after most of the perturbed lines have been identified and omitted. This was the course we followed in the case of ~4 and 2p4 of C H d . Table I lists the single-band frequency expression which was used to analyze v4 and 2~4 separately. I t was obtained from the Amat-Nielsen generalized frequency expression shown in Table I I of P a p e r I. The appropriate selection rules on AC4 have been represented AG = /oAK, where k = 1 for ~4 and k = - 2 for 2~4 (see Table I I I of Paper I ) . When the resulting linear dependences among various terms had been eliminated, the expression in Table I resulted. The ~,, T]44 , and 7 terms, which occur in the generalized frequency expression, are expected to be negligible and have not been shown. I t should be noted t h a t this is only one of several possible equivalent forms which the expression could take, even after the linear dependences have been removed. I t should be stressed t h a t this expression is not appropriate for simultaneous fits of v4 and 2h4 (see Table IV of Paper I) for which a number of the linear dependences are removed. A large number of lines in each band were assigned by inspection on the usual basis of missing lines in the various series, due to the requirement that J > K in TABLE
I
FREQUENCY EXPRESSION FOR SINGLE-BAND FIT OF ~4 OR 2v4 ~
aKaJK(J) -- {B0[(J + A J ) ( J + 1 q- AJ) -- J ( J Jr- 1) - (K q- AK)2 + -- DoJ[(J -~ z~J)2(J Jr- 1 -b Z~J)2 - j 2 ( j Jr- 1)2] DJK[(K + AK)2(J -F ~ J ) ( J '}- 1 t- 2~J) - K2J(J q- 1)]}
-
K s]
-
F ~o(~4)or1 as a p p r o p r i a t e
= | ~ 0 ( 2 v 4 ± ) or
+ + + + + + + + + + + 4-
--
k(,~K)2(A£~
z
-
1/~#4K)]
L,,o(2,,, II ) kA~¢4 z - ~ k ~ 4 x [ [ ( K + A K ) 2 - - K 2] I - D o K -- J/~k,4 K] [(K + a K ) 4 - K q [-a4 A + ~ k v 4 K] [(av4)(K + aK)q [Ao -
[--o~4B] [(Av4){(J -I- zXJ)(J -~- 1 + zXJ) -
(K + 2~K)2}] [~4J] [(kZ~K)(K q- A K ) ( J q- Z~J)(J + 1 + z~J)] [f14J] [(Av4)(J -q- ,,,j)2(j q_ 1 q- aJ)q [fls~] [(av4)(K + aK)2(J + a J ) ( J + 1 + a J)] [~,q [(av~)(K + aK)q [H0z] [(J + aJ)3(J + 1 + a J) 3 - J~(J + 1)3] [HJoK] [(K + z~K)2(J --t-/~j)2(j q_ 1 q- zxJ) 2 - K2J~(J Jr- 1)q [H KJ] [(K + AK)4(J + A J ) ( J + 1 q- aJ) - K4J(J + 1)] [H0K][(K+ AKP - K 61
k = 1 for v4 ;
k = -2
for2~4.
L)ETERMINATION OF A0 FOR CH~I
305
b o t h the upper and lower states. C o m p u t e r fits of these lines were m a d e for each b a n d to the expression in Table I. Microwave values of Bo = 0.2502167 c m -~ D~K = 0.0000033 (tm-~, and Do J = 0.00000021 c m -1 (6) were t a k e n as k n o w n quantities. As shown in Table I, the terms corresponding to the parameters were subtracted f r o m each line before it was included in the fit. N e w assignments were predicted on the basis of the constants obtained f r o m these fits, and then new fits were m a d e including these lines, etc. p4 was f o u n d to be, on the whole, an excellent band. A l t h o u g h several sub-bands appeared to be p e r t u r b e d and therefore were left out of the fit, viz., the K A K = - 6 , - 5 , + 5 , + 6 , + 7 , and + 8 sub-bands, there remained 364 a p p a r e n t l y u n p e r t u r b e d lines. T h e s t a n d a r d deviation of the single-band fit to these lines was 0.005 c m -~. T h e perpendicular c o m p o n e n t of 2r~ did not permit t r e a t m e n t in the same way. Almost the entire P-side of the band, K A K = - 2 and beyond, was overlapped and overwhelmed b y the parallel c o m p o n e n t of 2~4. I n addition, the subbands K A K = + 1 t h r o u g h + 7 all appear to be perturbed to various degrees. On the basis ot a single-band fit to the remaining p a r t of the band, it was not possible to m a k e an u n a m b i g u o u s decision as to which ot the series, if any, were unperturbed. Fortunately, the simultaneous fit of v4 and 2vt, which was our p r i m a r y objective, p r o v e d feasible. F r o m the perpendicular c o m p o n e n t of 2~4,97 lines of the types R P o ( J ) , RRo(J), " R s ( J ) , and " R g ( J ) , together with 56 l o w - J lines of the 2v4 parallel c o m p o n e n t were found to fit v e r y well ( s t a n d a r d deviation 0.007 TABLE II MOLECULAR CONSTANTS FOR CH,~I
Parameter v0(v4) ~'0(2u4]_)
v0(2p4 H) A0 A£4 z -- 1/~n4 D oK
Value
95% s.c.iY
3060.057 cm-1 6101.89 6052.04 5.134 0.302 0. 00009
0.005 cm-1 0.02 0.01 0.003 0.003 0.00008 0 . 0009
a 4 "4
0. 0311
4K
0.0003
0.0001
000003 0. 00008 0. 00003 H oK - - 0. 0000022 0. 0000008 Other molecular constants were found to be not significant. 0.2502167 B0 a O.00000021 DJ ~ 0.0000033 DoJ~ 4B
-- 0. 000122
0.
~4~
95% simultaneous confidence intervals; here ~ 6 X standard error of the coefficients. b Values for CH3I taken from Thomas, Cox, and Gordy (3).
306
BARNETT AND EDWARDS
cm--' ) in a simultaneous fit with the 364 unperturbed lines of p4 , tO the frequency expression in Table IV of Paper I. Because they fit well with ~4, these series of 2u, were assumed to be relatively unperturbed. The simultaneous analysis was carried out in the same manner as described for CHaBr in Paper II. RESULTS The results of the simultaneous fit are listed in Table II. The value of A0 was 5.134 ± 0.003 c m - ' (95% simultaneous confidence iiltervals used here and throughout). This value of A0 for CHaI is not as precise as that obtained previously for CHaBr (2), mainly because there are fewer good lines from the 2v4 perpendicular component, fewer sub-bands represented, and most likely, some perturbed lines included. For comparison, previous values of A0 for CHaI, obtained by application of the zeta-sum rule to Q-branch analyses ol all the degenerate fundamental bands, are given by Herzberg as 5.077 (7), Burke as 5.104 (8), and Jones and Thompson (9) as 5.119 cm -1. From a study of a Coriolis interaction between the va -k v6 and v5 bands, Maki and Hexter (10) have obtained a value A0 = 5.158 + 0.02 cm -~. Under the approximations A~ ~ A0 and ~4 ~-~ 0, one finds ~'4~ ~ 0.059. Jones and Thompson list the same value. I n the same manner as described for CHaBr in Paper II, one finds also x44 ~ - 2 6 . 5 7 cm -I and xe~q ~ 12.46 cm -~. Calculations of a substitution structure, such as were made for CHaBr in Paper II, could not be carried out for CHaI since there exists only one stable isotope of iodine. RECEIVED December 30, 1966 REFERENCES 1. W. L. BARNETTAND W. H. EDWARDS, J. Mol. Spectry. 9.0, 347 (1966). 2. T. L. BARNETTAND W. H. EDWARDS,J. Mol. Speetry. 20, 352 (1966). 3. K. N. RAO, C. J. HUMPHREYS, AND D. H. RANK, "Wavelength Standards in the In-
frared." Academic Press, New York, 1966. 4. D. H. RANK, D. P. EASTMAN,B. S. RAO, AND T. A. WIGGINS, J. Op[. Soc. Afft. 51,929 (1961); D. H. RANK, D. P. EASTMAN,B. S. RAO, AND T. A. WIGGINS, J. Opt. Soc. Am. 52, 1 (1962); D. H. RANK, G. SKORINKO, D. P. EASTMAN,AND T. A. WIGGINS, J. Mol. Spectry. 4, 518 (1960). 5. W. E. PLANS,thesis, Michigan State University, 1963. 6. W. J. O. THOMAS,J. W. Cox, AND W. GORDY,J. Chem. Phys. 9.2, 1718 (1954). 7. G. HERZnERG, "Infrared and Raman Spectra of Polyatomic Molecules," p. 437. Van Nostrand, Princeton, New Jersey, 1945. 8. RICHARDJ. BURKE,thesis, University of Maryland, 1954. O. E. W. JoNEs ANDH. W. THOMPSON, Proc. Roy. Soc. 288A, 50 (1965). 10. A. G. MAKI AND R. HEXTER (to be published).
23,302-306 (1967)
Determination of A0 for Axially Symmetric Molecules Part III . CH31t THOMAS L. BARNETT AND T. H. EDWARDS
Department of Physics, Michigan State University, East Lansing, Michigan 48823 A value of A0 = 5.134 -4- 0.003 cm-1 was obtained for methyl iodide from a least squares simultaneous analysis of ~4with band origin at 3060.057 cm-I and 2~ with perpendicular component band origin at 6101.89 cm-1 and parallel component band origin at 6052.04 cm-1. Values of other molecular parameters which proved significant in the fit are also reported. INTRODUCTION Our method of obtaining an accurate value of A0 for axially symmetric molecules, b y means of a simultaneous analysis of two suitably related bands, was outlined in Paper I of this series (1). [A0 = h/(8~r2CIoA), where I0 ~ is the principal m o m e n t of inertia of the molecule about its s y m m e t r y axis in its ground vibrational state.] I n Paper I I (2) the method was applied to determine Ac for CH3Br. I n this paper a value of A0 for CH3I is determined from a simultaneous analysis of the ~4 and 2~'4 bands. EXPERIMENTAL PROCEDURE Spectra of ~4 and 2~4 of CH~I were obtained using a high resolution v a c u u m recording spectrometer employing an f/5 L i t t r o w - P f u n d monochromator of focal length 1 meter, in both single-pass and double-pass configurations. The experimental procedure used to obtain the frequencies of the observed lines is outlined in the book by Rao, Humphreys, and R a n k (3). Frequencies for the lines of ~4 and 2~4 were obtained by calibrating t h e m with bands of simple molecules measured by R a n k et al. (4), viz., HC1 (1-0) and H C N (0, 0, 1) for ~4, and N20 (3, 0, 1) and H C N (0, 0, 2) for 2,4. The standard deviations of the calibration fits were 0.004 cm -1 for p4 and 0.006 cm -1 for 2~4. The resolution limits in the spectra were ~ 0 . 0 4 cm -1 for ~4 and ~ 0 . 0 6 cm -1 for 2~'4. Survey spectra of ~4 and 2~4 of CH3I are shown in Fig. 1. Except for the perpendicular Q-branches, the rotational fine structure is clearly resolved in both This work was supported by a grant from the National Science Foundation. 3O2
303
D E T E R M I N A T I O N OF Ao FOR CH~I PQ3
v4
RQ0
RQ3
PQ6
RQ6
3000 C~n-I
3050
j
RQ9
3100
i
3150
t
PQ3
RQ 0
2v 4 I
I
RQ 3
RQ6
RQ9
6050 cm -I i
6100 I
6150 !
6200 |
FIG. l. Absorption spectra of CH3I (a) ~4 (pressure: 6 mm Hg, path length: 6.4 m); (b) 2 ~4 (pressure: 10 mm Hg, path length: 9.6 m). bands. Note, in particular, the anomalous intensity of the RQ6(J) Q-branch ill ~4, and the split RQs(J) Q-branch in both bands. To the right of the Q-branches in the perpendicular bands one m a y observe what we believe to be the Q-branches of hot bands. ANALYSIS The Nielsen-Amat generalized frequency expression representing a v i b r a t i o n rotation absorption transition from the ground vibrational state to any upper vibrational state is given in Table I I of P a p e r I. The energy expression from
304
BARNETT
AND EDWARDS
which this expression was obtained is listed through third order and partially through fourth order in a thesis by Blass (5) and will also be given, with a few more terms in('.luded, in a forthcoming thesis by one of us (T. L. B.). When the two bands to be analyzed simultaneously show evidence of perturbations, the most productive course of action is usually to begin by analyzing the bands individually, and then to combine t h e m in a simultaneous analysis only after most of the perturbed lines have been identified and omitted. This was the course we followed in the case of ~4 and 2p4 of C H d . Table I lists the single-band frequency expression which was used to analyze v4 and 2~4 separately. I t was obtained from the Amat-Nielsen generalized frequency expression shown in Table I I of P a p e r I. The appropriate selection rules on AC4 have been represented AG = /oAK, where k = 1 for ~4 and k = - 2 for 2~4 (see Table I I I of Paper I ) . When the resulting linear dependences among various terms had been eliminated, the expression in Table I resulted. The ~,, T]44 , and 7 terms, which occur in the generalized frequency expression, are expected to be negligible and have not been shown. I t should be noted t h a t this is only one of several possible equivalent forms which the expression could take, even after the linear dependences have been removed. I t should be stressed t h a t this expression is not appropriate for simultaneous fits of v4 and 2h4 (see Table IV of Paper I) for which a number of the linear dependences are removed. A large number of lines in each band were assigned by inspection on the usual basis of missing lines in the various series, due to the requirement that J > K in TABLE
I
FREQUENCY EXPRESSION FOR SINGLE-BAND FIT OF ~4 OR 2v4 ~
aKaJK(J) -- {B0[(J + A J ) ( J + 1 q- AJ) -- J ( J Jr- 1) - (K q- AK)2 + -- DoJ[(J -~ z~J)2(J Jr- 1 -b Z~J)2 - j 2 ( j Jr- 1)2] DJK[(K + AK)2(J -F ~ J ) ( J '}- 1 t- 2~J) - K2J(J q- 1)]}
-
K s]
-
F ~o(~4)or1 as a p p r o p r i a t e
= | ~ 0 ( 2 v 4 ± ) or
+ + + + + + + + + + + 4-
--
k(,~K)2(A£~
z
-
1/~#4K)]
L,,o(2,,, II ) kA~¢4 z - ~ k ~ 4 x [ [ ( K + A K ) 2 - - K 2] I - D o K -- J/~k,4 K] [(K + a K ) 4 - K q [-a4 A + ~ k v 4 K] [(av4)(K + aK)q [Ao -
[--o~4B] [(Av4){(J -I- zXJ)(J -~- 1 + zXJ) -
(K + 2~K)2}] [~4J] [(kZ~K)(K q- A K ) ( J q- Z~J)(J + 1 + z~J)] [f14J] [(Av4)(J -q- ,,,j)2(j q_ 1 q- aJ)q [fls~] [(av4)(K + aK)2(J + a J ) ( J + 1 + a J)] [~,q [(av~)(K + aK)q [H0z] [(J + aJ)3(J + 1 + a J) 3 - J~(J + 1)3] [HJoK] [(K + z~K)2(J --t-/~j)2(j q_ 1 q- zxJ) 2 - K2J~(J Jr- 1)q [H KJ] [(K + AK)4(J + A J ) ( J + 1 q- aJ) - K4J(J + 1)] [H0K][(K+ AKP - K 61
k = 1 for v4 ;
k = -2
for2~4.
L)ETERMINATION OF A0 FOR CH~I
305
b o t h the upper and lower states. C o m p u t e r fits of these lines were m a d e for each b a n d to the expression in Table I. Microwave values of Bo = 0.2502167 c m -~ D~K = 0.0000033 (tm-~, and Do J = 0.00000021 c m -1 (6) were t a k e n as k n o w n quantities. As shown in Table I, the terms corresponding to the parameters were subtracted f r o m each line before it was included in the fit. N e w assignments were predicted on the basis of the constants obtained f r o m these fits, and then new fits were m a d e including these lines, etc. p4 was f o u n d to be, on the whole, an excellent band. A l t h o u g h several sub-bands appeared to be p e r t u r b e d and therefore were left out of the fit, viz., the K A K = - 6 , - 5 , + 5 , + 6 , + 7 , and + 8 sub-bands, there remained 364 a p p a r e n t l y u n p e r t u r b e d lines. T h e s t a n d a r d deviation of the single-band fit to these lines was 0.005 c m -~. T h e perpendicular c o m p o n e n t of 2r~ did not permit t r e a t m e n t in the same way. Almost the entire P-side of the band, K A K = - 2 and beyond, was overlapped and overwhelmed b y the parallel c o m p o n e n t of 2~4. I n addition, the subbands K A K = + 1 t h r o u g h + 7 all appear to be perturbed to various degrees. On the basis ot a single-band fit to the remaining p a r t of the band, it was not possible to m a k e an u n a m b i g u o u s decision as to which ot the series, if any, were unperturbed. Fortunately, the simultaneous fit of v4 and 2vt, which was our p r i m a r y objective, p r o v e d feasible. F r o m the perpendicular c o m p o n e n t of 2~4,97 lines of the types R P o ( J ) , RRo(J), " R s ( J ) , and " R g ( J ) , together with 56 l o w - J lines of the 2v4 parallel c o m p o n e n t were found to fit v e r y well ( s t a n d a r d deviation 0.007 TABLE II MOLECULAR CONSTANTS FOR CH,~I
Parameter v0(v4) ~'0(2u4]_)
v0(2p4 H) A0 A£4 z -- 1/~n4 D oK
Value
95% s.c.iY
3060.057 cm-1 6101.89 6052.04 5.134 0.302 0. 00009
0.005 cm-1 0.02 0.01 0.003 0.003 0.00008 0 . 0009
a 4 "4
0. 0311
4K
0.0003
0.0001
000003 0. 00008 0. 00003 H oK - - 0. 0000022 0. 0000008 Other molecular constants were found to be not significant. 0.2502167 B0 a O.00000021 DJ ~ 0.0000033 DoJ~ 4B
-- 0. 000122
0.
~4~
95% simultaneous confidence intervals; here ~ 6 X standard error of the coefficients. b Values for CH3I taken from Thomas, Cox, and Gordy (3).
306
BARNETT AND EDWARDS
cm--' ) in a simultaneous fit with the 364 unperturbed lines of p4 , tO the frequency expression in Table IV of Paper I. Because they fit well with ~4, these series of 2u, were assumed to be relatively unperturbed. The simultaneous analysis was carried out in the same manner as described for CHaBr in Paper II. RESULTS The results of the simultaneous fit are listed in Table II. The value of A0 was 5.134 ± 0.003 c m - ' (95% simultaneous confidence iiltervals used here and throughout). This value of A0 for CHaI is not as precise as that obtained previously for CHaBr (2), mainly because there are fewer good lines from the 2v4 perpendicular component, fewer sub-bands represented, and most likely, some perturbed lines included. For comparison, previous values of A0 for CHaI, obtained by application of the zeta-sum rule to Q-branch analyses ol all the degenerate fundamental bands, are given by Herzberg as 5.077 (7), Burke as 5.104 (8), and Jones and Thompson (9) as 5.119 cm -1. From a study of a Coriolis interaction between the va -k v6 and v5 bands, Maki and Hexter (10) have obtained a value A0 = 5.158 + 0.02 cm -~. Under the approximations A~ ~ A0 and ~4 ~-~ 0, one finds ~'4~ ~ 0.059. Jones and Thompson list the same value. I n the same manner as described for CHaBr in Paper II, one finds also x44 ~ - 2 6 . 5 7 cm -I and xe~q ~ 12.46 cm -~. Calculations of a substitution structure, such as were made for CHaBr in Paper II, could not be carried out for CHaI since there exists only one stable isotope of iodine. RECEIVED December 30, 1966 REFERENCES 1. W. L. BARNETTAND W. H. EDWARDS, J. Mol. Spectry. 9.0, 347 (1966). 2. T. L. BARNETTAND W. H. EDWARDS,J. Mol. Speetry. 20, 352 (1966). 3. K. N. RAO, C. J. HUMPHREYS, AND D. H. RANK, "Wavelength Standards in the In-
frared." Academic Press, New York, 1966. 4. D. H. RANK, D. P. EASTMAN,B. S. RAO, AND T. A. WIGGINS, J. Op[. Soc. Afft. 51,929 (1961); D. H. RANK, D. P. EASTMAN,B. S. RAO, AND T. A. WIGGINS, J. Opt. Soc. Am. 52, 1 (1962); D. H. RANK, G. SKORINKO, D. P. EASTMAN,AND T. A. WIGGINS, J. Mol. Spectry. 4, 518 (1960). 5. W. E. PLANS,thesis, Michigan State University, 1963. 6. W. J. O. THOMAS,J. W. Cox, AND W. GORDY,J. Chem. Phys. 9.2, 1718 (1954). 7. G. HERZnERG, "Infrared and Raman Spectra of Polyatomic Molecules," p. 437. Van Nostrand, Princeton, New Jersey, 1945. 8. RICHARDJ. BURKE,thesis, University of Maryland, 1954. O. E. W. JoNEs ANDH. W. THOMPSON, Proc. Roy. Soc. 288A, 50 (1965). 10. A. G. MAKI AND R. HEXTER (to be published).