ANALYTICAL CHEMISTRY
1418
These overpunches remove plus or minus signs on the card, so that interpretation is easy. Only one number for a given compound can be punched into a card. 3. .4 code list of book5 and journals for punching references into columns 71 and 7 2 follows: NO.
Journal or Book
1
ANILITICILCHESIISTRY Journal of the American Chemical S o c i e t y Journal of the Optical Society of America Journal of Research of the National Bureau of Standarda Transactioiw of the Faraday Society “Infrared Determination of Organic Structures,”
2 3
4 5 6
Randall Others will be added as needed, and all users of the cards notified. 4. The code list of libraries as punched into column 70 follolvs: Letter A B C D
Library American Petroleum Institute Research Project 44 User’s own library Sadtler Library of Spectrograms Sational Bureau of Standards Cards (Creita)
Others will be added as needed. 5.
A code list of types of data to be punched into column 80
follows: Letter A B C D E
Type of Data Infrared absorption ( 2 to 50 microns) X-ray diffraction (dSTM powder data) Ultraviolet absorption Raman Mass specti.osropic
Others will be added as needed, including bibliographies. The ways in which cards punched according to these codes can be sort,ed are almost limitless. As each punch is a direct, independent code, 3 sort, at any given position nil1 segregate all cards having the property or character coded by the position. Further sorts of the cards segregated by the first sort isolate groups of cards that represent compounds having two, three, or more features in common. Such sorting can be carried as far as available information permits. The order in which the sorts are made often determines the speed with which unwanted cards are eliminated. Usually a well-chosen first sort eliminates 90% or more of the
cards from further consideration. Thus, nhen sorting a b s o r p tions it is timesaving to make the first sort on an absorption t,hat appears to be unique or characteristic. It is easy to segrrgate cards coding melting or boiling points in as wide or as narrox a range as desired. Private codes further classifying compounds into such groups as wett,ing agent?, dyes, sugars, plastics, etc., depending upon local interests are useful. Finally, having the spectrograni serial numhers punched into the cards enables one to sort the cards quickly into numrrical sequence for a periodic check for missing cards. The operation of the sorter is very simple and straightforward. The machine operates on one column a t a time and can be set to segregate all cards punched a t any one or more specific numbers, regardless of what other numbers may also be punched in the column. Instructions for a series of sorting operations can be written or phoned to a sorter operator, who can carry them out and report back the serial numbers on the resulting cards. These cards will accurately represent compounds that match the data indicated by the codes selected, regardless of the order in which the sorts are made. -1s the sorting is practically effortless and automatic, human error is reduced to a minimum. Finally, it is possible to make quick and accurate comparisons or correlations between all types of data punched into the card. The number of uses to which the coded information can he put grows with increased familiarity with the code and sorting system. Decks of punched cards indexing all published infrared spectrograms h a w been prepared and are av;dable a t very low cost from publishers of catalogs of spectrogr:ims. LITERATURE CITED
( I ) Brattain, R., private communication, March 1951. (2) Eckert, W., J. Chem. Education, 24, 54-7 (1947). (3) Ferris, L., Taylor, K., Perry, J., and Torok, M., “Bibliography on the Uses of Punched Cards,” Punched Card Committee,
AMERICAN CHEXICAL SOCIETY. (4) National Research Council, Washington, D. C., Chemical-
Biological Coordination Center, “Method of Coding Chemicals for Correlation and Classification,” 1950. ( 5 ) Ohio State University, Punch Card Committee, Report, June
1950. (6) Stroupe, J., private communication, June 1950.
(7) Wright, Norman, Abstracts of Papers, 108th Meeting, CHEM.SOC.,p. 6L. New York, September 1944. RECEIVED April 2 5 , 1951. Presented before the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy. Pittsburgh, Pa., March 5 to 7. 1951.
Spectrometric Analysis Employing Punch Card Calculators Calculation Method W. H. KING, JR., AND WILLIAM PRIESTLEY, JR. Esso Laboratories, Standard Oil Deoelopment Co., Linden, N . J .
ORKERS in the field of quantitative analytical spectrometry are confronted with the problem of converting measured data, such as light absorption or mass spectral measurements, into percentage composition. The data obtained fall into two classes: unique and nonunique. I n the first case calculations are simple. An absorption maximum or mass spectral peak for a particular compound is found which is not influenced b y the other constituents in the mixture being analyzed, except by their dilution effect. Therefore, a simple comparison of the analytical peak intensity in the mixture relative to that of the pure compound gives its percentage in the mixture. I n the second case unique analytical peaks are not available; consequently rorrections must be applied for the
effect of each substituent at the analytical points chosen. Needless t o say, it is usual to choose analytical points for each compound in the mixture such that interferences-and correctionsare as small as possible. This results in rapidly converging linear equations which must be converted, by some calculation procedure, into percentage composition. It is this problem with which this paper is concerned. METHODS
SOLV1NG
LINEAR EQUATIONS
There are two approaches to the solution of this problem-a particular and a general solution. The particular solution requires establishing equations for each sample and inserting the calibration and sample data for each solution. The general
’
V O L U M E 2 3 , NO. 10, O C T O B E R 1 9 5 1 solution employs equations in which the calibration data are incorporated and only the sample data must be inserted. Which method is employed depends on the number of samples for analysis; the general solution is usually employed where a large number of samples are to be analyzed. Particular Solutions. Where only a small number of samples of similar nature are involved, a particular solution is usually employed. This may be achieved by a rigorous solution employing determinantti or the Crout short-cut method (with calculating machines), or by the c1assic:il iterative method of succwsive :ipproximations. The rigorous solution by determinants is usually employed for ternary or quaternary mixtures. The time involved in solving more than four simultaneous linear equations becomes escessive. The Crout short-cut method ( 1 ) may reduce the time requireinent by 50'% and is often applied to equations in four, five, and sis unknowns, but bcyond this point the time factor bwomes c~cessive. Ai1 Ain
Ai3
Alr
. ....
A21 AaAza A n a . . . . . A31 A32 A33 As4 . . . . , , A 41 A u Au Arr . . . . .
'
. .
. .
.
,
. . ..... . . ....
XI
bi
XI
b?
Xa
x,
=
b3 br
. I . . .
Figure 1.
B I IB I ZB13 B14 * . . . * Bzi Bn Bn B24 . . . . . Bti B3z B33 Bar , . . . . Bri Baz B43 Bar . . . . . . .
. .
. .
. .
21
Xt
xa X4
..... . . . ..
A = calibration coefficients
B = elements of inverse matrix 6 = sample coefficients r =
YGcomposition
Figure 2.
Analytical techniques for mu1ticomponent mixtures frequently involve tedious and time-consuming calculations. When such analyses are performed on a routine basis and reasonable volumes of calculations are involved it becomes economical and expedient to use automatic calculating and tabulating machinery. This paper considers a common type of problem facing many industrial analysts-the routine solution of high order simultaneous equations, using IBM punched card calculators. Such equipment may already be available where companies employ these machines for accounting, payroll, and allied purposes. On a basis of 100 samples per week 125 manhours per week could be saved in the routine calculations involved in the determination of 19 component gases by the mass spectrometer. Previous techniques using analog compu ters and hand calculators required 90 minutes per sample for the calculation which takes 12 minutes using the punched card calculator. Using calculation techniques described, coniplex problems and analytical techniques become possible which heretofore were prohibited because of the mass of calculations involved.
Given Matrix
The c1:issical interative method of successive approGmations ( 3 , !+) may be performed in a mechanical manner by calculating machine or by the electrical or analog computer. I n this method correction coefficients are wed in a set of equations. In selecting the order of approximations to obtain the best speed and accuracy in the Polution, the size of the correction coefficients and the relative amounts of the compounds present are considered. This method is described by Heigl et a!. ( 2 ) as applied to the analysis of liquid hydrocarbon mixtures.
~
1419
Inverted Matrix
The ~ 1 n principle e ib employed in certain types of electrical coniputers. These may be termed analog instruments-that is, certain circuits and components are analogous to the terms of the equations and the mathematical operations to be performed. Whether the mechanical or electrical iterative method is employed, twelve unknowns are usually the maximum number handled. Both methods are rapid, particularly if convergence is rapid. The computer is about twice as faqt as the mechanicalcalculating machine procedure for a rapidly converging set of twelve equations, and much faster when convergence is slon (greater than two or three approximations). General Solutions, Inverse Matrix. When a large number of samples involving the same components are encountered, a particular salution may be employed; but a general solution using an inverse matrix is preferred to achieve greater speed and accuracy. The conversion of spectrometric data to percentage composition by the general method consists of two parts: obtaining the
inverse mibtris employing calibration data and solving the inverted matrix for each set of sample data. The matrix and inverted matris may be reprrsented ae shown in Figures 1 and 2. The inverted matrix is advant.ageous becauae the solution is reached simply by multiplying the inverted matrix hy the vectors, or sample coefficients. The inverse matrix may be obtained employing an analog computer, the Crout short-cut method, or an International Business Machine Corp. (IBhI) calculator. The analog computer is limited in capacity and accuracy. The Crout method, employing a calculating machine, allows t.he carrying of sufficient figures to obtain satisfactory accuracy, but the time requirement is escepsive where a large number of components are involved. The IBhI calculators employ any of the classical methods of inverting the matrix. The time required for this step varies with the typr of calculator used. The authors are in a fortunate location with respect to the S e w York office of the IBhI Corp. and consequently can obtain an inverse matrix in a few hours. This is required each time a spectrometer is calibrated. Mass spectrometer calibrations are seldom required-usually two or three times a year. Infrared absorption calibration data are usually constant for an even longer time. Consequently the detailcd procedure for obtaining an inverse matrix on an IBRI calculator is not discussed in this paper. PUNCH CARD CALCULATORS
The Intcrriational Business 3I:ichinr Corp. has developed a varirt;\-of ralculating equipment for obtaining and solving inverse matrices. As the ease and speed of calculation depend upon the type of calculator employed, a brief description of each is presented. There are t.hree types of calculators, the 602A (electromechanical), the 604 (electronic), and the card-programing calculator (CPC). The complexity of the calculators increases from the 602.4 to the 604 to the CPC. In calculation speed the 604 (6000 cards per hour) exceeds the 60214 (2000 or less cards per hour) by a factor of 3 or more. The speed of the 604 is independent of the type and extent of calculat,ion being carried out, whereas the speed of the 602.4 is influenced markedly by the type and extent of calculations. The CPC is a composite grouping of several pieces of equipment, including the 604 calculator. In addition to the 604 calculator, t,he CPC comprises addit.iona1 storage capacity. The relative speed of these t,hree calculators can be
ANALYTICAL CHEMISTRY
1420
judged by the time required to invert a 20th order simultaneous equation matrix. The 602.4 requires 30 to 35 hours, the 604 6 to 8 hours, and the CPC approximately 2 hours. Along with these units go auxiliar equipment for transcribing information to and.from cards, a n g for sorting, collating, verifying, matching, and duplicating punched cards. The choice of the calculator to be used is based upon a comparison of its use versus its rental fee. In the authors’ particular situation, the 602A was chosen for three reasons: the much lower rental fee of the 602A than of the 604 or CPC equipment; the availability of the 604 and CPC equipment a t IBM for rapidly obtaining an inverse; and insufficient samples to require the Rpeed of a 604 or CPC calculator, which -would then not be utilized for the full 8-hour day. Operation of Calculators. In order to describe the procedure used for calculating composition values from an inverse matriv employing the 602.4 calculator, it is necessary t o go into some detail as to the component step8 required in operation of the instrument. This procedure also applies to the other ralculators.
There are several methods of calculating composition values on the 602A calculator. In Figure 3 is a tvpical inverse matrix for which 19 multiplications are necessary to obtain the percentage of component S. I t is necessary to summarize the products of bl X B1 b2 X B I , ~ ba X B I , .~ blP X Bl,,9, where bl - bl9 are the analytical data for a given sample. The main consideration in selecting the method to be used is that the 602A calculator can carry out only one multiplication a t a given time-that is, the multiplier must be entered into a particular component of the 602A (storage unit 1R). However, it is possible to carry out several multiplications at one time if the same multiplier is used. Figure 1 shows that the condition of simultaneous multiplication can be satisfied by developing the products vertically-that is, (bl X & , I ) , (bt X &.I), (bl X & , I ) . . . (bl X B I ~ J ) However, . the use of this method requires that the individual products be punched upon R card, as the 602A cannot accumulate 19 individual sums. After punching, the cards must be resorted by rows, as the answer is the sum of the products in any given row ( b ~X B1.1 B1,?. bls X B1,19). The anewer is then obtained by running the cards through the ralculator n vcond time to provide the Punis of these products.
+
+
...
.
+
62 hi
1
I
Bti,i
B17.2
= b = x =
BU,J
Bii,4
bl7
B10.3
Rts,r
E1813
Rl9,4
bm b1s
I
ZBn,z rBn,3 ZBrt,p elements of inverse matrix sample coefficients. unnormalized % romponition
Figure 3.
19
x
x 3
br
TBn,l
R
Xt X I
i B M , ~ B1a.p B I Q , ~B I ~ , z
. ..
Xl7
XI8
XI0 CX,,
19 Inverted Matrix Plus Summation Check
The first step is to determine the capacity of the 602A for the problem in question. In this case we are desirous of obtaining the acrumulative results of a eeries of multiplications. The 602A is composed of storage units and counters. The storage units are available for storing data supplied from a punched card and for results obtained on the counters. The main function of the counters is to add, subtract, multiply, and divide. Multiplication and division are actually accomplished b addition and subtraction--e.g., multiplication is successive a&ition. The counters may also be used as storage units. In the standard 602A there are ten units of storage of six digits each, and a storage unit, S o . 1R (eight digits), which has a special purpose in that, in order to perform multiplication or division, one of the factors to be multiplied or divided must bp entered into 1R. The six counters are set up as follows: Nos. 1 and 2 are six digits, Nos. 3, 4, and 5 are four digits, and No. 6 is six digits. In the type of roblem discussed, the inverse matrix values are four digits and t f e sample values are five digits. Thus nine digits arp required for the result. To provide the necessary nine digits, counters 2 and 3 (ten digits) and counters 5 and 6 (ten digits) arc coupled together. It is not possible to use counters 1 and 4 together, as counters may be coupled only by joining adjacent counters. In the operation of the calculator the data to be supplied to the calculator are punched on a card. As this card is fed to the calculator, the data are read from the card by electrical brushes which receive an impulse whenever a hole is present. Thus, the data are transferred from the card into the storage units mentioned above. The card a t this point may be held for punching of the results, or ejected from the calculator. After the data have been entered, program steps are set up on an electrical contact board capable of many operations, in order to carry out the required calculation. These boards operate in a fashion analogous to the operation of a railroad system, being divided into a “track system” and a “signal system.” The track system is the wiring over which data are transferred from one point to another, such as the transformation of data on the punch card to the storage units. The signal Bystem is the actuation of electrical signals in the proper sequence for the transmitting information or carrying out calculatione. When the calculations are complete for one card, the results can be punched o r accumulated as desired. At the same time the calculator resets itself for the ne\t card.
Howevcr, if the calculations are cari ied out horizontally instead of vertically, it is possible to accumulate the sum of 19 products without punching the individual results. This accuniulative result is then punched on a plain card, known as the trailer card, which follows the 19 matriv cards. The complete description of this method i R available from the authors. 1. The inverse matrix shown in Figure 3 is divided into blocks of eight numbers, such R R
2. These eight values a.lonc, with the corresponding b values (for this example b,, bt, b?, ?nd b4),are punched in a single card called a matrix card. This i~ a maximum number of items which can be st.ored in the standard 602A. 3. The calculator is t’hen programed t.0 carry out two multiplications simultaneously-t’hat is, bl X & , I and bl X B2,1. This is possible because counters or accumulator8 are available for two individual sums. 4. The second prograin step multiplies b, X B1.2 and b2 X R,,?, and the third program step multiplies ba X B1.3 and ba X E&,,, t’hen b? X b1.r and b, X & , I . The resulting products are accumulated in the counters that performed the multiplication. 5. Steps 2 to 4 are carried out in t,he passa e of one matrix card t,hrough the 602A. .4 second matrix car! containing the followingis then fed into the c:ilculat’or. 2 3 1 . 6 R1.6
B1,i B,,!
B2,5B2.6 B2.7 & , a bs
b6
bi
bs
6. In order to develop the 19 products, five matrix cards are needed. However, because of the procedure used, two answers (on answer cards) are obt’ained with every five matrix cardst,hat is on the first five cards answers for row 1 and row 2 are developed. Thus, to calculate a 19 X 19 inverse matrix requires 50 matrix cards and 19 answer cards. After the 19 answers have been obtained it is necessary to normalize to 100%. In the case of mass spectrometer calculations, the mole per cent (air-free), t,he mole per cent (air, nitrogen, carbon monoxide, carbon dioxide-free) and the wei ht per cent (air. nitrogen, carbon monoxide: carbon dioxidefree? are required.
V O L U M E 23, NO. 10, O C T O B E R 1 9 5 1
1421
Table I. Time Required for Solving Problems IBM,
Min. I.‘irst step“ (obtain unnormalized mole 70, includes check) Second step (divisors for normalization) Third step (normalized answers) 1 Fourth step (tabulation) Total time for one sample 12 ’/ Each step is a separate pars of cards through machine.
I:
-
Analog Computer Plus Machine Min.
60 30
90
The three divisors to be used for calculating the above mole per cent values are obtained by running the 19 answer cards through the calculator a second time. At the same time, the mole per cent unnormalized is multiplied by the molecular weight factor
(si).
After pamng through the 602-4, the 19 answer cards contain mole per cent unnormalized and the products of mole per cent unnormalized times the molecular weight factor. Trailer cards, introduced with the 19 cards, contain the three divisors and the suin of the products of mole per cent unnormalized times the molecular weight factor, excluding air, carbon monoxide, nitrogen, and carbon dioxide. The trailer cards are then fed into the 602.4, followed by the 19 answer cards for division, The normalized answers niole per cent, mole per cent (air-free), mole per cent (air, nitrogen carbon monoxide, carbon dioxide-free), and weight per cent (air, nitrogen, cnrlion monoxide, carbon dioxide-free) are calculated and punched 011 the individual answer cards. .In addition to the above results, the specific gravities and the weight per cent (air, nitrogen, carbon monoxide, carbon dioxidc-free) are required. These valucs :ire calculated at the same time as the normalized mole per cent. The final step is to reproduce the results which are on the 19 aiistver cards on a form for distribution to the interested parties. Thiz is carried out on the I B V tabulating machine.
Economic Justification of Punch Card Calculators. In order to justify the application of IBhI calculating equipment to spectrometric analyses, a saving in money and/or manpower must be realized. This means that the type of calculation must be chosen to achieve this end. It i3, of course, not economically feasible to utilize the IBM equipment for simple calculations, unlesz the number of such calculations is extremely large. The number of unknowns must be large and the number of samples using the eame matri\ must be numerous. However, with the
general procedure as outlined above, it is possible to carry out the multiplication of any other matrix without changing the n-iring of the calculator. The time requirement to solve for 19 unknowns on an IBhl calculator is compared to conventional analog computer-mechanical calculator methods in Table I. These figures are based on duplicate calculations for the calculating machine method. Calculations are made in duplicate to reduce the possibility of human error, as experience indicates that this is the main source of error. This factor is eliminated in the IBM method. An internal check is carried as the 20th equation in the IBhl calculator to verify the calculations. It is known that the sum of the elements of the product of a matrix times a vector is equal to the product of the vector and a row representing the sums of all the matrix elements for each column. Considering Figure 3, it can be seen that Z X , results from multiplication of the ZB and b values, where, for example, ZB,,r represents the total of the matrix elements of the fourth column. To check the multiplication, the total of the per cent composition values (XI X 2 X , , etc.) is compared with the Z X , value. On the basis of 100 samples per week, the IBhl method would require 25 hours (conservatively) and the computer-calculating machine procedure 150 hours, a saving of 125 hours, or 3 men. In addition to these savings, about 15 hours of calculation time per week are available for the solution of other problems.
+ +
ACKNOWLEDGRIENT
The authors wish to thank the International Business Machines Corp. and in particular Stanley Rothman of the Watson Laboratories and J. J. Hatch, Jr., J. F. Bel1,and C. E. Thamni of the Elizabeth, N. J., office of the I.B.M. Corp. for their assistance in the solution of this problem. LITERATURE CITED
( 1 ) Crout, P. D., Trans. A m . I m t . Elec. Eizgrs., 60, 1235 (1941). (2) Heigl, J. J., Bell, M.F., and IYhite. ,J. U.,ANAL.CHEM.,19, 293
(1947). (3) Leland, 0. M., “Practical Least .squares,” 1st ed., p. 40, Yew York, XlcGraw-Hill Book Co., l??l. (4) Runge, C. D. T., and Konig, H., Xunlerisches Rechnen hlonograph,” KO. 11, p. 65, Grundlehren Math. Wissenschaften, 1024
RECEIVED April 27, 1951. Presented at the Pittsburgh Conference on Analytical Chemistry and ripplied Spectroscopy, Pittsburgh, Pa., March 5 to7.1951.
improved Method for Determination of Oxygen \ I N C E S T i. CAMPANILE, JACK H. BADLEY, EDWARD D. PETERS, ELIGIO J. AGAZZI, AND FRANCIS R. BROOKS Shell Development Co., Emeryville, Calif.
0
S Y G E N is one of the most coininon constituents of organic
materials, yet it is most often determined by difference, after the determination of all other elements present. This approach requires the precise determination of two or more elements, and places the sum of the errors of these analyses on the oxygen value. In addition, it is a very expensive and time-consuming practice, especially when the ovygen value is the only one of real interest. Furthermore, the accurate determination of low oxj-gen contents by difference is very difficult, if not impossible, therefore, numerous attempts have been made to devise methods for its direct determination. In an excellent review of the literature, Elving and Ligett ( 4 ) indicated that the most advantageous method devised was the Schiitze-Unterzaucher (10-12) method. This method, first pro-
posed by Schutee, is based on thermal decomposition of the Sample in a stream of nitrogen and passage of the pyrolysis products over carbon a t 1000° C., resulting in conversion of all oxygen present to carbon monoxide. The carbon monoxide is carried over iodine pentoxide, where it reacts to form carbon dioxide and iodine. Either the carbon dioxide or iodine is then determined, the former gravimetrically by absorption on Ascarite and the latter by titration with standard thiosulfate solution. This method was adapted to a micro scale by Zimmermann ( 1 4 ) and, later, considerably improved by Unteraaucher (12) who presented analytical data for a number of compounds which showed an average error of only 0.1 % oxygen. Subsequent investigators have experienced difficulties with the method; few have been able to achieve the negligible blank re-
