Table 11. Correlator Performance with Background and Reference Variationa Rei. freq., M H Z
Background Cycle Reference Cycle
Theoretical
% T
...
A v . meas.
% T
...
Deviation
% T
...
Std. deviation
% T
...
5.00000 5.00000 5.00000
0.30000 4.30000 2.30000 1.30000 0.70000 0.50000 0.40000
100.000 50.000 25.000 10.000 5.000 2.500
99.998 49.998 24.999 9.998 5.001 2.502
0.002 0.002 0.001 0.002 0.001 0.002
0.0015 0.0013 0.0014 0.0013 0.0009 0.0009
1.40000 1.40000 1.40000 1.40000
1.10000 0.70000 0.50000 0.40000
100.000 50.000 25.000 12.500
100.002 49.996 25.000 12.501
0.002 0.004 0.000 0.001
0.009 0.007 0.005 0.006
0.50000 5.00000 5.00000
5.00000
a
Sample freq., h4Hz
Footnotes b-e of Table I apply.
certainty in the initial background measurement can contribute to error in this case. The net sample and reference frequencies were than both reduced by a factor of 5, without putting the correlator through a new background or reference cycle. For 100% T, the net reference sample channel frequency was 0.9 MHz and the net sample channel frequency was 0.8 MHz. The 0.5 MHz of reference and the 0.3 MHz of sample background frequency still present gives a total reference frequency of 1.4 MHz and a total sample frequency of 1.1 MHz for 100% T. Table I1 shows that with these input frequencies, the correlator output was indeed still 100% T. Similarly, with the net sample channel frequency reduced from 0.8 MHz to 0.4 MHz for a total sample channel frequency of 0.7 MHz, an output reading of 50% T was obtained. The table shows that even with a large amount of background and a sub-optimum number of reference and sample channel net counts, the average transmittance is still within about 0.002% T of the theoretical value. This is because, as before, the one count uncertainty in t,he net counts tends to be, averaged out over repeated measurements. The standard deviations of the individual measurements, however, increased to about 0.007% T . This is as expected since the uncertainty is now one out of 8000 sample counts (for 100% T ) , which gives an expected maximum standard deviation of 0.5 divided by 8000 or 0.00625% T . This may be increased somewhat by the reference count
uncertainty. It should be noted that these uncertainties are present in any digital frequency measurement, and are not a direct function of the digital correlator. Applications. The digital correlator has been used for nearly one year in conjunction with charge-to-count converters in a double beam optical system. The combination of the correlator and converters provides a measurement system of sufficient accuracy that attention can be focused on improving the light-to-charge transducers and the mechanical and optical characteristics of the system. Consideration is being given to the incorporation of the digital correlator, with the resolution decreased to 12 bits and its speed correspondingly increased by a factor of 16, in a high speed kinetic analyzer. The correlator data for these specific applications are included with data on the total analytical system performance for each application. The basic concepts of simple, economical digital data correlation presented in this paper are being extended to provide the digital correlator with several additions which permit it to convert transmittance into absorbance and to provide a derivative output.
RECEIVED for review May 6, 1974. Accepted August 5, 1974. One of the authors (T.A.W.) expresses his appreciation for a Mobil Foundation Fellowship for part of this work, and the authors are grateful for partial support of the work by the NSF under grant G P 18910.
Bayesian Decision Theory Applied to the Multicategory Classification of Binary Infrared Spectra H. B. Woodruff, S. R. Lowry, and 1.L. lsenhour Department of Chemistry, University of North Carolina, Chapel Hill, N.C. 275 14
Bayes’ Theorem has been applied to the multicategory classification of infrared spectra. The information contrlbuted by all of the dlscriminant functions may thereby be used in making predictions. This study demonstrates how the ability to correctly classify the spectra increases with each additional discrlminant functlon used. When only the 2150
largest discriminant function is employed, 46% of the data set is correctly classified as belonging to one out of a total of fourteen possible classes. The five largest discriminant functions produce a 90% prediction, while twelve to fourteen discriminant functions result in the correct classlflcation of the entire data set.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 14, DECEMBER 1974
Pattern recognition techniques employed for the analysis of infrared spectra have been previously reported as acceptable alternatives to search and compare methods ( I , 2). The advantage of using pattern recognition is the ability to determine common characteristics of spectra from similar compounds. Other compounds displaying similar characteristics in their spectra can then be predicted to belong to the same class of compounds as the original set in which these characteristics were observed. Previous works in this field have reported results using binary classification techniques. This means that the answers were simply yes or no; e . g . , yes, the compound was a carboxylic acid or no, it was not. Similar questions were asked for esters, aldehydes, and each of the other classes of compounds being tested. For a given spectrum, if after all the questions were answered, only one answer was yes, then a specific prediction could be made. Otherwise the prediction would merely be that the compound belonged to one of the positive classes. Another approach is to use multicategory classification techniques. In this case, rather than asking a number of yes/no questions, only one question is asked. To which class does the compound belong? Selection of the proper discriminant function results in a prediction for the correct answer to this question. This paper reports an investigation of multicategory predictions using binary data. With the knowledge that the spectrum belonged to one of fourteen possible classes the goal was to select the proper class.
DATA SET The data for this study were obtained from a file of 91,875 spectra assembled by the American Society for Testing and Materials and made accessible by the Triangle Universities Computation Center (TUCC) in North Carolina. Twenty-eight hundred spectra were randomly selected and were evenly distributed among each of the fourteen classes (Table I). The criterion used in selecting the classes was that they were similar to ones reported in previous work ( 1 ), thus simplifying the comparison of results. Each compound contained only one of the functional groups tested, so each spectrum belonged exclusively to one class. The compounds contained only C, H, 0, and N atoms with the carbon content ranging from Cl-15. The ASTM file contained no intensity values. One hundred thirty-nine dimensions were selected with each dimension representing a 0.1-pm interval. The range covered was from 2.1 to 15.9 fim. Thus, the bit corresponding to a given dimension was turned on only when a peak maximum occurred in that tenth micrometer interval. Computations were done on the TUCC IBM 370/165 teleprocessing with the University of North Carolina Computation Center IBM 360/75 using FORTRAK IV and PL/I computer programs.
RESULTS AND DISCUSSION For a given spectrum, the fourteen discriminant functions, G , (X), were obtained in the following manner: Gi(X) = W i . X where i ranged from 1 to 14 depending on the class, X was the spectrum, and Wj was the weight vector for class i. Each Gi(X) was merely the dot product of two 139-dimensional vectors. The values of Gi(X) were ordered and the spectrum X was assigned to class i when Gi(X) was the maximum discriminant function. For future discussion, let (1) B. R. Kowalski, P. C. Jurs, T.L. Isenhour, and C. N. Reilley, Anal. Chem., 41, 1945 (1969). (2) R . W. Liddell 111 and P. C. Jurs, Appl. Spectrosc., 27, 371 (1973).
Table I. Chemical Classes Used in the Study Class NO.
1 2
3 4 5 6 7 8 9
10 11 12 13 14
C h e m i c a l functionality
Carboxylic acid Ester Ketone Alcohol Aldehyde 1" Amine 2" Amine 3" Amine Amide U r e a and derivatives E t h e r and a c e t a l Nitro and nitroso Nitrile and isonitrile Unsaturated hydrocarbon GI = largest G,(X)
I = value of i in l a r g e s t G,(x). (2b) T o obtain Wi, the sum spectrum of class i was obtained by adding the individual dimensions of all two hundred class members. The non-class i sum spectrum was obtained from the remaining 2600 members of the data set. These two sum spectra were converted to class conditional probabilities by dividing by the number of class members. Then the difference between the class and non-class conditional probabilities was taken. The result was a weight vector consisting of dimensions ranging from -1 to $1. Positive values indicated that a peak was more likely to be present a t that position in class i than in the average spectrum created from the non-class i spectra. For each of the 2800 spectra, GI was obtained and the spectrum was predicted to belong to class I. The results of these predictions are shown in Table 11. Large values along the diagonal would be desirable as that would indicate that the class predicted and the actual class were identical. Major interferences can be found by looking down the columns. For example, ketones (i = 3) interfered substantially with esters (i = 2). Also, every class interfered with the unsaturated hydrocarbon class (i = 14). The section concerning a criterion for learning in reference ( I ) is appropriate to this discussion. Since all fourteen classes were of equal size, the best possible success rate for guessing would be 1/14 or just over 7%. The overall prediction rate of about 46%, obtained from Table 11, was substantially better than random, but still not extremely impressive. With a binary classification technique, there is only one discriminant function, while there is one for each class in a multicategory classification scheme. By employing only the largest Gi(X), the information contributed by the second largest Gi(X) is neglected. One addition to the terminology would be useful for further discussions. Let Gi(X), mean the i t h discriminant function is the j t h largest one. Hence, Gi(X)l = GI. As j is incremented from one through fourteen, additional information is added each time. By adding new information, one should affect the prediction in some manner. This effect can be found by using Bayes' Theorem. The Bayesian approach may be presented in a variety of methods (3-6), but the result is to render the probability of (3) P. C. Kelly, Anal. Chem., 44 ( l l ) ,28A (1972). (4) J. Berkson, Ann. Math. Statistics, 1 , 42 (1930). (5) M. Tribus, "Rational Descriptions, Decisions and Designs," Pergamon Press, New York, N.Y.. 1969, p 73. (6) R . 0. Duda and P. E. Hart, "Pattern Classification and Scene Analysis," John Wiley & Sons, New York, N.Y.. 1973. p 10.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 14, DECEMBER 1974
2151
Table 11. Predictions Using Largest Discriminant Function Predicted class ( I ) Actual class ( I )
1
2 3 4 5 6 7
8 9 10 11
12 13 14
1
2
112 3 12
17 151 51
1
0 21 0
8 0 1
2 6 11 0
2 12 0
Total 170 % c o r r e c t 65.9
5 4 13 10 3 3 12 3
3
5 1
58 3 5 0
2 2 5 5 0 2 1 4
293 93 51.562.3
4
0 0 3 113 3 11 14 7 8 4 12 3 11 4
193 58.5
5
6
7
8
9
10
11
12
13
3
5
9 6
10 1
0
10
0
5
0
0 0 0 1
0 0
11 11
19 6 42 121
1
0 0
8 9 9 3 4 5 5 14
0
0
1
0
4 4
8 2 9 23
92
1
7
0 1 0
92 6
1 4 0 1 2 1
13 33
33 93 19 15 30 20 25 19 3
106 86.8
0
1
5 7 0
306 171 53.8 30.4
an occurrence given some prior probability and some new information. Assume there are three events to be considered, A, B, and C. Event C has already occurred, so it is known to be true. The probability of event A occurring given that event C is true is likewise known. The symbol p ( A C ) expresses this probability. Now, one obtains new information, namely event B occurred. Bayes’ Theorem shows how to determine the probability of event A occurring now that both B and C are known to be true, p (AlBC). Thus, the Bayesian approach shows how the addition of new information alters the probability of A occurring. One expression for the equation used in this determination is
Again, in the probability expressions, the terms on the right side of the bars are the events known to be true, while those on the left are the desired events. Examples and the proof of the theorem are found in references (3-6) and elsewhere, with one example ( 5 )being included in this paper to clarify the use of the Bayesian approach. In this example, there are three identical boxes each of which contains two coins. I t is known that one box contains two silver coins, a second box contains two gold coins, and a third contains one gold and one silver coin. One box is selected and a coin is removed. The coin which is removed is gold. What is the probability that the remaining coin in the box is gold? By proper selection of events A, B, and C, one can solve this problem using Bayes’ equation. Event C is the one originally known to be true. In this case C is the fact that there are three boxes with the coin distribution as stated above. The new information, B, is that a gold coin is withdrawn from the selected box. Event A is that the box selected contains two gold coins, the desired event. So expressed in words, p(A/BC) is the probability that the box selected contains two gold coins, given that a gold coin is withdrawn and the coin distribution is as stated above. This is the probability asked for in the problem. Consolidating the facts one has: A = The box selected contains two gold coins. B = The coin withdrawn is gold. C = The coin distribution is as given in the problem. p(AIC) = 1/3, since the boxes are alike. 2152
24 3 2 81 40
7 7
25 23 12 5
4 7
15 0
0
2
2 0 1 0 0 0 0
25 0
3 83
1 1 0 0 1 1
1 1 0
11 7
66 2
38
3
1
0
0 0 0
203 27 304 39.8 39.9 92.5
7
14
23 27 30 36 36 28 27 29 44 26 51 51 61 176
1 0 0
76 42 86.8 90.5
171
48.5
645 27.3
Total
200 200 200 200 200 200 200 200 200 200 200 200 200 200 2800 46.5
p ( B ( C ) = 1/2, since half the coins are gold. p(B1AC) = 1, since if both coins are gold, a gold one certainly will be withdrawn. Therefore, P(A1BC) = (1/3)
X
1/(1/2)
= 2/3
(4)
Intuitively, one’s first inclination might have been to respond that the probability sought was I/!. A gold coin had been selected. Therefore, the box containing two silver coins was eliminated from contention, and the probability of the two-gold-coin box having been selected should have increased to l/*. The fallacy in this logic can be seen by approaching the problem from a somewhat different direction. I t is correct that the two-silver-coin box is eliminated from contention. The contents of the two remaining boxes are three gold coins (Gl,Gz,G3) and one silver coin. The probability that the first coin selected was GI, for example, is 1/3. The same is true for Gz and Gs. However, both G I and Gz belong to the same box. So the probability that one of them was withdrawn and, hence, that the box containing two gold coins was the one selected is actually ;5, as found using the Bayesian approach. The following specific example demonstrates the applicability of the Bayesian approach to the problem of utilizing more places than just the largest discriminant function for the multicategory classification of infrared spectra. Let the symbols A, B, and C be represented by the following statements: A: The spectrum belonged to class 1 (acids). B: The second largest discriminant function was number 2 - Gz(X)z. C: The largest discriminant function was number 1 Gi(X)i. Again, A was the desired event, C was the information already known, and B was the new information. So p(A1BC) was the probability that the spectrum belonged to class 1 given that the order of finish for the discriminant functions was 1-2. p ( q C ) , which was the probability that the spectrum belonged to class 1 given G,(X)1 was found from Table I1 to be 112/170. The probability, p ( B J C ) ,was easily determined from the data set to be 7/170. That is, only seven of the 170 times that G I ( X ) l was true, was G2(X)2 also true. Likewise, p(B1AC) was simply determined to be 3/112. Substitution into Bayes’ equation gave
ANALYTICAL CHEMISTRY, VOL. 46, NO. 1 4 , DECEMBER 1974
spectrum belonged to class 2 was calculated. Similarly, the probabilities for classes 3-14 were found. The class for which p ( 4 B C ) was largest was predicted as the correct class any time the order of the discriminant functions was 1-2. Next the probabilities for each of the classes were determined when G1(X)1 and G 3 ( X ) 2 were true. The class corresponding to the largest probability was predicted whenever the order was 1-3. Similarly, the class predicted for every other possible order was found and the results are shown in Table 111. The results obtained when these predictions were made on the 2800 spectra are shown in column 2 of Table IV. The extension of these concepts to include third largest, fourth largest, and subsequent discriminant functions until all fourteen were considered was trivial in concept. The ability to predict on the data set is shown in Table IV. As the number of places considered increased, the predictive ability improved, but the computation time increased as well. The fact that 100% recognition was achieved in under fourteen places was not surprising. Once the fourteen
~~
Table 111. Class Predicted for E a c h First a n d Second Place Order Gi(Xll Gi
i
(XI2
1 2 3
...
1 1 ...
3
4
3
4
5 10
4
3
4
5
9
5
6 6 6
7 7 7
i
2 ... 4 3 ... 1 5 9 5 . 12 10 3 4 4 2 3 4 1 2 3 4 1 10 3 4 9 2 10 4 1
4 13 5 6 7 8
2
2
5
d
8
7
3 3
3
10
11
12
11
13
1 1 10 12 12 13 8 10 10 11 12 13 4 9 1 0 1 1 1 2 5 4 9 10 11 12 13 5 9 1 0 1 1 1 2 1 3 8 9 10 12 12 13 8 9 10 11 12 1 3 ... 10 10 11 12 13 9 ... 10 11 12 1 3 8 10 ... 11 12 13 11 13 10 ... 12 13 12 9 10 12 ... 3 13 9 10 13 12 ... 8 9 10 11 1 2 13
. . 5 5 ... 6 3 6 ... 5 6 7 5 10 7 3 10 10 3 11 5 6 7
9 10 11 1 2 12 3 1 13 13 13 14 1 2
9
4 12 12 12 4 13 13 1 3 4 5 6 7
1 2
14 14 5 6
14 14 12 14 14 12 13
...
Table IV. Predictions Using Additional Discriminant Functions K u m b e r of discriminant functions used
Class
1 2
3 4 5 6 7 8 9 10 11 12 13 14 Total
1
2
3
4
5
6
7
65 51 62 58 86 53 30 39 39 92 48 86 90 27 46
66 55 57 63 66 62 35 46 53 53 51 58 88 32 53
67 65 70 63 80 63 48 58 75 67 59 80 97 40 64
84 76 81 72 87 77 69 63 83 92 78 93 97 56 78
91 86 90 81 95 89 84 82 91 98 91 97 98 83 90
99 95 98 92 98 97 94 94 97 98 95 99 99 99 97
100 98 99 95 100 99 97 97 99 99 99 100 100 98 99
P(AIBC)
=
1.2-1170
100 100 99 98 100 100 99 98 99 100 100 100 100 100 99+
3
112
7 -
= 3/7.
9
8
(5)
170
For this case, then, given only that discriminant function 1 was the largest, a prediction that the spectrum was of an acid was (112/170) or about 66% certain of being correct. With the new information that discriminant function 2 was the second largest, one was only (3/7) or about 43% certain that the prediction of class 1was correct. In this example, the probability that the spectrum belonged to class l decreased substantially. This indicated that a spectrum with discriminant functions 1 and 2 as the two largest ones had an increased probability of belonging to one of the other thirteen classes. In fact, including the second largest discriminant function could decrease the percentage of spectra correctly recognized for an entire class (see class 12 in Table IV). But, the overall correct percentage necessarily increased with each subsequent discriminant function used. The procedure was continued with only event A changing, thirteen different times. The first change made event A become “the spectrum belonged to class 2.” Given that G,(X), and G 2 ( X ) 2 were true, the probability that the
100 100 99 98 100 100 99 99 100 100 100 100 100 100 99+
10
100 100 99 99 100 100 99 100 100 100 100 100 100 100 991
11
100 100 99 99 100 100 100 100 100 100 100 100 100 100 99+
12
13
14
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
values of G, (X) were ordered, each spectrum could be categorized by a sequence of fourteen numbers. There were 14 possible sequences (a number in excess of 87 billion) while there were only 2800 ,spectra to be correctly recognized. The criterion for 100%recognition was that the sequence of fourteen numbers for any spectrum in class i had to be different from the sequence of numbers for any of the 2600 non-class i spectra. It seemed reasonable that the criterion would be met, since there was such a large excess of possible sequences over number of spectra in the data set. Of course, searching 14! possible sequences would have been more difficult than searching 2800 spectra and looking for an exact match. However, the same could not be said for just the first five places of finish. There were 14 13 ~ 1 211 10 or 240,240 possible orders when considering only the top five finishing dot products. For each of the possible orders, one hexadecimal character ranging from 0 to E was entered in the array representing the five-dimensional counterpart of Table 111. The hexadecimal characters 1 through E represented the class to be predicted, 1-14. An entry of a 0 meant that none of the training set members gave the dot product order that the entry in question represented. This required four bits (one byte) of storage for each entry or a total of 240,240 bytes. On the other hand, 2800 spectra each of which was 139 bits
-
-
ANALYTICAL CHEMISTRY. VOL. 46, NO. 14, DECEMBER 1974
2153
long would have required 722,800 bytes to be completely stored, or almost exactly three times as much storage. Ninety per cent recognition for the time invested to check on the 240,240 possible orders was quite acceptable. The obvious extension of this technique would be to use a much larger data set to create the table described above. Clearly, most of the 240,240 entries were 0 for the 2800 spectra training set. The more members from which the table was generated, the more information the table would have contained. In addition, the table would always require the same amount of storage regardless of the number of spectra from which it was generated. Although generation of the table would be a time consuming process for larger data sets, once the table was generated, the search of the entries for the appropriate prediction would require no more time than that required in the present experiment. CONCLUSIONS The recognition results obtained using a Bayesian approach were considerably better than the 7% figure expected from random guessing. Bayesian approaches are not used very often, usually because of the difficulty of obtaining p ( A ( C ) , known as the a priori probability. However, in a situation such as the one described here, it is quite easy to estimate the a priori probabilities from the training set. Given that p (A( C) is obtainable, the Bayesian
approach can then be viewed merely as a formalization of common sense ( 6 ) .If the order 1, 2, 3, 4, 5 most frequently occurs when a compound belongs to class 1, then it is common sense to predict a spectrum giving that same order is of an acid. As was mentioned, the most likely next step for this type of approach would be to use very large training sets incorporating fewer restrictions. Also, the fourteen classes selected for this study would most likely not be the ones selected for a thorough investigation of a large data set. When using a table generated from a large data set, if the percentage of recognition still was near 90%, then one would have a quick and accurate means of predicting the type of compound without having to search large numbers of spectra. This study demonstrated the feasibility of employing a Bayesian approach for the classification of infrared spectra, but varying degrees of utility should be found when using discriminant functions generated from other types of data. ACKNOWLEDGMENT The authors are indebted to J. C. Marshall for assisting in the formation of the data set.
RECEIVEDfor review April 11, 1974. Accepted August 19, 1974. The financial support of the National Science Foundation is gratefully acknowledged.
Multielement, Nondispersive Atomic Fluorescence Spectrometry in the Time-Division Multiplexed Mode E. F. Palerrno,’ Akbar Montaser,2 and S. R. Crouch3 Department of Chemistry, Michigan State University, East Lansing, Mich. 48824
A new nondispersive multielement atomic fluorescence (AF) technique, which operates in the time-division multiplexed (TDM) mode, is capable of analyzing 4 to 8 elements in a flame in less than 3 seconds. The technique is rapid enough to allow multielement determinations on a transient atom population, such as that produced from a nonflame atomizer. The system employs computer-controlled pulsed hollow cathode lamps, a sheathed burner or nonflame atomizer, and a computer-controlled synchronous integrator as well as computerized data acqulsltlon and processing. The effects of sheath gas flow rates and burner position on AF signals and flame background are reported for the analysis of Hg, Cd, Zn, and Pb. Detection limits obtained with a 4-channel TDM-AF flame spectrometer are compared with those obtained with a conventional sequential, dispersive multielement AF system. The results Indicate that the TDM system can achieve excellent detection limits for certain elements. Detection limits are also reported for a 3-channel TDM, nonflame AF spectrometer and compared to those obtained by a single-element, dispersive technique.
Present address, E. I. duPont de Nemours & Company, Experimental Station, Bldg. 269, Wilmington, Del. 19898. Present address, Ames Laboratory-USAEC and Department of Chemistry, Iowa State University, Ames, Iowa 50010. Author to whom requests for reprints should be addressed. 2154
In recent years, there has been an increasing demand in the analytical laboratory for instrumentation capable of performing multielement analysis. Several workers have shown that atomic fluorescence (AF) spectrometry is suitable for multielement determinations in the ppm or subppm concentration range ( 1 - 4 ) . The features of AF spectrometry that make it a useful technique for multielement analysis include the low detection limits which can be achieved for many elements, the specificity of resonance fluorescence, the ease with which an array of narrow line sources can be focused on an atomic vapor cell to excite atomic fluorescence, and the relative simplicity with which the fluorescence intensities of the various elements can be separated. Multielement AF systems have been described in which the fluorescence intensities of the emitting elements have been separated in time, with a rotating filter wheel ( I , 5 ) , with a scanning monochromator (2, 6-10), or with a se(1) (2) (3) (4) (5) (6) (7)
D. G.
Mitchell and A. Johansson, Spectrocbim. Acta., Part E, 25 175 (1970). G. B. Marshall and T. S. West, Anal. Cbim. Acta, 51, 179 (1970). H.V. Malmstadt and E. Cordos, Amer. Lab., p 35, August (1972). E. Cordos and H. V. Malmstadt, Anal. Cbem., 45, 425 (1973). D. . Mitchell and A. Johansson. Spectrocbim Acta, Part E, 26 677 (1971). A. Fulton, K. C. Thompson, and T. S.West, Anal. Cbim. Acta, 51, 373 (1970). M. S. Cresser and T. S. West, Anal. Cbim. Acta., 51, 530 (1970).
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