ANALYTICAL CHEMISTRY.1 . INTRODUCTION.ANALYTICAL chemistry is relatively, but not absolutely, an esact science.All determinations are subject to errors, and it is essential to have a properappreciation of their magnitude; it is important to know what real weightcan be placed upon such terms as accuracy and precision. Statisticalmethods are being increasingly applied for this assessment, and in additionthey are used both as a guide when designing an experiment to obtain thedesired information with a minimum expenditure of time and material, andas a tool when the experiment is completed to abstract maximum informationfrom the data. It is appropriate, therefore, that a substantial part of thisReport should be devoted to the application of such methods to chemicala iialysis .During recent years an enormous amount of work has been directed tothe application of X-rays for analytical purposes.This subject was dealtwith ten years ago and short references have appeared in other Sectionssince. It seemed desirable, however, to enumerate the more importantinstances where information of value has been obtained, as this mill suggestpossibilities in other directions.The introduction of a variety of new surface-active agents has raisedmany analytical problems. This field impinges on that of the oils and fatsand the common ground leads in several directions. A survey has thereforebeen made of some of the work in both fields. J. R. N.2. THE APPLICATION OF STATISTICS TO CHEMICAL ANALYSIS.The use of statistical principles both in designing experiments and inextracting from them the information sought has been common practicefor many years among thosc employing biological methods of assa8S;.Theinherent variability of the dosc-response rehtionship from aniinal to animal,and even from day to day in the same animal, is so large that the recognitionof effects genuinely caused by controlled factors, as distinct from those dueto the random fluctuation of uncontrolled factors, is hardly possible unlessstatistical methods are employed. On the. other hand, it is characteristicof chemical and physical methods of analysis as a class that the inherentprecision is relatively high and the relation of the quantity actually measuredto the parameter it is desired to estimate is constant, or sufficiently so toneed only occasional checks.In consequence, while an estimation of thevitaniin-D content of a food may necessitate simultaneous observations on40 or more rats, a determination of its nitrogen content will often mean butone observation, even duplimte analyses being regarded in many laboratoriesas an unnecessary and time-wasting refinement\VOOL) : APPIIICATION OF STATISTICS TO CHEMICAL ANALI-SIS. 265It will not be surprising, therefore, if a report of progress in the applic-ation of statistics to chemical analysis appears to contain a disproportionatenumber of‘ references to biological methods. Nevertheless, there is a growingappreciation of the need for attention to a t least the more fundamentalstatistical principles in all analytical investigations.The Society of PublicAnalysts and Other Analytical Chemists held a joint meeting with theFood Group of the Society of Chemical Industry in December 1946 to discuss“ The application of statistics to food problems ”, and while three of thepapers 1, 2, described the use of statistical techniques in elucidating andinterpreting analytical results, the introductory paper * stressed even morethe value of a stat’istical approach when designing the experiment.Appreciation by experimenters of the need for calling the statisticianinto consultation before rather than after the experiment is a growth ofrecent years-largely stimulated no doubt by R. A. Fisher’s well-knownbook 5-b~t analysts are beginning to realise how this can ensure the maxi-mum return for their experimental work.So often the devising of a newanalytical technique involves an investigation of the iiifluence of manyrariables-the concentration of one or more reagents, the temperature ofreaction, the time factor at this or that stage of the analysis, and SO on.The type of experimental design known to statisticians as “ factorial ”, inwhich the effect of changing several variajbles simultaneously can be examined,offers many advantages over the older type of experiment in which onefactor is varied a t a time, all others being held constant, so that “inter-action ” effects cannot be detected, much less measured. The Rfinistry ofSupply has published a book by K. A. Brownlee in which this point isvery clearly made, and it is stressed in another recent book by a team ofworkers employed by I.C.I.Ltd. This also summarises the statisticaltechniques and computations most likely to be useful to laboratory workers,with a clear exposition of the conditions in which each is applicable.An instance of an analytical investigation with a well-planned designis afforded by a paper on the correct empirical factor to be used in thedetermination of pyrethrin I by the mercury method. Five observerstested the effect of many variables on the factor obtained, and the analyseswere so randomised (duplicate analyses never being performed on the sameday, for instance) * that the influence of each factor, the relative precisionof the workers, and the standard errors attaching to each set of conditions,could be separately evaluated.In consequence, those details of the tech-nique which need to be rigidly standardised could be identified and anW. B. Adam, Anal@, 1948, 73, 7.E. H. Shiner, ibid., p. 15.“ The Design of Experiments ”, Oliver and Boyd Ltd., 4th edition, 1947.“ Industrial Experimentation ”, H.M.S.O., 2nd edition, 1947.“ Statistical Methods in Research and Production ”, editecl by 0. L. Daviesa G. T. Bray, S. H. Harper, I<. A. Lord, E’. Major, :m(L E’. 13. Tresttciern, J . ~ 5 ’ ~ .D. I<. L. Blnxter, ibid., p. 1 1 .D. J. Finney, ibid., p. 1.Oliver and Boyd Ltd., 1947.C ‘ ? L C ~ . IME., 1947, 66, 275.* On this point, see also refs. (17)-(21)266 ANALYTICAL CHEMISTRY.empirical factor stated with known and high precision.N. T. G~idgeman,~in order to estimate the relative potencies of vitamins-D, and -D3, devisedspecial designs adapted to the subsequent use of covariance analysis toimprove the precision of the results. In all analytical research the valueof modern experimental designs can hardly be overstated ; too many papersstill appear in which a most painstaking investigation involving perhapshundreds of analyses has not yielded anything like the amount of inform-ation that the investigator’s labours deserved-and could have achieved,if he had given to the planning of the experiment a fraction of the timedevoted to the practical work.Once the experiment has been planned, the work of the analyst beginswith the taking of the sample.The necessity for the sample to be trulyrepresentative of the bulk has often led to the drawing of a sample fromevery container. The U.S. Customs Regulations of 1937, for example,called for this method when sampling imported raw sugar in bags. Theprocess is time-consuming and damages the bags. Experiments weretherefore conducted 10 to examine the possibility of sampling a proportiononly of the bags without thereby incurring an excessive risk of error in thefinal result. The standard Customs trier was first compared with twoalternative patterns ; they were found to give almost identical standarddeviations and offered no advantages, and the standard trier was used forall subsequent tests. Knowing the standard deviation, it was now possibleto determine what proportion of bags would need to be sampled for anygiven sampling error, and calculation indicated that to sample 1 in 7 of theaverage cargo of 20,000 bags should be satisfactory.This was verifiedexperimentally; in a series of 5 cargoes, the maximum difference betweenthe revenues as estimated from sampling all the bags and from 1-in-7sampling was $68 in a total of $124,000. A method for mixing sampleswas developed experimentally which was less laborious than the older handmethod and did not lead to any loss of precision.A novel approach to the question of sampling made by A. Wald l1 hasresulted in the creation of a new technique known as “ sequential sampling ”which has many advantages in certain circumstances, while the sequentialprinciple, of which a lucid exposition has been given by G.A. Barnard,12is capable of wide application. Instead of taking a fixed number of samples-more generally, instead of making a fixed number of observations-thenumber of observations is determined by the results obtained. At eachstage after making the lst, 2nd, . , , etc., observation, calculations aremade which enable one of three decisions to be taken-to take action 1,which may be the acceptance of the material under examination; to takeaction 2, which may be its rejection ; or to make another observation. Theexperiment terminates with the taking of one of the f i s t two decisions,Quart. J . Pharm., 1945,18, 15.lo E. F. Kenney, I d .Eng. Chem. Anal., 1946,18, 684.l1 Ann. Math. Stat., 1945, 16, 117; J . Arner. Stat. ASSOC., 1945, 40, 277.l2 J . Roy. Stat. SOC., Suppt., 1946, 8, 1WOOD : APPLICATION OF STATISTICS TO CHEMICAL ANALYSIS. 267which happens as soon as enough information has been accumulated topermit of the acceptance or rejection of the material with a predetermineddegree of confidence, and no more work is done than is sufficient for thispurpose. The average sample size over a period using this technique isalways less-sometimes much less-than the size of the fixed sample requiredin the usual technique for equal improbability of wrong decisions.An example is afforded by C. W. Churchman’s application l3 of thcsequential principle to the problem of discriminating with as few analysesas possible between alternative empirical formule for an organic compound.In the simplest instance, only one element is determined, the theoreticalpercentages of this element for the two formule being a, and u, respectively.An element should be chosen for which (a, - a2)/s is as large as possible,where s, the standard error of the determination, is assumed to be knownfrom previous experience.After n determinations the results are summedand the total compared with two quantities A , and A , which are simplefunctions of n and the known quantities, a,, u,, and 9. If the sum of theresults is less than A,, then a, is accepted as correct; if it is greater thanA,, then u, is accepted. If the sum lies between A, and A, another analysisis performed. A somewhat more complicated procedure is necewary iftwo or more elements are determined, but the principle is the same.F.Yates pointed out in 1935 l4 that the precision with which a numberof small objects could be weighed was much improved for a given numberof operations by weighing them in combinations rather than singly.H. Hotelling l5 has examined the general problem both for the type of balancewith which objects may be placed in either pan and for the spring balanceor other type in which one pan only is available. The principle involvedapplies whenever the weights of n objects are of the same order and lightenough for their sum to be within the capacity of the balance. It is assumedthat s, the error of one weighing, is constant whether the objects be weighedsingly or in groups.Then the n weighings which must be made in anyevent can be used to better advantage than merely weighing each objectseparately. As an illustration, consider the weighing of four objects, a,b, c, d, on a balance not needing a zero correction. The variance of a singleweighing is s2, whether one object be weighed or four. Let the followingfour weighings be made :a + b + c + d = y,;a - b + c - d =g3;a + b - c - d =y,;a - b - c + d = yq.Objects with a minus sign in these expressions are placed in the right-handpan and those with a plus sign in the left-hand pan. The weight of objecta is now given by t(y, + y, + y3 + yq), with similar expressions for theweights of the other three objects.The variance of any one y/4 is s2/16,so that the variance of the weight of a is $/4, which is a quarter of thevariance of a single weighing of u by itself. It is not possible, however, togive schemes for p weighings of n objects with minimum variance for all14 J. Roy. Stat. SOC., Suppt., 1935, 2, 211. l3 I n d . Eny. Che~ra. Anal., 1946,18, 267268 ANALYTICBL CHEMISTRY.values of p arid n though solutions have been given 15y16 for several specialcases. The technique is interesting and elegant but does riot appear tohave much practical application to analytical work. Apart from otherconsiderations, the error of a single weighing is nearly always so much lessthan other experimental errors that its reduction would not modify appre-ciably the combined error of an analysis, and against such reduction as iseffected must be offset the risks of experimental mistakes in selecting theobjects for each group-weighing, and of arithmetical mistakes in the calcul-ations ! In gravimetric work of high precision, however, or if analyses areto be carried out on quantities which are smaller than is desirable havingregard to the sensitivity of the balance to be used, the group-weighingtechnique may be of value.The improvement in precisioii which theoretically results from replication,and the insistence of statisticians that there should always be some estimateof the error of an analysis, has led to a commendable spreading of thepractice of performing analyses in duplicate or even in higher replication.There is a trap here, however, to which attentionwas drawn over 30 yearsag0.17 An apparent concordance between duplicates may give a misleadingimpression that all is well if the anaIyses are not independent.The differ-ence? between pairs of truly independent analyses may contain componentsdue to differences between the samples analysed, the techniques of theindividual workers, the days of the week or the months of the year whenthe analyses were performed, the reagents or the apparatus of different-laboratories. So-called duplicate analyses are, however, often made bythe same worker in the same laboratory on the same day, so that the lastthree components disappear. Sometimes, howibile dictu, only one portionof one sample is weighed out and the alleged duplicates are but aliquotparts of the same filtrate! In such circumstances, there may be a largesystematic error which will completely escape detection.R. F. Moran l8points out that, since the ratio of the standard error of a single determinationto that of the mean of two independent determinations is theoretically \'2,a test of the independence of duplicate analyses is afforded by examiningthe ratio actually obtained in practice. In one example which was investi-gated from this point of view the ratio was foiind to be not 1414 but 1.05.The duplicates were thus highly correlated ; the additional genuine in-formation that was being obtained in return for the extra work involvedin duplication was quite negligible, while the true magnitude of the errorsinvolved was as unknown as if only single analyses had been performedJ.Mandel19 has extended this argument to cover the estimation of thevalue of AT-fold replication in terms of the ratio of the variance of one deter-mination to that of the mean of AT determinations, which he calls the PO-efficient of improvement. It will clearly vary from 1 for no improvementto N when the analyses are quite independent. A proper examination ofAnn. Math. Stat., 1944, 15, 297. l8 I(. Kishen, ibid., 1945. 16, 294.l9 Ibid., 2946, 18, 280.l 7 " Student ", Riometrika, 1909, 7 , 210; 1914, 10, 179.l8 Ind. Eng. C1m.m. Anal., 1943, 15, 361tihc matter, however, woiild require a fairly full investigation by a " researchanalyst ", to use Mandel's phrase, and if in a particular instance this weredeemed to be worth while, the experimental design ought to be such thatthe results could be used for an analysis of variance.The practical moral of these considerations is that replicate analysesshould as far as is practicable be so performed that none of the possiblecomponents of error is suppressed in the results.If, for example, ananalyst is to make triplicate analyses on each of 3 samples, it is far betterthat he should perform one analysis on every sample on each of 3 days than3 analyses of sample 1 on day 1, 3 of sample 2 on day 2, and 3 of sample 3on day 3.20 Checks by independent workers, if possible in another laboratory,are always useful and sometimes revealing, as is shown by H.G. MacColl 21in describing a system of controlling the accuracy of routine analyses.From a large number of analyses of the same sample the standard deviations of the determination is first estimated. A4nalyses of a reference sampleof known composition are then made daily and plotted on a control chartof the kind familiar to users of " quality control " methods in industry,with a line drawn a t the true value and other lines either side of it at distances&29 and 3 3 9 apart. Determinations falling outside the outer or " action "lines suggest investigation of the reason. The averages of the 6 analysesmade every week are also plotted on a control chart with lines &2s/1/6and 3s/& apart; divergences shown on this chart call for more seriousattention as being indicative of persistent causes.Samples are regularlyinterchanged between laboratories and the differences plotted on a similarchart with a central line at zero. The method of setting up such controlcharts, and their uses in general analytical work, have been discussed byG . Wernimont 22 and J. A. MitchellY23 while others have described theirapplication in special case^,^*^ 25 including organoleptic tests.26 Theyinvolve little labour once the necessary initial data have been obtained,and enable both occasional sudden alterations and slow persistent driftsin accuracy or precision t o be detected before damage is done.The use of the range of a set of observations as a measure of their " spread "or dispersion about the mean is a time-honoured practice.Statisticiansprefer the calculation of the standard error, on the ground that (given anormal distribution) it is the only fully efficient statistic in the sense that italone utilises the whole of the information available in the data. It is truethat the range is inefficient, for i t measures the difference between 2 only ofthe observations, the magnitude of the others being immaterial. It hasthe merit, however, of requiring no calculation other than a single subtractionand is sometimes quite suitable as a quick check in analytical ~ o r k . ~ ' An?O J. W. Tukey, Anal. Chem., 1947, 19, 957.22 I n d . Eng. Chena. Anal., 1946, 18, 587.2-1 W. N. W. MTallace, J . Proc. Austral. Chem Inst., 1945, 12, 239, 243.2.i J.D. Heide, India Rubber World, 1946, 114, 653, 66s.46 S. Marcuse, J . ditter. Stat. -4ssoc., 1945, 40, 214.2 7 1%. G . Newton, P?iem. and Id., 1945, 322.21 Chemn. and Irzd., 1944, 418.p3 Anal. Ghen,., 1947, 19, 961270 ANALYTICAL CHEMISTRY,est'imate s1 of the true standard deviation c can be made by dividing therange w by a factor d, where d depends on the size of the sample a n d hasbeen tabulated by 0. L. Davies and E. S. Pearson.as Compared with theestimate of 0 afforded by the standard error s as usually calculated, s1 isa t its best when the set of observations is broken up by the experimentaldesign into m sub-sets of n observations each. The range is then calculatedfor each of the m sub-sets separately and the mean range ii? is divided bythe correct value of d to give sl.When n is in the neighbourhood of 2-6,this estimate is reasonably efficient, and E. C. Wood 29 has pointed oiit thatthese conditions obtain in microbiological assays, in which about this numberof observations is usually made a t each of several dose-levels. A checkcan thus be kept with very little trouble on the error of routine assays andany tendency to loss of precision noted and investigated. The estimatea1 may also be used as is the standard error s for testing the significance ofthe difference between two means; just as the ratio of a difference to itsstandard error s is the bmis of " Student's " well-known t-test, 80 an analogousstatistic G is obtained by dividing the difference by the estimate sl, and itsefficiency is little inferior to the t-test when the sample size is less than ten.30E. Lord 31 has given tables of the distribution of G for various values of mand n which can be used in the same way as tables of the distribution of t .The quantities actually observed or measured in the course of an experi-ment are not necessarily suited as they stand to the computation by standardstatistical processes of the result and its standard error.For reasons whichare discussed below, it may be desirable to transform the independentvariate x, the dependent variate y, or both, into other functions. A familiarinstance, or rather class of instances, is the use of the logarithm of the doseas the dose metameter * in biological assays. J. H. Gaddum 32 has collectedmany examples from widely varied fields of investigation in which thetransformation X = log x or its alternative X = log (x & x,,) has beenfound valuable for the reason that the distribution of X is normal whereasthat of x is not. He refers to the distribution of x in such cases as " log-normal ", and suggests that, whenever the variance is relatively large, thetransformation can do little harm and may facilitate interpretation of thedata.N. T. Gridgeman33 has also discussed the handling of assays inwhich this transformation is made, with special reference to vitamin-Dassays, while E. C. Fieller 3* has surveyed the principles involved in applyingtransformations not only to the dose but also to the response in biologicalassays.There is a fundamental distinction between these two possibilities ;the transformation of the independent variable x may affect the wholedesign and method of' computation of the experiment, whereas the trans-28 J . Roy. Stat. SOC., Suppt., 1934,1, 76.30 J. F. Daly, Ann. Math. Stat., 1946, 17, 71.31 Biometrika, 1947, 84, 41.33 AnaEyst, 1946, 71, 376. * A word introduced by A. L. Bacharach at the suggestion of L. Hogben to meanthat function of a quantity actually measured in an experiment which is iised in thesubsequent calculations.2Q Chem. and Ind., 1947, 334.82 Nature, 1945, 156, 463.34 Ibid., 1947, 72, 37WOOD : APPLICATION OF STATISTICS TO CHEMICAL ANALYSIS. 271formation of the dependent variable y may-subject to considerationsdimmed below-be regarded as a purely arithmetical device without effecton the experimental or statistical techniques used.An excellent summaryof the uses of transformations in general has been given by M. 8. Bartlett,35and D. J. Finney36 has emphasised the essential unity of the principlesunderlying all biological assays by bringing together the transformationsused in different types of assay and laying down certain generalisationscovering them all.Whatever method is used for calculating the result of an assay, twoassumptions are implicit-that the dose and response metameters are sochosen as to be linearly related to each other within the range used in thecomputations, and that the response metameter is normally distributed a tall dose-levels.These may be referred to as the assumptions of linearityand normality. A moderate degree of departure from normality is notvery important ; * but the assumption of linearity is necessary if the calcul-ations are to be reasonably simple, and the transformations used in practiceare in nearly every instance chosen from this point of view. Usually,however, the formula.? and computations then applied have been based on athird assumption, namely, that the variance of the response metameter isindependent of the dose-level, or in other words that no more weight is tobe attached to observations a t any one dose-level than a t any other. Ifin any instance this assumption is untrue, then the results obtained may beto that extent erroneous. In consequence, Fieller 34 advocates that thattransformation should be sought which leads to stability of variance, withlinearity as a desirable but secondary consideration.The reverse approachmay be dangerous if a transformation which achieves excellent linearitycauses the variance to become unstable. Fieller gives a method for deter-mining the correct transformation to stabilise the variance in any instancein which the law connecting the variance with the mean response is known.On the other hand, if a transformation is found which stabilises thevariance but gives a marked deviation from linearity, the efficient estimationof the result and its standard error will be very difficult and even impossible,and Pinney36 suggests that the better line of attack is to make linearitythe primary objective.If as a result the variance is found to alter fromone dose-level to another, then the appropriate weights should be attachedto the observations in the ensuing calculations. This may complicatematters somewhat, but the complications are not excessive, and at leastthe conclusions reached will be trustworthy.In certain circumstances, moderate departures from linearity may havelittle effect on the accuracy of the results-as in the well-known " 4-point "design used in biological assays 37-though unless the linearity can bechecked there may be no criterion of the validity of the so that morecomplex designs are sometimes desirable. The general method of computing35 Biornetrics, 1947, 3, 39.37 E. C.Wood, Nature, 1944, 153, 84. * See the concluding paragraph of this section.36 J . Roy. Stat. SOC., Suppt., 1947, 9, 46.38 D. J. Finney, ibid., p. 284272 ANALYTICAL CHEMISTRY.the result of assays in which the response metameter is linearly related tothe “ logdose ” has been given by, iizter a h , J. 0. Irwin,39 and for assay?of the cross-over type a complete description of the computations is givenby K. W. Smith, H. P. Marks, E. C. Fieller, and MT. A. Br0om.~0 Morerecently, L. I. Pugsley 41 ha9 well summarised the calculations of ’’ logdose ”assays both by Irwin’s method and vin a11 analysis of variance; the secondmethod is particularly useful for symmetrical 6-point designs since i t enables5 components of the “ between-doses ” variance to be examined separatelyfor significance.I n quanta1 assays, where the response is of the “ all-or-none ” type, thetransformation of the response to the normal equivalent deviate or “ probit ”as suggested originally by C.I. Bliss42 has been widely used to convertthe typical sigmoid logdose-response curves into approximations to linearity.D. J. Finney43 has recently published a book on the many applications ofprobit analysis. C. W. Emmens44 found that the relation between thelogdose of a hormone and its effect on the growth of an organ \vas oftenbetter fitted by the “ logistic ” curvewhere IY, p, and L are constants. In consequence, J. Berkson 45 has proposedthe use of “ logits ”, based on this curve just as probits are derived from thenormal curve; the logit of y = log(1 - y) - log y.He finds that logitsfit certain examples better than probits. \V, R. Thompson 46 has describeda method based on interpolating between two adjacent “ moving averages ”,these being the means of k consecutive values of the response metameter(it is assumed that logdoses are equally spaced) ; k is chosen from experienceof the type of assay being performed and will often be 2 or 3, and the twomoving averages used are those which bracket a probability of responseof 0.5. The method is fairly simple, but the calculation of the standarderror of the result can only be performed approximately. The well-triedprobit iiiethod is by no means as laborious as those who have not muchexperience of it tend to think ; with practice, the process becomes automatic,and most of the work involves little more than the intelligent use of tables.The various procedures discussed above are none of them applicableto microbiological assays, in which other relationships are found to prevailbetween the dose and the mean response.In a few types of assay, thesequantities are linearily related to each other, and no transformation isneeded. The potency of the Test Preparation (T.P.) relative to that ofthe Standard Preparation (S.P.) is then calculated from the ratio of theslopes of the T.P. and S.P. dose-response lines, so that these may conveniently39 J . Roy. Stat. Soc., Suppt., 1937, 4, No. 1 ; J . Hyg., 1943, 43, 121.4 O Quart. J . Pharm., 1944, 17, 108.42 Ann. App. Biol., 1935, 22, 134.43 “ Probit A4nalysis ”, Camb.Univ. Press, 1947.4 5 .J. =Imer. Stat. ASSOC., 1944, 39, 357; 1046, 41, 70.4 6 Rnct. RPP., 1917, 11, 115.‘l E17docriuology. 1946, 39, 161.44 t7, Endoc~in., 1940-41, 2, 194WOOD APPLICATION OF STATISTICS TO CHERITCAT, ANALYSIS. 27.3be referred to as slope-ratio assays.47 The most efficient experimentaldesign, with the correct methods of computing the result and the fiduciallimits of such assays, and of testing their validity have been discussed fairlycompletely both for the case in which there is only one T.P.48349.50 and alsowhen several T.P.s are to be assayed sim~ltaneously.~~Tn most microbiological assays, however, the dose-response relationshipis curved throughout its length. The transformation of both the dose undthe yesponse to the corresponding logarithm was found 52 to linearise therelationship for assays of many amino-acids and some vitamins.It is truethat the variance after transformation appears to be no longer independentof the dose-level, an effect which, as stated above, is theoretically disastrous.The high precision of microbiological assays fortunately reduces the dangerconsiderably, and D. J. Finney 53 has found in two assays he has testedthat, when due allowance is made for the heterogeneity of the variance, theresulting rabher lengthy computations give a result negligibly different fromthat given by the usual simple calculation assuming constant variance.The same '' log-log " transformation has also been found to linearise therelation between dose and diameter of the zone of inhibition in a method ofpenicillin assay; between concentration of disinfectant and time to effectsterilisation under standardised conditions ; 55 and between titration andconcentration of sugar in the well-known Lane and Eynon volumetricmethod.56 G.E. P. Box and H. Cullumbine 57 found in experiments withcertain toxic substances that the dose was linearly related to the reciprocalof the survival time and that this linearising transformation also normalisedthe distribution and stabilised the variance-an unusually complete set ofadvantages.A few papers have appeared recently in which the inherent errors ofmalybical methods have been statistically investigated. A. C. Oertel andH.C. T. Stace 58 have examined the various factors contributing to the errorof apectrochemical (flame) analysis of cations. It was found that evenwith an element&ry technique the standard error was less than 4%, and thatmost of this was due to the variations in the photographic plates used.J. Geffner 59 has investigated the same question. 0. L. navies, C. H.Giles, and T. Vickerstaff 60 have compared the precision obtainable with4 7 33. C . Wood, Nature, 1945, 155, 633.4 0 D. J. Finney, Quart. J. Pharm.. 1945, 18, 77.4s E. C. Wood, Analyst, 1946, 71, 1 .j0 E. C. Wood and D. J. Finney, Qtcurt. J . PJLarm., 1946, 19, 112.j1 C. I. Bliss, Ann. Math. Stat., 1946, 17, 232.62 E. C. Wood, Nature, 1946, 158, 835; Analyst, 1947, 72, 84.53 Private communication.'* F.81. Goyan, J. Dufrenoy, 1,. A. Strait, and R. Pratt, J . A w p r . Pharm. Assoc.,6 5 R. C. Jordan and S. E. Jacobs, J. Hyg., 1944, 43, 275 and subsequent papers. '' I!'. T;c'. Zerban, W. J. Hughes, and C . A. Nygren, Ind. Eng. ClrenL. Anal., 1946,G 7 Brit. J . Pharnzncol., 1947, 2, 27.** Anal. GItP?)b., 1947,1g, 1053,1947, 36, 65.18, 64.5 0 .I. LSOC. Chent. Ind., 1946, 65, 350.so J . Xnc. Dyprs Col., 1947, 63, 80274 ANALYTICAL CHEMISTRY.the Hilger photoelectric absorptiometer, the Hilger-Nu t ting spectra-photometer, and a Duboscq-type colorimeter, in determining the strengthsof various dye solutions. The coefficients of variation in the three case8 were1-00, 1-35, and 2.49, respectively. The accumulation of sound data con-cerning the inherent errors of analytical techniques and apparatus is asine qua non for any objective evaluation of the relative merits of alternativemethoda, and it is greatly to be hoped that these papers will inspire verymany more investigations of the same sort.W. J.Youden 61 has pointed out that, whenever an analytical investig-ation involves replicate estimations of a ratio (as, for instance, when theaccuracy of a proposed analytical technique is to be assessed by comparingthe results obtained by its use with those obtained on the same samplesby a standard method), the regression line should be calculated. The slopeof the line is then the best estimate of the ratio sought, while any systematicerror is detectable as a failure of the regression line to pass through theorigin.Several interesting exampIes are given; this paper is worth theattention of every analyst.Finally, a letter from V. J. Clancey 62 should be mentioned which raisesan important point. He has examined the results which have accumulatedin the course of analysing chemically a wide variety of metals, chemicals,and other industrial products, with the view of ascertaining if‘ the distributionof the results was or was not ‘( normal ” in the statistical sense. He foundthat only l0-15% could be so regarded; the remainder were significantlynon-normal. Some 15% were truncated normal curves,* while others wereleptokurtic, J-shaped, or skew. His main conclusion is that great cautionshould be used in applying ordinary statistical tests to the data of chemicalanalysis. The matter needs further enquiry, but the danger seems to theReporter to be small so long as attention is directed, as it usuallyis, primarilyto the mans of a series of observations, for it is well known that the dis-tribution of the means of a series of samples drawn from a population willusually approach closely to normality even if that of the population is widelydifferent from normal.W. G. Cochran 63 gives a thoughtful discussion ofthe consequences to be expected if the assumptions made in an analysis ofvariance are not satisfied, and concludes that while extreme skewness maylead to serious errors, the cases in which the departures from normality aresufficiently serious to give misleading results should be detectable from aknowledge of the nature of the data and from a careful scrutiny of the figuresbefore the statistbal analysis is begun.of some actual experimental data found to be distributed non-normally asshowing that ( ( no serious error is introduced by non-normality in theHe summarises an investigationG 1 Anal.Cheira., 1947, 19, 946.63 Biometrics, 1947, 3, 22.* The Reporter has experieaced this kind of distribution in the moisture content ofmalt extract; it was found to be due to the rejection by the manufacturers of batcheshaving a content above or below the specification limits set by the consumer, so thatthe “ tails ” of the normal curve never reached the consumer’s laboratory.62 Nature, 1947, 158, 339.G4 G.B. Hey, Biometrika, 1938, 30, 68DOTHTE : X-RAY ANALYSTS. 275significance levels of the P-test or of the two-tailed t-test." In any event,it would be foolish to allow the arbitrary 5% level of significance to createa rigid line between conclusions on which, because " significant ", immediateaction is taken and those which, because " not significant ?', are completelyignored. Tests which lead to a result expressed as P = 0.05 " will cor-respond to relative frequencies of exactly 1 in 20 only if certain underlyingdistributions are truly normal (at least for the large majority of statisticaltests in common use), a point of which we can never be certain. In practice,however, we need seldom worry that sometimes we work at a 4% significancelevel and sometimes at a 6% level." 65 Provided the user of statisticalmethods employs the same intelligent judgment and knowledge based onexperience that he brings to bear on his use of chemical and physical methods,the decisions to be taken on the results obtained will be as sound in the onesituation as in the other, while the consequences arising from a mechanicaland unthinking application of text -book rules are equally fraught with danger.Statistics is the tool of the intelligent man, but that is a reason why analystsshould welcome its addition to their workshop.E. c. w.3. X-RAY ANALYSIS.No Report in this series has been exclusively devoted to X-ray analysissince 1938,' though it has been usual to touch upon this subject in Reportscovering other analytical methods.2This period has witnessed developments, not only in technique, but alsoin the evolution of new methods of X-ray analysis.The methods havebecome firmly established, particularly those based on X-ray powderdiffraction, and are well recognised as offering valuable applications tochemistry and metallography, especially where used in conjunction with otherphysical or chemical method^,^, and with a due regard to their limitations.It is important to remember that X-ray technique fills a position in thegeneral scheme of analysis, and brings its own contributions towards aproblem which may be completely solved only with the aid of other methods.Thus, spectroscopy, microscopy, analytical chemistry, diffraction, andphysical testing all have their parts to play,5 and, in addition t o theinformation provided by X-ray methods alone, such properties as refractiveindex, hardness, and density should be used wherever possible.Side by side with advances in X-ray diffraction analysis, other methodsof attack have come to the fore, such as X-ray spectroscopy where greatsensitivity is required, and microradiography where problems relating totexture are involved, and these aspects have contributed to the study of therarer elements and to microanalysis.e 5 D.J. Finney, private communication. Ann. Reports, 1938, 35, 381.Ibid., 1939, 36, 404; 1942, 39, 87; 1943, 40, 32; 1944, 41, 32, 92; 1946, 43, 332.L. K. Frevel, Ind. Eng. Chem. Anal., 1944, 16, 209.C. S. Smith and R.L. Barrett, J. Appl. Physics, 1947, 18, 177.D. Goodman, Iron Age, 1946, 158, 63276 ANALYTICAL CREMISTRY.In this Report) it is proposed to deal with each of these three methods,(a) powder diffraction, ( b ) spectroscopy, and ( c ) microradiography.The literature on the subject of X-ray analysis is widely scattered, asamply illustrated by the references which follow. This underlines the needfor a ceiitralised medium of publication, parallel to the proposed ActnCrystullogruphicn which is to deal with strwctnres and physical and chemicalproperties closely allied to structiwe.G(a) Powder Diffraction.Qualitative A ~ialysis.--'rhe particular value of the X-ray powderdiffraction method lies in its ability to detect chemical compounds or alloyphases and to distinguish between the different polymorphic forms in whichit substance may exist,' whereas many other analytical methods yield noinformation regarding the state of combination of the elements present.Following the work of J.D. Hanawalt, H. W. Rinn, and 1,. K. Frevel,8the outstanding event during the period under review has been thepiiblication by the American Society for 'resting Materials, in co-operationwith the American Society for X-Ray and Electron Diffraction and theInstitute of Physics, of the X-Ray Diffraction Index.g The first issue (June1945) comprises some 4000 cards and gives data for 1300 elements andcompounds, and the first supplement (August 1945) covers an additional1500 substances.Each card shows the interplanar spacings of the three strongest powderdiffraction lines given by a substance, followed by a list of all the lines forwhich data are available, together.with their relative intensities. Theprocediire for identifying an unknown substance 4 9 8 y is to compare thespacings of the three strongest lines with those given in the index, and thento check the remaining lines both for spacing and for relative intensity. Itis possible in this way to identify mixtures of two or three components.In the future there will be a tendency towards using the innermost line,i.e., the line of greatest spacing, irrespective of its intensity, in addition tothe three strongest lines. In this case it will be necessary also to specify the'' cut-off )', or greatest spacing measurable on the apparatus used.14'Fables of diffraction data for minerals have also been pub1ished,l5-l8 inJ .C'herrL. Physics, 1947, 15, 847; J . Xci. Instr., 1947, 24, 280.H. 1'. Hooksby, J . Roy. SOC. Arts, 1942, 90, 673.l i d . Eng. Cheiri. Anal., 1938, 10, 437.Data Cards for the Identification of Crystalline Materials by the Hanawalt X-RayDiffraction Method, A.S.T.M., Philadelphia, Pa.lo -4.S.T.M. Standards, 1948, Part 1, 1537.11 H. P. Itooksby, (2. E. c'. Journal, 1940,11, 83.l3 W. P. Davey, J . Appl. Physics, 1939, 10, 820.1 4 A . J. C. Wilson, J . Sci. Instr., 1947, $34, 304.l5 A. K. Boldyrev, V. I. Mikheev, G. A. Kovalev, and V. N. Dubinina, -4nn. ???st.l6 M. Mehmel, Portschr. Min., 1939, 23, 91.1 7 V. I. lllikheev and V.N . Dubinina, Ann. Inst. M i r t e s (Leningrad), 1939, 13, I .18 G . A. Harcoiirt. -4nzer. &fir/., 1912, 27, 63.l 2 A.S.T.M. gtandards, 1946, 1R.Mines (Leningmd), 1938,11, Part 2 , 1DOTHIE : Ly-RAY ANALYSIS. 277some of which the indices of the reflections are listed. Further data areavailable for alkylnted phenol derivatives,lg calcium phosphates,20mont bray it e,Z1 delafossi te ,22 vreden b ~ r g i t e , ~ ~ manganosite , p,yrochroite andstilpnomelane ,24 magnesiurii tungstates,25 uranium compounds,26 manganeseminerals ,27 cement clinker components and cementl hydration products ,281)DT,29 hexadecyl trisulphide and tetrasiilphide,30 cobalt carbide,31tantalite,32 lead orthosilicate, rhombic lead oxide (PbO), lead metasilicate,arid basic lead silicate (Pb,SiO,) ,% her~ynite,~* sodium ~ u l p h a m a t e , ~ ~ opiumalkaloids,3, explosi~es,3~ lithium and barium silicates,38 nluminium-copper,silver-copper, aluminium-zinc and copper-beryllium alloys,39 c e l l ~ l o ~ e , ~ ~$-sodium disilicate (Na,Si,0,),41 tantalum, tantalum nitride and columbiumhpdride~,,~ l u z ~ n i t e , ~ ~ cobalt ancl zinc oxide hydrates,44 hea~leu-oodite,~~t x o forms of fr~hbergite,~’ ramnielsbergite,48 glauco~lot,~~hiitchinsonite,50 c h a r n o ~ i t e , ~ ~ and aniIides of aliphatic a ~ i d s .1 ~ ~.In interesting extension of diffraction analysis to the problem ofla ,J. B. McKinley, J. E. Nickels, ancl 8. S. Sidhu, Itbd. Eng. Chew. - ~ ? L c L ~ . , 1944,16,304.20 \I-. F. Rale, J. P’. Bonner, 11.C . Hodge, H. Adler, A. R. JVreath, and R. Bell,a 1 51. A. Peacock and R. M. Thompson, A?/zcr. J l i n . , 1946, 31, 515.2 3 A. Pabst], ibid., p. 539.23 S. Deb, Quart. J. Geol. iMiniitg Met. SOC. Ittdia, 1943, 15, 137.2 4 W. Epprecht, Beitr. Geol. Schuteiz, Geolecir. Xer., 1946, Lief 34.**j S. J. Dunning and H. D. Megau. 7’ram. Faraday ,SOC., 1946, 42, 705.i b i d . , 1945, 17, 401.H. S. Peiser and T. C. Alcock, I.C.I. Ltd., Alkali Div., Research Dept., Winnington,1945.2 i R. JI. Foose, P e m n . Topographic aid (reol. Survey, Brill. M27, 1945.2 5 R . H. Rogue, “The Chemistry of Portland Cement ”, Reinhold Pub. Corp.*@ G. L. Clark and F. W. Cagle, Science, 1945, 101, 465.30 J. 0. Clayton and D. H. Etzler, J. Amer. Chem. SOC., 1947, 69, 974.” L.J. E. Hofer and W. C. Yeebles, ibid., p. 893.’? S. I<. Chakravarty, Quart. J. Geol. Mining Met. Soc. lndia, 1943, 17, 91.33 H . Jagitsch and R. Bengston, Arkiu Kenii, M i n . Geol,, 1946, A22, No. 6.34 .I. Michel-LBvy, J. Wyart, and J i . Michel-LBvy, C’onzpt. rend., 1947, 225, 83.3i S. H. Laning and P. A. \-ail der RIeulen. .I. ,4 nier. Shenr. Boc.. 1947, 69, 1828.s x S. T. Gross and F. W. Oherst. J . Lob. C‘li)?. Mctl.. 1947. 32, 94.3 i -1. 11. Soldate and R. I€. Noyes, l n d . Ewg. Chew. Anal. 1947. 19, 442.38 A. F:. Austin, J. Amer. Ceravk* SOC., 1947, 30, 21 8.39 M. I,. V. Gaylor, J . Iizst. Metals, 1947, 73, Part 2 , Paper No. 1070.4 0 G. Peyronel, Chin). e Z’Ind., 1943, 25. 71.4 1 I,. A. Burkardt and C. E. Imhoff, Ind. Eng. C h c ? ~ ., 1947, 39, 1427. ’’ F. H. Horn and M’. T. Ziegler. J . Anzer. Chew. SOC.. 1947, 69, 2763.43 I<. Hocart and R. Weil, Compt. Tend., 1947, 225, 194.4 4 -1. Nicol, ibid., 1947. 224, 1355.” 11. -4. Peacock, TJniv. Toronto Studies, Geol. Ser., 1946, No. 51, 59.“ D. S. Belyankin, P. V. Lapin, and Y. P. Siinanov, Conzpt. rend. Acad. I%;.‘’ R. M. Thompson, Uniu. Toro)bfo Studies, Geol. Ser., 1946, No. 51, 35.S. Kaiman, ibicl.. p. 49.’” R . 11’. Nuffield, ibid., p. 59.j1 T. Sudo, J . Qeol. SOC. ,7apan, 1941, 48, 433.S.Y., 1947.U.R.S.S., 1947, 55, 6%.Q B R. B. Fergusoii. ibid., p. 41278 ANALYTICAL CHEMISTRY.isomorphous substances has been developed by L. K. Frevel and his co-worker~,~~ 52 who give tabulated data for cubic and tetragonal isomorphs.%,The whole question of a code for the tabulation of X-ray diffraction data isgone into by F.W. Matthews and A. 0. McIntosh,55 who also suggest the useof punched-card indexes.The applications of X-ray diffraction analysis with regard to t,heircapabilities and limitations are reviewed in a book by E. Brandenberger,56who also deals thoroughly with the preparation of specimens and theinterpretation of photographs, A. Guinier 57 gives a comprehensive reviewof the theory of diffraction and experimental techniques, together withuseful examples of applications and the choice of suitable wave-lengths.Applications to metallography are covered by A. Taylor 5~3 and H. Hirst 59who deal with alloy systems, identification of new phases, and t,hermalequilibrium diagrams.Powder-diffraction technique is described byC. W. Bunn.GO W. T. Sproull 61 gives a review of experimental andtheoretical diffraction, industrial applications, and a useful table of absorptioncoefficients.The basic principles and theory of X-ray diffraction are also reviewed byF. G. Firth,G2 and applications by Firth,62 E. E. Vain~htein~~3 G. L. Clark,640. Binder,65 and W. G. Burgers.66and applications to minerals are dealt with by M. A. Peacock,68 W. P a r r i ~ h , ~ ~and G. Nagelschmidt and D. Hicks,'O and to metallurgical problems byC. S. Barrett.'ISt. J. Thugutt 72 draws attention to limitations in the X-ray method inthe case of certain minerals; lublinite and calcite give identical X-raydiagrams, whereas their densities, solubilities, and other physical propertiesA symposium has also been52 L.K. Frevel, J. Appl. Physics, 1942, 13, 109.53 L. K. Frevel, Ind. Eng. Chem. Anal., 1942, 14, 687.5 4 L. K. Frevel, H. W. R h , and H. C. Anderson, ibid., 1946, 18, 83.55 Can. Chem. Process Inds., 1947, 31, 63, 67, 71.56 ' ' Rontgenographisch-analytische Chemie : Moglichkeiten und Ergebnisse vonCntersuchungen mit Rontgeninterferenzcn in der Chemie ", Base1 Verlag E. Birkhauser8z Cie, 1945.5i " Radiocristallographie ", Paris, Dunod, 1947.5 8 " An Introduction to X-Ray Metallography ", Chapman & Hall Ltd., London,59 " X-Rays in Research and Industry ", Melbourne, Tait Pub. Co., 1942.60 " Chemical Crystallography ", Oxford, 1946.61 " X-Rays in Practice ", New York, McGraw-Hill Book Co., Inc., 1946.62 Petroleum ReJiner, 1945, 24, No.4, 114, No. 6, 11 7, No. 6, 11 1.63 Uspekhi Khimii, 1944, 13, 64.G 5 Mkcanique, Suppl. Tech. ind. chim., 1939, No. 284, 125.6 6 Tech. Rundschau, 1940, 5, 157.6 7 Id. Eng. Chem. AnaE., 1941, 13, 695.G 8 Trans. Roy. SOC. Canada, 1941, 35, 105.69 Anales le. Congr. Panamericano Ing. Minus y Geol., 1942, 3, 1074.70 Yroc. Conf. Ultra-fine Structure of Coals and Cokes, B.C.U.R.A., 1944, 240.7 1 " Structure of Metals ", New York, McGraw-Hill Book Co., Inc., 1943.7 2 Arck. Il.;lineralogicxne, 1945, 15, 250.1945.64 J . Amer. Ceramic Xoc., 1046, 29, 175DOTHIE : X-BAY ANALYSIS. 279show them to be different minerals. Quartz and chalcedony also give identicalpatterns.73 X-Ray and allied studies have shown boksputite to be a mixtureof bismutite and r n a s s i ~ o t , ~ ~ and berthonite to be identical with b ~ u r n o n i t e .~ ~The sensitivity of the method is greatly dependent on particularconditions, but in some cases it is not possible to detect constituents whichare present in a mixture to the extent of less than about 76 In thecase of the opium alkaloids, however, it is possible to detect as little as0.7 p.g.36X-Ray diffraction analysis has been applied to a wide variety of problems.Boiler- and turbine-scales have been studied,3141> 773 78 organic compoundsanalysed,79~ 80, 8l and new alkaline-earth tungstates identXedas2 Thedifferences in melting points of certain organic compounds which give thesame X-ray pattern have been shown to be due to irnpuritie~,~~ anddifferences in colour to be due to differences in particle size.The methodhas also been used for checking the constancy and purity of calciumpho~phates,~~ for investigating unreduced ferric oxide Fischer-Tropschhigh-alumina sIag,s6 chrome-steel slags,87 and nickel skeletoncatalystss8 It has revealed the presence of a- and @-cristobalite in opal,sgof spinel-type Fe2Ti04 in titaniferous iron ore:(' and of mercury containingfine particles of a-iron in iron amalgam,91 and a- and @-cobalt in cobaltamalgam,g2 and the relationship of three modifications of y-manganesedioxide to ramsdellite and pyrolusite.93 Other applications include theexamination of " oxine " pre~ipitates,~4 lead thioantimonates ini 3 J.Novttk, Ve'stnik Stat. Geol. Ostavu Rep. Ceskoslov., 1946, 21, 231.7 5 R. AT. Thompson, Univ. Toronto Studies, Geol. Ser., 1946, No. 51, 81.76 M. L. Fuller, Iron Age, 1942, 149, 65.7 7 P. E. Fitzgerald, Petroleum Engineer, 1940, 11, 161, 164; C. E. Imhoff and7 8 L. M. Clark and C. W. Bunn, J . Xoc. Chem. Id., 1940, 59, 155.79 W. G. Perdok, Pharm. Weekblad, 1946, 81, 194.8o H. G. Fletcher and C. S. Hudson, J . Amer. Chem. SOC., 1947, 69, 1146.X. S. Marsden, K. J. Mysels, and G. H. Smith, J . Colloid Xci., 1947,2, 265.82 H. P. Rooksby and E. G. Steward, Nature, 1946,157, 548.83 J . J . de Lange and J. P. W. Houtman, Rec. Trav. chim., 1946, 65, 891.E. W. Heinrich, Amer. Min., 1947, 32, 365.L. A4. Burkardt, Power, 1942, 86, 64.H.C. Hodge, M. L. Le Fhvre, and W. F. Bale, Ind. Eng. Chenz. A n d , 1938,8 5 L. J. E. Hofer, W. C. Peebles, and W. E. Dieter, J . Amer. Chem. SOC., 1946,8 6 D. S. Belyankin, V. V. Lapin, and Y . P. Simanov, Compt. rend. Acad. Sci.8 7 G. P. Chatterjee and S. S. Sidhu, J . AppZ. Physics, 1947, 18, 519.88 G. G. Urazov, L. M. Kefely, and S. L. Lel'chuk, Compt. rend. Acad. Xci. U.H.S.S.,89 V. Cirilli and A. Giannone, Rend. Accad. Sci. Napoli, 1940, 11.I?. Mogensen, Geol. Poren. B'orh., 1946, 68, 578.91 N. Katoh, J . Chem. Soc. Japan, 1043, 64, 1079.s2 Idem, ibid., p. 1211.93 W. F. Cole, A. D. Wadsley, and A. Walkley, Tvanu. Electrochem. SOC., 1947,92.R. C . Chirnside, C. F. Yritchard, and H. P. ICooksby, Analyst, 1941,66, 399.10, 156.68, 1953.U.R.S.X., 1946, 53, 649.1947, 55, 735280 ANALYTICAL OHEM1STK.Y.bo~langerite,~~ soil colloids,96, 979 98 clays,99 slates,lW iron ores,lOl lignites,1O2phosphors,lo3 nickel-tungsten and nickel-molybdenum catalysts,lO*thomsenolite and pachnolite,1O5 and cellulose in paper.40The method is of value in connection with pneumoconiosis, with regardnot only to dust analysis,106 but also to the presence of crystalline siliceousminerals in silicotic lungs.lo7 As little as 0.2% of d i c a has been determinedin dry lung tissue.lo8 Chemically extracted mineral residues of lung tissue,and tissue sections have also been successfully studied.1O6Recent applications include the analysis of condensation products fromarsenic vapour under different conditions,1og of the sulphur-rich residue afterthe chemical determination of sulphur in bronze,1l0 of bauxite ores ll1 andof acid-extracted non-metallic inclusions in steels.l12General reviews of qualitative and quantitative diffraction methods aregiven by W.P. Davey,la P. A. Thiessen,ll3 E. Brandenberger,l14 M. Patry,l15J. B. Nelson,llG J. S. Buhler,l17 I?. W. Ma,tthews 11* and Rooksby.' Furtherapplications 119-120 throw light on the constitution of bleaching powder,12fO 5 F. C. Foley, Microfilira Abs., h i 1 Arbor, 1943, 6, No. 2, 39.96 J. Shearer and W. F. Cole, J . Roy. SOC. TVcdern Australia, 193!1--40,26, 121, 133.97 J. S. Hosking, J . Counc. Sci. Ird. Res. Arrstrulk, 1940, 13, 206.ga E. Jung, Z . PJEanz., Diingung u. Boded., 1946, 37, 2.gg A.RiviBre, Conapt. rend., 1946, 222, 1446; G. Nagelschmidt, J . Sci. Instr., 1941,18, 100; 31. Rolla, Ind. cerana. e silicati, 1946, 1, 1 ; S. Yusjupove, Compt. rend. Acad.Sci. U.R.S.S., 1946, 51, 631 ; R. Michaud, It. Cerighelli, and G. Drouineau, Compt. rend.,1946, 222, 94; S. Oda, J . Chem. SOC. Japan, 1941, 62, 827.loo H W. Fairbairn, Anaer. Min., 1943, 28, 246.lol C. W. Correns, B'orschungen u. Portschr., 1947, 21-23, No. 416.lo2 C . Mahadevan, Proc. Indian Acad. Sci., 1946, 24, A , 216.lo3 R. Nagy and C. K. Lui, J . Opt. SOC. Amer., 1947, 37, 37.lo4 S. Tanida, Bull. Chem. SOC. Japan, 1943, 18, 30.lo5 R. B. Ferguson, Trans. Roy. SOC. Canada, 1946, 40, 1 1.lo6 L. H. Berkelhamer, J . I d . Hyg., 1941, 23, 163.lo7 H. C. Sweany, R. Klaas, and G.L. Clark, Radiology, 1938,31,299 ; C . 11. Jephcott,lo8 H. C. Sweany and R. Klrtas, J . Anaer. Med. ASSOC., 1939, 112, 610.lo9 I. N. Stranski and A. Korb, Naturwiss., 1946, 33, 220.110 L. SiIverman and W. B. Goodman, Chsir&t-Analyst, 1947, 36, 28.111 I. NBray-Szab6 and J. Neiigebauer, Tecknika, 1044, 25, 259 ; J. Il'eugehuer,112 G. Murfitt, J . Iron Steel Inst., 1947, 157, 96.113 2. EZektrochem., 1940, 46, 414.11* Tech. Id. Schweiz. Chem. Ztg., 1941, 24, 177.115 Chim. et Ind., 1941, 45, 259.1%'. M. Gray, andD. A. Irwin, Canadia,? Med. Assoc. J . , 1938,38, 209.Mwgyar Clrenz. Pol., 1944, 50, 102." Crystallographic Techniques in Chemical Analysis ", British Cod UtilisationResearch Association, Monthly Bulletin, (Sept.1946), Y, No. 9, 267.117 Metals and Alloys, 1944, 20, 1316.118 Canadian Chem. Process Inda., 1945, 29, 719.llg H. P. Rooksby, J . Sci. Instr., 1941, 18, 54.la0 Idem, J . Roy. SOC. Arts, 1940, 88, 308; A. J. Howard, Mfg. Chemist, 1942, 13,51; H. P. Rooksby, Elec. Times, 1942, 102, 116, 189, 360, 337, 347, 406, 476; J. A.Darbyshire, J . Sci. Instr., 1941, 18, 99.121 C. W. Bunn, ibid., p. 70DOTHIE : A--RAY ANALYSIS. %81electroplating,f22 refractories and steels,123 gla~ses,~2* interface compounds ofcoated filaments,125 and titanium enamels.126The most commonly used radiation hitherto has been Mo-Ka, but thereis a tendency to go over to Cu-Icy. as giving better dispersion, and chromiumtargets have been used in some cases.127 The question of optimum specimenthickness is dealt with by A.Taylor.12* B. E. Warren 129 discusses thedisplacement of the diffraction lines caused by absorption in cylindricalspecimens, and gives a correction factor proportional to the complement ofthe Bragg angle. The effect of particle size on intensities is considered byG. WT. Brindley.130 The construction and use of cameras are described,131and a camera has been designed for obtaining powder-type patterns fromsingle crystals up to 10 em. in diameter, or coarse aggregates, for identifyingThe method can be extended to low-temperature 133 and high-temperature 134 studies by the design of suitable cameras. Apparatus forthe accurate measurement of films is described by H. P. K1ug,1a5 and aphotometer by A.H. Jay.136 W, Hume-Rothery 137 describes an apparatusfor the preparation of metal filings in a vacuum or in an inert atmosphere.0. E. Brown 138 gives charts showing the relation between Bragg angle andintcrplaimr spacing for use with Cr, Pc, Co, Clu, and Mo targets. A rapidmethod of analysis has been used by A. T. M~Cord,l3~ in which the sample isformed into a rigid rod 3 mm. in diameter, and used as one of the definingedges for the collimating slit.Quantitative Analysis.-Quantitative X-ray diffraction methods can bedivided into two classes, according as (a) a shift in line position or ( b ) achange in line intensity is measured.In cases where there is formation of a solid solution or of a complex, aline may be shifted from the position it occupies when it arises from a purecomponent.140 The amount of the shift is dependent on the degree of solidsolution or complex formation.This method has been applied to the studylZ2 H. R. Isenburger, Proc. Awier. Electroplutcrs' Soc., June 1939, 77.lZ3 A. H. Jay, J . Sci. Instr., 1942, 18, 81.12* S. K. Majumdar and B. K. Bmerjee, X a / u r e , 1946, 158, 753.lZG H. P. Rooksby, ibicl., 1947, 159, 609.126 A . L. Friedberg, F. A. Petersen, and A. I. jlnclrews, J . A i i i c r . C'ercir,tic ~Soc., 1947,l Z i F. W. Matthews and J. H. Michell, Ind. E n y . Che7)L. A)~ul., 1946, 18, 661.lZ8 Phil. Mug., 1944, 35, 632. lZ9 J . Appl. Physics, 1945, 16, 614.Phil. Mag., 1945, 36, 347.131 &4. J. Bradley, H. Lipson, and H. J. Yetch, J . Sci. Instr., 1941, 18, 216.132 G.Switzer and R. J. Holmes, -47~er. Min., 1947, 32, 351.133 (Mrs.) I<. Lonsdale and H. Smith, J . S c i . Imtr., 1941, 18, 133.134 M. J. Buerger, N. W. Buerger. and F. G. Chesley, Amcr. Min., 1943, 28, 2 8 5 ;135 Ind. Eng. Chem. Anul., 1940, 12, 733.136 J . Sci. Instr., 1941, 18, 128.1 3 8 J . Appl. Physics, 1947, 18, 191.130 Itzd. Eng. Chem. Anul., 1942, 14, 793.140 R. Rigamonti, Gazzetta, 1946,76, 474 ; Atti R. Accad. Lincei, 1947, 2, 44G.30. 261.E. A. Owen, J . Sci. Instr., 1943, 20, 190.13' Ibid., 1947, 24, 75282 ANALYTICAL CHEMISTRY.of nickel-copper alloys,' and to lithium carbonate-barium carbonate mixtureson filaments.119 Changes in composition of 0*5y0 are detectable inmanganese orthosilicate-zinc orthosilicate mixtures in phosphors, but anaccuracy of 1-2y0 is normally obtainable.60The method of intensity measurement is of more general application.For this it is necessary to measure the relative intensities of certain diffractionlines and compare them with those given by a standard.There are twomethods available : (i) the direct comparison method, (ii) the internal-standard met hod.If the unknown substance contains not more than two or threecomponents, and if these can be identified, then the direct comparisonmethod may be used. A line due to each component is chosen, and theratio of their intensities is compared with that of the same lines given by amixture containing known amounts of the components. It is possible todetermine 0.1% of calcium oxide in magnesium oxide and 04% of zincoxide in zinc sulphide,141 and a method has been worked out for estimatingm~ntrnorillonite.~~~ The underlying theory of the method 143 and the choiceof the appropriate voltage 144 have been described.The internal-standard method has been used for the estimation ofquartz.145 Here, standard samples containing known- amounts of quartzare mixed with known amounts of calcium fluoride or nickel oxide as internalstandards.Intensity ratios of five internal standard lines and four quartzlines are determined, to give twenty analytical curves. These can then beused for comparison against similar ratios given by unknown samples. Thismethod is also described by S. T. Gross and D. E. Martin,146 who makegraphical corrections of the relative intensities for absorption and sampleshape.The estimation of quartz is also reported by similar methods.14'T. M. Durkan148 recommends concentration of the quartz by chemicalmethods, preliminary to X-ray study, in order to obviate lines due to otherminerals which may be superimposed on the quartz lines.I n ordinary case8 an accuracy of 1-5% can be expected,64 but accuraciesof better than 1% can be attained by careful working in favourable cases.'Quantitative methods have been applied to the determination ofm i n e r a l ~ , l ~ ~ of titanium nitride in ferro-alloys,lm and of aldehydes andketones as the 2 : 4-dinitrophenylhydrazones using sodium fluoride as141 H. P. Rooksby, Analyst, 1945, 70, 166.142 D. M.C. MacEwan, J. SOC. Chem. I n d . , 1946, 65, 298.143 K. Schiifer, 2. Krist.,1938, 99, 142.144 L. Rivoir and J. M. G. Barredo, And. Pis. Quim., 1941,37,48.145 J. W. Ballard and H. H. Schrenk, U.S. Bureau of Mines, Report of Investigations146 I n d . Eng. Chena. Anal., 1944, 16, 95.14' J. W. Ballard, H. I. Oshry, and H. H. Schrenk, U.S. Bureau of Mines, Report of148 J. I n d . Hyg., 1946, 28, 217.149 T. N. Agafonova, C'orwpt. Tend. Acad. Sci. U.R.X.S., 1937, 16, 367.160 L. Silverman, Iron Age, 1947, 159, 68, 163.3888, 1946.Investigations 3520, 1940; G. Venturello, Bass, med. ind., 1942,13, 273DOTHIE : X-RAY ANALYSIS. 283internal standard.151 The question of photometers is dealt with by a numberof a ~ t h 0 r s . l ~ ~The introduction of the Geiger-counter spectrometer 153 has constituteda great improvement in quantitative X-ray diffraction methods.This,more than any other single development, has increased both the speed andthc accuracy of quantitative determinations. In this instrument, theX-rays diffracted by the specimen, instead of being recorded on aphotographic film, are passed into a Geiger-Muller counter. The countercan be swung in a horizontal plane along an arc about the specimen, i t bposition being indicated by an accurate scale, and the X-ray energy itintercepts a t its various positions is thus converted, by suitable countingcircuits, into figures on an arbitrary scale. In this way both the position andthe intensity of the lines are measured directly.The Geiger-counter spectrometer has been applied to metallurgicalproblems,l= as, for example, cemented carbides in powder .metallurgy.155F.G. Firth 156 describes a recording instrument which is able to give thepattern of cc-Al,O, powder in 35 minutes. Another instrument is used inconjunction with a continuously balanced high-speed recording electronicp0tentiometer.1~' The use of the Geiger-counter spectrometer for back-reflection work is also described.158Alloys and Equilibrium Diagrams.-X-Ray methods have been usedextensively in the field of alloy studies, the usual procedure being to identifyconstituents by means of their powder diffraction patterns. The subject isreviewed by H. L i p ~ o n , l ~ ~ J. L. Abbott,l= L. Rivoir and A. andC. Schaub.161and deal with binary 1 6 * 7 lti5 and ternary alloys.164, 166It is possible to determine phase boundaries 7 5 Iti2 for transitionThe study of diffusion151 G.L. Clark, W. I. Kaye, and T. D. Parks, I n d . Eng. Chem. Anal., 1946,18, 310.152 J. W. Ballard, H. I. Oshry, and H. H. Schrenk, U.S. Bureau of Mines, Report ofInvestigations 3638, 1942 ; M. Spiegel-Adolf and R. H. Peckham, I n d . Eng. Cheni. Anal.,1940,12,182 ; E. E. Berkley and 0. C. Woodyard, ibid., 1938,30,451; H. R. Ronnebeck,J . Sci. Instr., 1943,20, 154; J . C. M. Brentano, Reu. Sci. Instr., 1945, 16, 309.lS3 H. Friedman, Electronics, 1945, 18, 132.154 Iron Age, 1947, 159, No. 7, 50, No. 8, 57, No. 9, 56.lS5 E. S. Kopecki, ibid., 1946, No. 9, 48.D. M. Considine and D. P. Eckman, J.Chenz. Educ., 1946,23,274.lS8 L. A. Carapella and H. F. Kaiser, Rev. Sci. Instr., 1945, 16, 214.lS9 Nature, 1940, 146, 798.161 I n g . Vetens. Akad., Stockholm, 1940, 161.lG2 W. Hume-Rothery and G. V. Raynor, J. Sci. Instr., 1941, 18, 74; Metal, I n d .(London), 1942,60, 412 ; V. Montoro and E. Hugony, Ric. sci., 1941,12, 1032.163 G. Borelius, T e k . Tid., 1942, 72 A, 500; K. G. Brummage, P. W. Cooke, andK. R. Gordon, Instr. Petrol. Rev., 1947, 1, 33, 65.164 A. J. Bradley, W. L. Bragg, and C. Sykes, J . Iron Steel Inst., 1940,141, 63.lG5 W. Trzebiatowski, H. Ploszek, and J. Lobzowski, I n d . Eng. Chem. Anal., 1947,19,93; N. V. Ageev andD. L. Ageeva, Bull. Acud. Sci. U.R.S.S., C1. Sci. Chim., 1946, 143.IG6 H. Lipson, Rep. Pmg. Physics, 1940, 6, 361; W.Guertler and G. Itassmam,Alelullw., 1943, 22, 1, 34, G6; W. Hofmann, Aluminium, 1938,20, 865; H. W. L.Phillips,J . Inst. Metals, 1946,72, 151 ; C. S. Barrett, J. Appl. Physics, 1941,12, 385.156 Colloid Chemistry, 1946, 6, 108.160 Anal. 3'3s. Quim., 1940, 36, 20284 ANALYTICAL CHEMISTRY.in alloys is described by A. H. S ~ 1 1 y . l ~ ~ 0. S. Edwards and H. Lipson Ici8discuss the experimental technique, choicc of radiation, and p-filterthicknesses.Closely akin to the subject of alloys is the study of the solubility ofhydrogen in palladi~rn,16~ and of gallium, germanium, and arsenic in copperand in ~ilver.1~0 Similar methods are used in investigations into equilibriumdiagrams, including the systems NiO-A1,0,,171 Fe,O,-BaCO, in presence ofoxygen,172 Bi20,-MOO,, Bi203-W03, PbO-Moo,, and PbO-W0,,173Mg0-Mg,P20,,174 TiC-WC,175 and carbides of tantalum, titanium,niobium, and zirc0nium.1~~ A new crystalline phase was found byexamining the Fe,O,-Cr,O, mixed gel and the phase compositionof calcined magnesite 178 and the reduction-equilibrium of ferric oxide bycarbon monoxide in presence of silica 179 and in presence of alumina,lsOhave been studied.(b) Spectroscopy.For the detection and estimation of small amounts of elements thespectroscopic method is becoming well established.Here the sample isplaced on the anticathode and the radiation excited by it is diffracted by acrystal and examined as a spectrum. The chief advantage of this over tlicoptical spectroscopic method is the simplicity of the X-ray spectra. Theseconsist of five lines in the K-series, as compared with the multiplicity of linespresent in optical emission spectra.l*lFor qualitative work it is possible to detect the elements from magnesiumto uranium, and the method has been applied to the study of minerals andrare elernents.182 Keys are given by P.A. Herrlin.l=Applications to quantitative work have been made, and progress in thisfield has been stimulated by Y. Cauchois, who describes a new method inwhich the sample and comparison sample are placed on the anticathode, andthe rays from each are separated by means of a crystal.ls4 The method is1 6 i J . Sci. Instr., 1945, 22, 244.l i 0 E. A. Owen and V. W. Rowlands, J . Inst. MetaZs, 1940, 66, 361.lil 11'.0. Milligan and L. Merten, J . Physical Chenz., 1946, 50, 466.l i 2 M. Erchak, I. Fankuchen, and H. Ward, J . Anher. Chevt. Soc., 1946,88, 2085.l i 3 L. G. Sillen and K. Lundborg, ArEiv Kern& Min. Geol., 1943, A, 17, No. 21.174 R. Jagitsch and G. Perlstrom, ibid., 1946, A , 22, No. 5.175 A. G. Metcalfe, J . Inst. Metals, 1947, 73, 591.l i G A. E. Koral'skii and Ya S. Umanskii, J . Phpical Cl~em. U.S.S.K., 1946, 20,177 W. 0. Milligan and L. Merten, J . Plqsical CIien2., 1947,51, 521.l i 8 V. T'. Goucharov, Compt. rend. Acad. S c i . U.R.S.S., 1947, 55, 743.17s V. Cirilli, Gazzetta, 1946, 76, 331.180 Idem, ibid., p. 339.181 H. Hirst, Chem. Eng. iMin. Rev., 1939, 31, 208.168 Ibid., 1941, 18, 131.D. P. Smith and C. S.Barrett, J . Anter. CJLem. Xoc., 1940, 62, 2565.769, 773.I. B. Borovskii and M. A. Blokhin, BUZZ. Acad. Sci. U.R.S.S., 1937, 929;31. A. Blokhin, Zavod. Lab., 1945, 11, 1069.ln3 Medd. Lunds Geo1.-Mineral Inst., 1941, A'o. 87, 16.lS4 Bull. Seci. sci. roumaine, 1942, 24, 479DOTTITE : -X-RAY ANALYSTS. 2%very sensitive both in mixtures and in the pure static, it being possible todetect 5 i(Methods of X-ray spectroscopy 186 are discussed by H. Hirst,I*l whogives the estimation of minute amounts of elements in metals and alloys.The accuracy obtainable depends on the atomic number of the clemc~nt, andfalls off for elements of lower atomic number than that of niagnesium.For other elements an amount of impurity as small as one part in lo5 partscan be detected and measured.When analysing alloys with large amountsof constituents the accuracy is about O.OSyo if the elements are close togetherin the periodic system, but if they are far apart the accuracy may fall to 1 yo.The method is therefore best suited to the estimation of minute amounts ofimpurities. Spectroscopic methods are also reviewed by Clark,64 whoconsiders their application to ceramics, by I. B. Borovskii 18' on the methodof Cauchois and Johann, by Vainshtein 63 and by 0. Alvfeldt.188 Estimationsof the rarer elements, using an optical wedge and of minuteamounts of nickel ancl cobalt,lW are also described. In the latter case anexposure time of 60 minutes was given, using a copper anticathode, a tungsten-filament cathode, ancl running at 18 kv.with an emission of 5 ma., and usinga calcite crystal.A vacuum spectrograph for use with light elements has bsendescribed ; lgl electrostatic shielding of the anticathode gives rapid andexact analysis,lg2 and ionic X-ray tubes have been deve10ped.l~~Y. Cauchois lg4 describes a spectrograph for use up to 20 A.The necessity for demounting the tube after every determination hasprevented the wide application of this method, but this difficulty can beavoided by placing the specimen outside the tube, and irradiating it with theprimary rays.64 The specimen then gives rise to secondary fluorescentradiation which may be diffracted by a crystal and thus formed into aspectrum. High-intensity tubes which produce a dosage of 5,500,000 r.perminute lg5 are particularly valuable for this technique. L. v. Ham05 lg6discusses the formation of true X-ray images by reflection from cylindricalcrystal surfaces, anti the determination of very small quantities ofs i i b ~ t a n c e s , ~ ~ ~ utilising the secondary X-radiation of an element.la5 Y. Canchois, J . Chini. physique, 1942, 39, 161.l B 6 I. B. Rorovskii and 31. A. Blokhin, Btill. -4cad. isci. lJ.R.s.S., S6r. phys., 194.1,g. of uranium in the pure state.185196.Trudy Vsesoyuz Ronferentsii, A?zaL. Khi?r/., dkad. Xutilu'., S.S.S.R., 1939, 1, 13.5.l S s Ing. I'efens. Akad., Niockholnz, 1943, 217.lS9 S. Sinoda, J . C'hem. SOC. Japan, 1941, 62, 629.lg0 I<. Rimura, M. Nrtkamura, and N. Tanaka, ibid., 1043, 63, 349.lgl N. D.Borisov and Ya. M. Fogel, J. Tech. Phys. U.S.S.K., 2938, 8, 1709.lg2 P. Brauer, 2. tech. Physik, 1938, 19, 232.IB3 G. F. Komovskii and Ya. Golovchiner, J . Twit. Phys. U.S.S.R., 1942, 12, 579;Ig4 J . P h p . Radium, 1945, 6, 89.lgB T. H. Rogers, Ind. Iludiograpliy, 1946, 4, 36, 61.Ig8 Arne?.. &!in., 1938, 23, 215; Z. Krisr., 1939, 101, 17.l e i ilrkiv Mat. A8tTOTL. Fysik, 1946, A , 31, NO. 25,Btcll. Acad. Sci. U.R.S.S., S6r. phys., 2941, 201286 ANALYTICAL CHEMISTRY.E. Abbolito lg8 gives details of the v. Hamos method, including the use ofa curved mica focusing crystal; the method is applicable to the detectionof those elements whose characterstic radiation lies in the wave-lengthregion between 0.7 and 2-7 A.( c ) Microradiogruphg.It is noteworthy that the absorption of X-rays by materials has beenused to advantage as an analytical tool, and by its means it is possible todistinguish phases.64, Ig9 A.Guinier 200 uses minute quantities of materialplaced on a photographic plate; this is irradiated and the absorptiondetermined by microscopic examination. It is possible to distinguishbetween the composition and diffraction effects.199 A. Engstrom m1 uses afine-grained calcium tungstate fluorescent screen in place of a photographicplate. A further advance 202 is the use of a fluorescent screen in conjunctionwith a photomultiplier tube, in which case the intensities are read as electriccurrents. In another method 203 the absorption coefficient is measured bycomparing the ionisation currents caused by the X-rays before and afterabsorption.The composition of binary compounds can be determined, and the methodhas been applied to the study of organic compounds.2m The absorptioncoefficients of hydrogen, carbon, nitrogen, and oxygen have been measuredrelative t o aluminium, and the additive law of absorption coefficients foundto be valid for liquid hydrocarbons.Developments along similar lines havebeen made in the field of mi~roradiography,~05 and the subject is reviewed byVain~htein.~~ Applications to metals and alloys are described by M. Paiq206G. L. Clark and W. M. Shafer,207 and Taylor,58 and to colloidal materials byG. L. Clark.208 Details of technique 209 and industrial applications 210 aregiven, and a stereoscopic camera is described.211 H.F. Sherwood212lg8 Ric. sci., 1940, 11, 856.leg R. Smoluchowski, C. M. Lucht, and J. M. Hlird, J. Appt. Physics, 104G,l?, 864.2oo Compt. Tend., 1943, 216, 48.202 H. A. Liebliafsky and E. H. Winslow, Gen, Elec. Review, 1945, 48, 36; 11. A.Liebhafsky, H. 31. Smith, H. E. Tanis, and E. H. W7inslow, I n d . Eng. Ghen2. A d . ,1947, 19, 861.201 Experientia, 1947, 3, 208.203 J. Devaux and A. Guinier, Compt. rend., 1944, 218, 318.204 Idem, ibid., 1945, 220, 44.205 G. L. Clark and 8. T. Gross, Ind. Eng. Chem. Anal., 1942, 14, 6 7 7 ; J. J. Trillat,Rev. aluminium, 1945, 22, 44; C. S. Barrett, Trans. Amer. Inst. Min., Met. E92yrs.Inst. Met. Div., 1945, Tech. Pub. No. 1865.206 Rev. mdt., 1944, 41, 169.207 Trans. Amer.SOC. Metals, 1941, 29, 732.208 J. Alexander, " Colloid Chemistry ", 1944, Vol. V, 146.sos G. L. Clark, Phototechnique, 1939, 1, (7), 19; Ind. Radiography, 1942, 1, 21;S. E. Maddigan, J. Appl. Physics, 1944,15, 43; J. J. Trillat, B d . soc. franc. elect., 1943,(6), 3, No. 25.S. T. Gross and G. L. Clark, Ind. E n g . Chem. Anal., 1942, 14, 676; G. L. Clarkand S. T. Gross, Iron A g e , 1943, 152, 44.211 G. L. Clark and R. W. Eyler, Rev. Sci. Instr., 1943, 14, 277.*12 Ibid., 1947, 18, 80SEXTON : OILS, FATS, AND SURFACE-ACTIVE AGENTS. 287describes an exposure holder suitable for the microradiography of thinspecimens such as metal sections, paper, and textiles. The good contactneeded to ensure maximum sharpness is obtained by means of a vacuumframe in which the apecimen i s covered with a film of vinylite.The questionof the accurate interpretation of radiographs is gone into by H. R. Clauser?l3together with the influence of film contrast and definition on sensitivity,film blemishes and viewing lamps. An interesting development is the useof a phosphor possessing X-ray storage properties, the energy being releasedon subsequent infra-red i r r a d i a t i ~ n . ~ l ~A. Engstrom 215 and his co-workers have developed a quantitative methodof microradiography suitable for the analysis of elements, of atomic numberabove 6, in extremely small quantities of biological tissues. It is capableof determining 10-lo-lO-ll g. of calcium or phosphorus with an error of 10%.H. J. D.4. OILS, FATS, AND SURFACE-ACTIVE AGENTS.The analytical description of natural fats may be based either onempirical " constants " of the fat as a whole (e.g., saponification or iodinevalues) or on its content of definite chemical substances or radicals (e.g.,arachidic acid in arachis oil, squalene in olive oil, -OH in castor oil).Although a complete description of the latter kind is the ideal, analysts are,at present, largely restricted in practice to terms of the former kind.It istherefore proposed in the present Report to review recent developments inthe technique of determination of empirical constants, followed by someindication of the trends of research which may develop into acceptableanalytical procedure for the determination of specific ingredients.Certaincases where the determination of these can already be regarded as analyticalpractice are considered rather more fully. Finally, methods for theexamination of substances derived from natural fats (mono- anddi-glycerides ; surface-active agents) and now important in industry, andtherefore in practical analysis, are reviewed.Empirical Constants.77nsaturation.-0. Freire recommends W. A. Alexander's oxidationvalue in a study of the possibility of determining it a t 100". G. Knowles,J. C. Lawson, and T. McQuillen3 treat an oil in acetic acid plus anemulsifying agent with excess of potassium permanganate for an hour at25", then titrate the excess. The results agree with I.V.s, and whereunsaturation is due to conjugated linkages the true I.V.is obtained from this213 Materials and Methods, 1945, 32, 1418.2 1 4 0. E. Berg and H. F. Kaiser, J . AppZ. Phgsics, 1947, 18, 343.215 A. Engstrom, Nature, 1946, 158, 664; idem, Acta Racliol. Suppl., 1946, 63;A. Engstrom and B. Lindstrom, Experientia, 1947, 3, 191 ; A. Engstrom and M. A.Jakus, Nature, 1948, 161, 168.Chem. Abs., 1947, 41, 1470.J . Oil Colour Chem. ASSOC., 1940, 23, 4.Analyst, 1939, 64, 157288 ANALYTTCA4L CIIEMTSTRY.oxidation value. The oxygen consumed is equivalent to the I.V. as ameasure of unsaturation but is of inore general value.G. K. Jones * and J. W. McCutcheon discuss the Wi& method, andP. Levy criticises this and other methods.investigated sample : reagent ratio in the Wijs method and suggest a rapidtest for conjugated systems.H. D. Hoffman and D. E. Green,8 by addingmercuric acetate to the reaction mixture in the Wijs method, reduced thetime required from 30 t o 3 mins. The same salt in the Hanus method alsoaccelerates the reaction but the rapid method is unsuitable for castor oil and“ conjugated ” fats because the I.V. varies with the excess of reagent used.P. S. Skell and S. B. Radlove,lo using the Wijs rapid method, first protect thehydroxyl groups in castor oil, etc., by propionylation. H. Jasperson l1used direct bromine addition (D.B.A.) with mercuric acetate catalyst toobtain the I.V. of hydrogenated fats by titrating with bromine in glacialacetic acid. G. W. Priest and J. D. von Mikusch,l2 using a large excess ofreagent in the Hanus method, obtained satisfactory results for castor oil(dehydrating) ; and Mikusch and C.FrazierY13 using a large excess of double-strength Hanus solution, obtained theoretical 1.V.s for “ conjugated ” fats.The same workers,l4 using this method and a short-time contact Wijssolution at 0--5”, determine conjugated or non-conjugated unsaturation offats.During the war, bromine reagents were much used for I.V.s, the pyridinesulphate bromide method being used in B.P. work. Two modifications ofH. P. Kaufmann’s method were described.l59 l6 Bromine methods seem tobe the most popular for microchemical work. K. Schmidt-Nielsen l7determines the I.V. of g. of oil by treating it with bromine and sodiumbromide in methyl alcohol and estimating the excess; and N.Kretchmer,R. T. Holman, and G. 0. Burr l8 use a modified Rosenmund-Kuhnhennmethod on 10-100 pg. of oil.Kass andhis co-workers conclude that former hexabromide numbers are too high anddescribe a more adequate procediire which gives trustworthy, if empirical,results.Although it has been shown 21, 22 that the addition of -SCN is neitherW. C. Forbes and H. A. NevilleTwo studies 1 9 7 2o of the polybromide number have been made.Paint Manuf., 1946, 16, 58.Chinr. peint., 1945, 8, 123.* Oil and Soap, 1939,16, 236.F. A. Norris and R. J. Buswell, Ind. Eng. C‘hew. Anal., 1943, 15, 238.Itid. Eng. C’l~em. Anal., 1940, 12, 265.Ind. Eng. Clwm. Anal., 19.10, 12, 72.lo Ibid., 1946, 18, 67.l1 J . SOC. C’hem. Id., 1942, 61, 116.Ind. Eng. Chenr.Anal., 1941, 13, 782.l 5 A. Muller and L. Feher, Fetle u. S e i f e n , 1944, 51, 171.l6 S. Korpacsy, Ind. corps gras, 1945, 1, 49.18 Arch. Biochena., 1946, 10, 101 ; Oil and Soap, 1946, 23, 266.2o J. P. Kass, W. R. Roy, and G . 0. Burr, Anal. C‘hem., 1947, 19, 21.21 J. P. Kass, 11. G. T,oeb, F. A. Norris. and G. 0. Burr, Oil and Soap, 1940, 17, 118.s2 Analyst, 1940, 65, 437.l2 I n d . Eng. Chetr,., 1940, 32, 1314.l4 Ibid., 1943, 15, 109.l7 Chent. Abs., 1946, 40, 2011.E. 0. Aeulle and M. C. Pineda, Ion, 1945, 5, 257 ; Cheni. Abs., 1945, 39, 5099SEXTON : OILS, FATS, AND SURFACE-ACTIVE AGENTS. 289quantitative nor independent of the concentration of -SCN reagent used,this has not made the method obsolete but it has made it necessary to replacethe theoretical Kaufmann values by values obtained under standardisedconditions. The new values have been adopted by the A.O.C.S.,= theA.O.A.C., and by T.P. Hilditch and his co-workers.B. A. Ellis and R. A. Jones’s maleic anhydride or diene value 24 has beeninvestigated by R. S. McKinney, N. J. Hslbrook, and W. G. whoshow that the actual values of conjugated acids, like the SCN value ofunsaturated acids, vary with the conditions of reaction.26 The sameworkers 25 use the diene value to detect the adulteration of tung oil.A specific titration method for oxirane (epoxy) oxygen in unsaturatedfatty materials, based on the opening of the oxirane ring by 0*2~-hydrogenchloride in anhydrous ether, is described by D. Swern, T. W. Findley,G.N. Billen, and J. T. S ~ a n I a n . ~ ~Saponi$cution Value and UnaaponiJiable iMatter.-E. Andre 28 has studiedS.V. methods and possible errors ; and W. Rieman’s methods 29 for determiningthe S.V. by potentiometric analysis 01‘ double indicator avoid “ blank ”determinations and are suitable for micro-work. The micro-procedure isdescribed30 for O*l--O-OOl-g. quantities of fat as well as a modified semi-micromethod.31 J. P. Wolff,32 using potentiometric methods to find thebest indicator for use in alcohol, concluded that thymolphthalein was bestfor fatty acids and rosin. Some years ago W. R. Street 33 proposed potassiumhydroxide in “ cellosolve ” for samples difficult to saponify ; B. H. Knight 34advises the addition of alcohol to this, while S.Rovira 36 saponifies “ difficult”samples with this hydroxide in benzyl alcohol, ethylene glycol, or glycerol.G. Kirsten,36 reporting on standard methods for unsaponifiable matter,preferred the Society of Public Analysts’ (S.P.A.) method. This is now“ official ” in the A.O.A.C. methods ; the F.A.C. method has been deleted.N. D. Sylvester, A. N. Ainsworth, and E. B. Hughes 37 improved the S.P.A.method by using adsorption. M. L. Karnovsky and W. S. Rapson38modify the S.P.A. method in analysing marine oils. They determine thea-glyceryI ether content of the isolated unsaponifiable matter by periodicn* Official and Tentative Methods of the A.O.C.S., 1946 ; A d y e t , 1947,73,167.er Ibid., 1936, 61, 812.e6 W. G. Rose and G. S. Jamieson, ibid., 1943, 20, 227.c 7 Anal.(%ern., 1947, 19, 414.bo W. Rieman and K. Marcali, ibid., 1946, 18, 144.*l D. Ketchurn, ibid., p. 273.Analyst, 1936, 61, 687.Ann. Chim., 1946, 20, 660.A d y e t , 1946, 70, 296.8b Oil and Soap, 1942, 19, 141.Olkagineux, 1946, 1, 12, 68.Ind. Eng. Chem. Anal., 1943,15, 325.I d . corps gras, 1945, 1, 36.a4 Anal. Chem., 1947, 19, 359.B6 J . Aseoc. Off. Agric. Chem., 1946, 29, 248.81 J . SOC. Chem. Id., 1947, 66, 95.REP.-VOL. XLIV. 290 ANALYTICAL CHEMISTRY.acid oxidation.39 Although some marine oils contain much, amongother oils only tung oil has any appreciable a-glyceryl ether content.40 Theyalso41 use J. Fitelson’s squalene method to obtain the squalene contentof marine oils ; this method for olive oil in mixtures is now ( ( official ” in theA.O.A.C. methods.The average squalene content of olive oil is 330, arachis27, and teaseed 12 mg./100 g. ofAcetyl Value.--In a modification 43 of the Roberts-Schuette method foracetyl value, the hydroxyl number does not vary with the quantity ofsample. The AndrB-Cook method for acetyl values requires a fairly complexequation ; this, however, is capable of a simple graphical solution, and threenomograms are given.4Deterioration.-C. H. Lea’s comprehensive report 45 is now, unfortunately,out of print. Most of the tests described in it, or modifications, are still inuse. There are also some new tests. Much work has been done on theestimation of peroxides in fats by iodometric methods. D. H. Wheeler’s 46cold method, using saturated potassium iodide solution for one minute, ispopular in America.A. Taffel and C. Revis 47 used 8olid barium iodide or50% potassium iodide in glacial acetic acid, but no chloroform. W. Frankeand D. Jerche14* and Franke and J. Monch49 use carbon tetrachloride andhydriodic acid and dilute acetic acid for one hour in diffused light. J. Gangland W. Rurnpel 5o determined the undecomposed iodide. Lea’s originalmethod was a hot method using solid potassium iodide. Later, N. N. Dasturand C . H. Lea 51 gave a modified method estimating the undecomposediodide as in Gangl and Rumpel’s method. Lea,62 following his work 53 onthe ferrometric procedure and de-aeration of reagents, showed that in theiodometric method also it is necessary to de-aerate the solvent beforedissolving the fat. Lea describes a piece of apparatus and a hot and a coldmethod of determining peroxide values-cold, one hour a t room temperature ;hot, boiling for two minutes.C. B.Stuffins and H. Weatherall 54 studied Lea’s and Wheeler’s methodsand proposed a cold method, using saturated potassium iodide solution andan inert gas. M. E. Stansby 55 uses a similar method for fish oils.K. Nozaki 56 uses sodium iodide and acetic anhydride in the cold whendetermining organic peroxides. J. H. Skellon and E. D. Wills 67 for benzoyl39 Ibid., 1946, 65, 138.4s K. Helrich and W. Rieman, Anal. Chem., 1947, 19, 691.44 T. C. Patton, J . Amer. Oil Chem. Soc., 1947, 24, 158.45 D.S.I.R. Special Report No. 46 : Rancidity in Edible Fats, 1938.40 Ibid., p.425.J . Assoc. Off. Agric. Chern., 1945, 28, 282.4 1 Ibid., 1947, 66, 124.Oil and Soap, 1932, 9, 89; A. E. King, H. L. Roschen, and W. H. Irwin, ibid.,Annalen, 1937, 533, 46.1933, 10, 105.4 7 J . SOC. Chem. Ind., 1931, 50, 87T.49 Ibid., 1944, 556, 200.51 Analyst, 1941, 66, 90.m Ibid., 1945, 64, 106; Analyst, 1945, 70, 306.b4 Ibid., p. 403.6b I d . E q . Chem. Anal., 1941,13,627.6 7 Analyst, 1948, 73, 78.bo 2. Untersuch. Lebensm., 1934,68,533.b2 J . SOC. Chem. Id., 1946, 65, 286.Ibid., 1946, 18, 683SEXTON : OILS, FATS, AND SURFACE-ACTIVE AGENTS. 291peroxide use a cold method with sodium hydrogen carbonate as a source ofgas. S. Siggia 58 uses an arsenious oxide method for benzoyl peroxide,where an iodometric method could not be employed.C. D. Wagner,R. H. Smith, and E. D. Peters 59 tested various methods and described theirown recommended procedure using sodium iodide and isopropyl alcohol.The ferrous thiocyanate colorimetric 60 and the ferrous-titanous procedurehave also been studied.The ferrometric method is based on the oxidation of ferrous to ferriciron by the peroxides present. The reagent is a dilute solution of ferrousammonium sulphate and ammonium thiocyanate in 96% acetone. Thecolour developed is measured by a spectrophotometer. The peroxide valuesare double the iodometric values. C. H. Lea showed that the ferrometricvalues were reduced by about 75% if the reagents were de-aerated.G. Hills-Loftus and C . C . miel63 modify the method by usingbenzene : methanol (7 : 3) as solvent with ferrous chloride.The Kreis test for acetals of epihydrinaldehyde has been investigated bymany w0rkers.M Perhaps the single-phase technique of W.P. Walters,M. M. Muers, and E. B. Anderson 66 or a modification 66 is the mostsatisfactory. 0. Frehden's diaminofluorene colour-test for peroxides 67 andJ. Stamm's diphenylcarbazide test 68 for hydroxy-aliphatic acids (modifiedby Frehden) 69 are still used. The salicylaldehyde test45 for ketonicrancidity was modified by N. N. Dastur and C. H. Lea.51 The Schibstedtest has been modified by W. R.The Schaal test by oven incubation a t 60" or 63" was used by someworkers,71 and Swift's stability test wag investigated by V. C. Mehlenba~her,'~who accelerates it by using 110" thus saving 60% in time : hours a t 110"multiplied by 2.5 give the 97.9" values.An all-glass improved apparatusin which one tube is required for each sample was devised for the Swifttest.73 E. W. Eckey's apparatus and procedure 74 for measuring the oxygenabsorption of fats records the time required for 1 g. of fat to absorb 3 ml. oioxygen. Another apparatus 75 shows the volume absorbed under constant6 8 Anal. Chem., 1947, 19, 872.6o C. D. Wagner, H. L. Clever, and E. D. Petors, ibid., p. 980.b 1 C. D. Wagner, R. H. Smith, and E. D. Peters, ibid., p. 976.62 A. Lips, R. A. Chapman, and W. D. McFarlane, Canadian J. Res., 1943,21B, 153 ;63 J . Dairy Res., 1946, 14, 340.b4 B. M. Watts and R. Major, Oil and Soap, 1046, 23, 222.g5 J .SOC. Chern. Ind., 1938, 57, 53.6 6 M. F. Pool and A. N. Prater, Oil and Soap, 1945, 22, 215.6 7 Analyst, 1938, 63, 536.'l N. T. Joyner and J. E. McIntyre, Oil and Soap, 1938, 15, 184; K. F. Mattil and72 Oil and Soap, 1942, 19, 137.7L Ibid., 1942, 23, 38.7 6 R. Gilmont, H. 8. Levenson, and L. W. Elder, ibid., 1046, 23, 248.59 Ibid., p. 976.Oil and Soap, 1943, 20, 240.Ibid., 1926, 51, 416.Mikrochim. Acta, 1937, 2, 214. 70 J . Dairy Res., 1947, 15, 55.H. C. Black, J. Amer. Oil Chem. SOC., 1947, 24, 325.R. W. Riernensehneider, J. Turer, and R. M. Speck, ibid., 1943, 20, 169292 ANALYTICAL CHEMISTRY.pressure ; the rate is plotted and the induction period is shown by a break inthe curve.There are two new colorimetric methods for a-dicarbonyl compounds.E.A. Bill 76 converts these into their oximes, forms the nickelous, cupric, orferrous derivative of these, and then extracts the characteristically-colouredcomplexes with benzene, finally measuring the colour. L. O’Daniel andL. B. Parsons 77 state that autoxidised fats treated with alcoholic potashgive colours due to quinonoid compounds formed by aldol condensation ofa-diketones in a manner analogous to the formation of p-xyloquinone fromdiacetyl, and describe a simple and rapid method of estimation.H. Jasperson, R. Jones, and J. W. Lord 78 have investigated both thesemethods. G. A. Grant and H. J. Lips,79 studying rancidity in lard, conaiderthat the determination of stable a-dicarbonyl compounds is the best forassessing deterioration ; and S.A. Kaloyereas 80 considers the Wheelerperoxide method the most reliable and the Kerr-Issoglio test of no value.W. H. White,81 F. C. Vibrans,82 and B. W. Beadle a3 discuss the various testsfor rancidity and their limitations.Miscellaneous Tests.-An accurate semimicro-method for determiningReichert-Meissl, Polenske, and Kirschner values on 1 g. of fat is given.84Methods for the determination of ash in oils, refining and bleaching tests arereported R. T. O’Connor, D. C. Heinzelman, and M. E. Jefferson 86describe an emission spectrographic method for traces of metals in oils (fewp.p.m. in 2.5 g. of oil). The detection of argemone oil in mustard oil isde~cribed.8~ The specific heats of vegetable oils over the range 0-280”were determined by P.E. Clark, C. R. Waldeland, and R. P. Cross.88K. A. Williams 89 modifies the method 90 for “ tristearin ” in lard. Thismethod is still “tentative ” in the A.O.A.C. Methods.s1 R. W. Sutton,A. Barraclough, R. Mallinder, and 0. Hitchen’s long and important paper 92on the adulteration of lard contains useful photomicrographs. T. Connorand G. F. Wright s3 describe a novel procedure for the analysis of mixtures ofgeometrical isomers, using methoxy-mercuration and taking advantage ofthe fact that cis-isomers react more quickly than trans-forms. F. A. Norrisand K. F. Mattil s4 used catalysed interesterification for a new approach toglyceride structure.76 Oil and Soap, 1942, 19, 107.78 J . SOC. Chem. Ind., 1945, 64, 143.82 Oil and Soap, 1941, 18, 109.** B.Dyer, G. Taylor, and J. Hamence, Analyst, 1941, 66, 355.7 7 Ibid., 1943, 20, 72.79 Canadian J . Res., 1946, 24F, 450.8 1 Canadian J . Res., 1941, 190, 278.83 Ibid., 1946, 23, 33.J . Amer. Oil Chem. SOC., 1947,24, 39.J . Amer. Oil Chem. SOC., 1947, 24, 76.Ibid., p. 185.Ind. Eng. Chem. Anal., 1946, 38, 350.A d y s t , 1940, 65, 596. 90 [bid., p. 508.91 ‘‘ Official and Tentative Methods of the A.O.A.C.”, 1945.Oe A d y e t , 1940, 65, 623.94 Oil and Soap, 1946, 23, 289.ST A. K. Sen, Chem. Abs., 1947, 41, 2261.J . Amer. Chem. SOC., 1946, 68, 256SEXTON t OILS, FATS, AND YURFAUE-ACTIVE AGENTS. 203U. T. Hill 95 describes a colorimetric method for fatty acids and estersbased on a ferric hydroxamate colour complex.The preparation of thehydrazides of n-aliphatic acids (Cl-C,,) from 20 mg. of their esters isdescribedg6 as a means of identification in mixtures from melting points;and F. L. Breusch and E. Ulusoy 97 isolate and identify fatty acids its theircrystalline ureides with bis - ( p -dimet nylarninopheny1)urea.After much collaborative work, an A.O.C.S. committee 98 recommend thegrading of the colour of oils by a photoelectric system. L. K. Whyte 99describes the photometric determination of the colour of fats by a methodwhich even a colour-blind person can use.G. Zeidler loo gives a simple test for tung oil in mixtures, and a staidardrapid-chilling technique for melting points of fats and waxes isrecommended.lol The aluminiurn nurnber,lo2 hydrogen-addition ~ i t l u e , ~ O ~and amide value lo4 methods are described.Assessments of Ingredients.1’. P.Hilditch’s revised monograph lo5 includes a chptw 011 tlicexperimental technique used by the Liverpool school. J. A. Lovern lo6describes the methods of analysis used by him, and the new methods fordetermining the composition of fatty acid mixtures have been described byJ. A. Boyle 10’ and B. W. Beadle.lO*The methods commonly used in determining the detailed composition offats are :(a) Separation of saturated and unsaturated acids by the lead-salt methodor by the lithium-salt method log followed by the lead-salt method. TheA.O.A.C. methods 91 retain the lead-saltether method ; the A.O.C.S.methods 23 adopt the better Twitchell alcohol method.For larger amountsof fats the method of T. P. Hilditch loci is preferable.( b ) Estimation of saturated acids by permanganate oxidation, either bya Bertram method 110 or by Hilditch and co-workers’ method of solution inacetone .111, 105’j Ind. Eng. Chem. Anal., 1946, 18, 317 ; ,4?tal. Chern., 1947, 19, 932.9 6 L. Kyame, G. S. Fisher, and W. G. Bickford, J . Amer. Oil Chena. Soc., 1947,24,332.9 7 Arch. Biochem., 1946, 11, 489; Analyst, 1947, 72, 364.9 8 Oil and Soap, 1946, 23, 292. J . Amer. Oil C‘hem. SOC., 1047, 24, 137.loo Chem. Zentr., 1944, 11, 378.l o ‘ D. M. Copley, J . Amer. Pharrrz. ASSOC., 1946, 35, 7s.I o 2 E. Eigenberger, Pette u. A’eifen, 1944, 51, 43, 87.lo3 H. P. Kaufmann and M. C. Keller, ibid., p.223.lU4 S. Olsen, Die Chemie, 1943, 56, 202.lo5 ‘‘ The Chemical Constitution of Natural Fats ”, h t l etltn., 194T.Io6 D.S.I.R. Food Investig. Special Report, No. 61.Io7 Manuf. Chem., 1946, 17, 282.Io8 B:W. Beadle, Oil and Soap, 1946, 23, 140 (Review).log T. P. Hilditcli and L. Maddison, J . SOC. Chem. Ind., 1942, 01, 169.K. A. Pelikan and J. D. von Mikusch, Oil and Soap, 1938,15, 149.ll1 T. P.. Hilditch and C. H. Lea, J., 1927, 3106.Composition of Dep6t Fats ofAquatic Animals, 1942.K 294 ANALYTIOAL OHEMISTRY.(c) Eatimation of unsaturated acids by isolation and analysis of theirbromo-compounds. Although this method is not quantitative on accountof mutual solubility effects, different behaviours of isomers, etc., it can bemade to yield trustworthy re~ults.1~~ 2O(d) Estimation of oleic, linoleic, and linolenic acids by H.P. Kaufmann’sthiocyanometric method. Although W. Kimura in 1929 had pointed outthe shortcomings of this method, these were not generally recognised until1939 and later.ll3, 114 Since 1940 Kaufmann’s theoretical values have beenreplaced by empirical figures for thiocyanogen ~alues.10~~ 23 The thiocyanu-metric method may soon be superseded by the following method.(e) The spectrophotometric method of J. H. Mitchell, H. R. Kraybill,and F. P. Zscheile 115, lo* which directly estimates the proportions of linoleicand linolenic acids after alkali-isomerisation of these to conjugated acids.T. P. Hilditch, R. A. Morton, and J. P. Riley 116 confimed these findings andextended the method to the determination of these acids in the presence ofelaeostearic acid.l17 Spectrophotometric methods for a-elzeostearic acid 11*and a-, p-, and total elaeostearic acids 119 in tung oil are described. Thespectrophotometric method 115 is modified by using nitrogen to protect bothsamples and reagent during isomerisat ion.l20Although the thiocyanometric and spectrophotometric methods arenotable advances, there are indications that they need to be furtherinvestigated. R. T. Milner, reporting on collaborative work on SCNvalues,121 states that the results obtained gave compositions for the oilsstudied different from those obtained by the spectrophotometric method.T. P. Hilditch, M. L. Meara, and J. Holmberg 122 state that “ it has recentlybeen shown 123 that the spectrophotometric determination of linolenic acidmay proably give somewhat higher figures than the true values when theproportion of the latter acid is not large ”.(f) Separation of mixed fatty acids or glycerides by fractionalcrystallisation from solvents a t low temperatures, introduced by J.B. Brownand his c o - ~ o r k e r s , l ~ ~ ~ 125 which bids fair to oust the lead-salt method ofseparation 126s 127 and is the only available method for separating the mixedlla J . Soc. Chem. Ind. Japan, 1929, 32, 138B.113 R. W. Riemenschneider and D. H. Wheeler, Oil and Soap, 1939, 16, 219.114 T. P. Hilditoh and K. S . Murti, Analyst, 1940, 65, 437.115 Ind. Eng. Chem. Anal., 1943, 15, 1.117 T. P. Hilditch and J.P. Riley, J . SOC. C h m . Id., 1946, 65, 74.118 R. T. O’Connor, D. C. Heinzelman, A. F. Freeman, and F. C . Pack, I n d . Eng.1ls R. T. O’Connor, D. C. Heinzelman, and R. S. McKinney, J . Amer. Oil Chem. SOC.,lao R. T. O’Connor, D. C. Heinzelman, and F. G . Dollem, OiE and Smp, 1945,22,257.124 Ibid., p. 321.123 T. P. Hilditch and R. K. Shrivastava, Analyst, 1947, 72 (h the press).124 J. B. Brown and G. C. Stoner, J . Amr. Chern. SOC., 1937, 59, 3.125 J. B. Brown, Ohm. Reviews, 1941, 89, 533.126 T. P. Hilditch and J. P. Riley, J . SOC. Chem. Ind., 1945, 64, 204.127 F. A. Smith and J. B. Brown, Oil and Soap, 1946, 23, 321; 1946,23, 9.116 Araalyst, 1946, 70, 67.Chem. Anal., 1945,17,467.1947, 24, 212.J . Amer. Oil Chem. SOC., 1947, 24, 78SEXTON : OILS, FATS, AND SURFACE-ACTIVE AGENTS.295triglycerides of a fat. Incidentally, fractional crystallisation is nowcommercial practice.128 R. G. de Gray and A. W. de Moise 129 recommendthis method for separating fatty acids in analysis, and F. R. Earle andR. T. Milner 130 use it for the quantitative separation of the saturated acids ih5 g. of soya-bean oil fatty acids. F. E. Luddy and R. W. Riemenschneider 131prefer the crystallisation method in determining trisaturated constituents inedible oils. D. S. Anthony, F. W. Quackenbush, and H. Steenbock 132 alsofavour the technique for the analysis of 1 g . of oil. For the rapid estimationof saturated glycerides in edible fats, C. A. Coffey and H. T. Spannuth usecrystallisation .I33(9) Some form of distillation-by steam or by fractional distillation in avacuum, of the esters of acids, or molecular distillation.105 The first twomethods are in common use, the last has been somewhat disappointing.A.W. Weitkamp 134 found the amplified distillation of fatty acid methylesters satisfactory but not that of the acids themselves because of theformation of azeotropes with the hydrocarbon component. I n theester-fractionation procedure for the component acid analysis of fats thecompositions of the fractions are calculated from their saponificationequivalents and 1.V.s. With marine animal oils these calculations can bevery laborious, YO W. S. Rapson, H. M. Schwartz, and N. J. Van Rensburg 135describe and supply definite computation forms.Using a Valentineimproved precision refractometer, P. M. Althouse, G. W. Hunter, andH. 0. Triebold 136 determined the refractive indices of methyl, propyl, andisopropyl esters of the C6-C,, saturated fatty acids between 20" and 45".(h) Hydrogenation, either total or partial, in stages has been used withsuccess .lo5(i) Chromatographic methods. S. Claesson 137 has developed a flowingchromatographic method for the separation of fatty acids, using activatedsilica and a non-polar solvent. The members of a homologous series canbe separated in a similar manner by using activated carbon.122H. J. Dutton's 138 method for colourless compounds uses R. I. measurementof the percolate during continuous flowing. K. A. Williams 139 reviewed theuse of chromatography in fat analysis.A recent paper by the Liverpool school 122 shows how these methods wereused in determining the glyceride structure of soya-bean oil.Low-temperature crystallisation from solvents, the spectrophotometric method,fractional distillation, and adsorption methods were pressed into service.The Evers-Bellier test is discussed by C. M. Desai and A. H. Patel 140R. E. Kistler, V. J. Bluckerheide, and L. D. illeyers, Oil and Soap, l!kiG, 23, 146.lZD I d . Eng. Chent. Anal., 1941, 13, 22.131 Ibid., 1946, 23, 385.134 J . Amer. Oil Chem. SOC., 1947, 24, 236.135 Ibid., p. 84.13' Arkiv Kenzi, Min. Geol., 1946, 23A, No. 1 ; Rec. Trav. chim., 1946, 65, 571.138 J . Physical Chem., 1944, 48, 179.13@ Analyst, 1946, 71, 259.140 C.M. Desai and A. H. Patel, Curr. Sci., 1945, 14, 130; 1947, 16, 92.130 Oil and Soap, 1940, 17, 106.132 Ibid., 1943, 20, 53. 133 Ibid., 1940, 17, 216.136 Ibid., p. 267296 ANALYTICAL CHEMISTRY.and by 8. Naraya11ier.l~~ 5:. ‘l’. Voorhies and 8. 1’. Bauer 142 consider themodified Renard and Kerr tests for the determination of arachis oil unreliable.Despite this, the A.O.A.C. retain the method although it is not now consideredto be strictly quantitative.F. H. Smith’s two spectrophotometric methods 143 for gossypol in crudccottonseed oils require less than 2 hours compared with the 5 days of thegravimetric method. The A.O.C.S. gossypol committee 144 reported 011gravimetric and spectrophotometric methods for the determination ofMethods for the analysis of lecithin are given 85 and for lipids in feediiigstuffs by R.R e i ~ e r . 1 ~ ~ G. Gorbach 146 gives details of micro-methods forphosphatides in fats. Recent cases of poisoning lend interest toP. Malangeau’s method 14’ for tricresyl (tritolyl) phosphate in vegetable oils.gossypol.Mono- and Di-glycerides.These are rarely purc products-they are usually mixtures of all theetypes of glyceride with one type preponderating. For inst’ance, commercialglyceryl monostearate contains free glycerol, and mono-, di-, a,nd tri-stearinas well as stearic acid soaps.S. Kawai and S. Yamamoto,1*8 investigating the production of 1110110-glycerides from tea-seed oil by inter-esterification, determined the acid,saponification, and hydroxyl values at intervals and thence calculated themono-, di-, and tri-glyceride contents.K. S. Markley 149 states that thethree types of glyceride may be separated by fractionation from alcohol.J. H. Newburger 1.50 determines monostearate in a sunburn creamcontaining lanolin, by chloroform extraction, determination of free itndcombined glycerol by I. Shupes’s periodate method,156 of unsaponifiahlcmatter, fatty acids, and their equivalent weight, and then caIculatioii of theinonoglyceride content. A. Troy and A. C. Bell 151 use a somewhat similarmethod for cosmetics.E. Handschumaker 152 and his co-workers detect and estimate diglyceridesin hydrogenated oils by using the principles of Hilditch’s crystallisation fromacetone. N. Ivanoff,ls in a new method for monoglycerides in fats, oxidisesin alcohol with standard periodate and back-titrates with sodium arsenite.The hydroxyl groups give 2 mols. of corresponding aldehydes.W. D. Pohle,Io1 Curr. Xci., 1945, 14, 177.lo3 F. H. Smith, Ind. Eng. C’henb. Anal., 1!146, 18, 41, 658.146 t’ette u. Seife?), 1944, 51, 53; Che??~. Abs., 1947, 41, 1469.” 7 Ann. Phurnt. frunq., 1944, 2, 102; Chent. Abs., 1946, 40, 4900.148 J . SOC. Chem. Ind. Jupam, 1940, 43, 219.log ‘‘ Fatty Acids ”, p. 306.150 J . Assoc. Off. Agric. Chem., 1947, 30, 683.l 5 I Amer. Perfumer, 1946, 48, 54; Chem. Abs., 1946, 40, 6667.152 E. Handschumaker, S. W. Thompson, and J. E. McIntyre, Oil u i ~ d Soap, 1943,l m Chem. Abe., 1946, 40, 6361.142 Oil and Soup, 1943, 20, 175.J. .41ucr.Oil Chenb. Soc., 1947, 24, 369. l i t 5 Ibid., p. 199.20, 133V. 0. Mehlenbacbher, aiitl J. H . Cook IM determine inonoglywride by periodic.oxidation ; di- and tri-glycerides do not interfere. R. 0. F e ~ g e , ~ ~ ~ analysingpurified mono- and di-glycerides prepared by himself, from total combinedglycerol content by the A.O.C.S. clichromnte method, monoglyceridecontent,la free fatty acid content, and mean molecular weight of the fattyacids, calculated the mono-, di-, and tri-glyceride composition of the products.E. Handschumaker and L. Linteris 230 modify the periodate method,lM byusing an inert solvent. 'Phis avoids heat-induced secondary oxidat ioiire;tctions and the time required is reduced from 30 to 2 minutes.Surface-crct iue A gmts IThese fall into three main classes : anionic, cationic, an(\ non-ionic types(a general account with classification is to be found in works by H.K. Dean,and by C. B. Young and I<. W. C O O ~ ~ S , ~ ~ ~ and articles by C. G r a n a ~ h e r , ~ ~ ~J. A. Hill,159 R. Ackley,160 I. Hollenberg,lG1 J. Ripert,162 andJ. C. L. Resuggan 163). They are used either alone or with soaps, inorganicsalts, cellulose derivatives, etc., so their examination calls for all the ingenuityand skill of the chemist and the response to the challenge is to be observed inthe large number of papers published in the past few years.Evaluation and Cor,&parison.-This is generally done by wetting tests,surface and interfacial measurements, and detergency tests. The wettingtest is usually C.Z. Draves and R. G. Clarkson's sinking-time test or somemodification of it.lG4 I. J. Gruntfest, 0. B. Hager, and H. B. Walker 165criticise the test and propose it hydrometer modification. The German testis Surface and interfacial-tension measurements are made bysome convenient rneth0d.1~~6 A. E. Alexander and J. H. Schulman167determined benzene-water interfacial tensions in the presence of surface-active agents, and R. 0. Feuge155 measured the interfacial tension ofoil-water systems containing mono- and di-glycerides. As inorganic saltsare often present in large amounts in surface-active agents,l68 surface-tensionmeasurements are not of much value for comparison purposes.The detergency test is carried out by washing soiled material underIb4 Oil a d Soap, 1945, 22, 115.l x J . Awtcr. Oil Cheiti. Soc.., 1947, 24, 19..I. A4ssoc. OJ. A g r i c . P/wm., 1913, 26, 249; S. H. Sewburger an(l ('. F. Hriirning,15' H. K. Dean, " Utilisation of' Fnts ", 1938; ('. H. Young and K . IT, C'oon\,158 ('iba Review, 1945, 56, 2039.lsS J . SOP. Dyers Col., 1947, 63, 319.lb1 Soap, Perfumery, and C'osmetics, 1947, 20, 56.'.1 6 2 Ibid., 1945, 18, 885; 1946, 19, 552.ls3 Food Manzrf., 1947, 22, 163, 203, 299, 363.l b 4 A-l)wr. Dyestiif Rep., 1931, 20, 301 ; 1939, 28, 425.l C 5 Ibid., 1947, 36, 325.IfiQ I\'. Baird, C. P. Brown, and C . R. Purdue, J . SOP. Dyers Pol., 19-16, 62, 323.I G 7l f i 8 L. 11. Flett, C'heni. Enq. S e w s , 1942, 20, 1 3 ; J. A. Hill and C. L. Hunter, Xnttwe,ibid., 1947,30, 651." Surface Active Agents ".160 Boap clnd Snn.C ' h e t t i . , 1917, 23, 39.'I'mns. Faraday Soc., 1940, 36, 960.1946, 158, 585208 ANALYTICAL CHEMISTRY,standard reproducible conditions in a " launderometer ", in which 20 samplesof soiled cloth can be washed simultaneously in separate containers, and thencomparing the washed cloths either visually or by reflectance measurements.S. F. S y I ~ e s t e r , ~ ~ ~ instead of the Atlas " launderometer ", used a " detergencycomparator '' to compare synthetic detergents with soap, as regards scouringefficiency. W. G. Tiedeman l70 reviews the evaluation of some dish-washingdetergents, and a performance test for these is given by E. H. Mann andC. C. Ruchhoft.I7l A simple laboratory method of comparing detergents isdescribed by A.J. Kelly and D. H. G ~ n t h e r . l ~ ~ Using a " launderometer ",A. K. Epstein 173 and his co-workers determined the reflectance of the washedcloths with a photovolt reflectometer. The preparation of standard soiledmaterial and the construction of a soiling machine are described byB. S. Van Zile.174 Studies in soiling and detergency, standard " soils ", andwaahing procedure were made by J. R. Clark and V. B. H01land.l~~J. P. Sisley discusses the determination of the industrial value ofdetergents.228 The many methods for comparison of detergents aredescribed.176 R. B. Whitehead177 writes on the evaluation of wettingagents and criticises the tests. Information on washing tests is given byM.L. H ~ r w i t z , l ~ ~ 0. Bac0n,1~~ and E. Kornreich.lsoA colorimetric method for evaluating dispersing agents is described byG. C. Tesoro, W. T. Donahue, and J. A. Casey.ls1 The testing compoundwas Hansa-yellow YT-445D which is neither surface-active nor easilydispersed. The degree of solubilisation of water-insoluble dyes by soapsand detergents was measured by J. W. McBain and A. M. Green.182M. Z. Poliakoff describes a simple and well-tested method of evaluatingdetergent efficiency, using dispersion cylinders.la G. Davis, S. J. Ward,and P. D. Liddiard lE4 have constructed an instrument for measuring thestrength of detergents; and F. W. Gilcreas and J. E. O'Brien ls5 andR. C. Hughes and R. Bernstein ls6 describe photoelectric methods ofmeasuring detergent efficiency.E. L. Pouts and T. R. Freeman 187 describea simple apparatus for the same purpose.AnaZysis.-The analysis of surface-active agents is conveniently dividedinto (a) analysis of surface-active agents and ( b ) detection and determinationof these.169 Amer. Dyestu, Rep., 1947, 36, 91. 170 Soap and Sun. Chem., 1947,23, 48, 102.1 7 1 Pub. Health Repts., 1946, 61, 877. 172 Anaer. Dyestuff Rep., 1947, 36, 455.173 A. K. Epstein, B. R. Harris, M. Katzman, and S. Epsteifi, OiZ and Soap, 1943,20, 171.Ibid., p. 55. 175 Amer. Dyestuff Rep., 1947, 36, 734.178 Amer. Dyestuff Rep., 1946, 35, 83.180 Text. Manuf., 1946, 72, 271.l T G A.S.T.M. Bulletin, 1946, No. 140, 78; No. 141, 49; J. C. Harris.l i 7 Ciba Review, 1945, 49, 1789.l i 9 Ibid., 1945, 34, 556.Rubber A g e , 1946, 60, 319.lB2 J .Amer. Chem. SOC., 1946,68, 1731 ; J . Physical Cliem., 1947,51, 286.183 Anal. Chem., 1947, 19, 140.lE4 Abstr. Proc. Xoc. Agric. Bact., 1944, 53.Amer. J . Pub. Health, 1941, 31, 143.1e6 Ind. Eng. Chem., 1945, 37, 170. lB7 *J. Dairy Sci., 1947, 30, 61SEXTON : OILS, FATS, AND SURFACE-ACTIVE AQENTS. 299(a) The A.O.C.S. methods23 include a section (F) on the analysis ofsulphonated and sulphated oils, and D. Burton and G. F. Robertshaw’spublication 18* remains indispensable. I n further work 189 on thedetermination of free and uncombined unsaponifiable matter in oils, waxes,and sulphated products, Burton and Robertshaw investigated the S .P.A.,I.C.S.F., and Wizoeff methods and recommend the first for most oils as wellas describing procedures for sulphated oils and alcohols and petroleumsulphonic acids. D.Burton and L. F. Byrne,lgo~ l 9 1 on the constitution ofsulphated oils, give methods for determining the carboxyl, sulphato-, andsulphonic groups and their salts. S. L. Glicher Ig2 describes the tests used inanalysing sulphated oils, and much useful information can be found inarticles by M. G. de Navarre.l93 An early method for aryl alkyl sulphatesin solution was the benzidine method of W. Kling and F. P~schel.19~ Thishas been used by A. Brunzelllg5 in determining dodecyl sulphate in thepresence of sodium sulphate and soap. Dodecyl sulphate was determinedby titration of the acid liberated by acid hydrolysis.The Kling-Puschelmethod was used by D. A. Shiraeff Ig6 in the quantitative analysis ofIgepon T. T. V. Marron and J. Schifferlei lg7a describe a direct volumetricdetermination of the organic sulphate content of synthetic detergents, whichinvolves reaction of p-toluidine with sulphonates, extraction of the complexinto carbon tetrachloride, and subsequent titration. A reference sample isanalysed by the “ difference ” method of D. Berkowitz and R. Bernstein,lg8who separate “ active ” ingredients by 50% alcohol, determine soap, “ fat ”,and chloride in the alcoholic solution, and calculate synthetic detergent as thedifference between total alcohol-soluble matter and the sum of soap, “ fat ”,and chloride. Oil-soluble petroleum sulphonates are analysed by extractionwith chloroform, potentiometric titration, and adsorption on Attapulgus~lay.1~9Themethods of determination can be used for detection and vice versa Whensurface-active agents are to be detected or determined it is usually firstnecessary to extract them from the material in which they are contained bymeans of some suitable organic solvent, immiscible or otherwise.Eachsample has to be treated on its merits so as to obtain the surface-active agentin as pure and concentrated form as possible.2m, 201“ Sulphated Oils and Allied Products : Chemistry and Analysis ”, 1939.J . Inter. SOC. Leather Trades’ Chem., 1946, 30, 279.(b) Many methods are now in use or have been prop0sed.1~~6lgo lbid., p. 306. lgl Ibid., 1947, 31, 100.lg3 Soap, Perfumery, and Cosmetics, 1946-47.lg5 Svensk Parm.Tid., 1947, 51, 101 ; through Chem. Abs., 1947, 41, 3641.lQ6 Amer. Dyestuff Rep., 1947, 36, 313.l g 7 0 I n d . Eng. Chem. Anal., 1946,18, 49.19”, C. J. Pederson, Amer. Dyestuff Rep., 1935, 24, 137; F. M. Biffen and F. D. Snell,lg8 Ibid., 1944,16, 239.lQ9 F. Brooks, E. D. Peters, and L. Lykken, ibid., 1946, 18, 544; Ana7yd, 1946,2oo J . Amer. Oil Chem. SOC., 1947, 24, 54.201 Dr. Wurzschmidt, Chimie anal., 1947, 29, 44.lg2 Petroleum, 1945, 8, 130, 232.lQ4 Melliand. Textilber., 1934,15,21.Ind. Eng. Chem. Anal., 1935, 7, 234; J. C. Harris, ibid., 15, 254.71, 5933 0 ANATdYTTC-4Td ORRRITSTRY.Methods for the estimation of quaternary ammoninm compounds arereviewed by A. S. DuBois,202 who gives a titration met’hod 203 using 0.01%bromophtnol-blue and 0.04:/, sodium dodecyl sulphat e , and anargentometric 204 inethod with eosin or dichlorofluorescein indicator.M.E. Auerbach’s method205 consists in treatment of 2 mols. of thequaternary salt with 1 mol. of bromophenol-blue t,o form a blue dye, which isthen extracted with ethylene dichloride and examined colorimetrically ; hisown modified method 206 use8 benzene.avoids the extraction. T. H. Harris 208 estimates quaternary ammoniumcompounds in fruit juices by Auerbach’s method, the method of measurementbeing as described by J. B. Wil~on,~O~ who also describes two methods forthese compounds in foods. The first is a modified Auerbach method ; in thesecond the quaternary compound is precipitated as the ferricyanic acid salt,the unused ferricyanide being determined by titration. The ferricyanidemethod is described elsewhere.210 0. Hager, E. Young, T. Flanagan, andH. Walker 211 describe two qualitative and three quantitative methods forquaternary ammonium compounds based on the insolubility of theirtri-iodides in water. Determination by precipitation with anionic dyeswas proposed by G . S. Hartley and I>. F. Runnicles 212 and by A. Krog andC. G. Mar~hall.~l~ The determination of the concentration of quaternaryammonium solutions and their detection in milk are described.229 Thesolubilities of such compounds in organic solvents have been determined.214Methods for the estimation of small quantities of sulphonated or sulphatedsurface-active agents have been offered by F. M. Scales,215 J. C. Harris,216H. H. Jones, 217 and L. F. H0yt.~18 Jones’s method is based on the fact thatsulphonated surface-active compounds (colourless anion) formed colouredchloroform-soluble salts with methylene-blue (coloured cation). Thecoloured chloroform solution is read in a spectrophotometer : 1.0 mg. ofanhydrous methylene-blue chloride = 3.13 x equiv. of ‘‘ sulphonate ”.This method is also useful as a rapid qualitative test. Hoyt’s methoddetects surface-active agents by their solubilising action on the oil-solubleNational Brilliant-Blue B.M.A. The surface active agent, after isolation, isdissolved in water. The dye in 2% dilution in sodium chloride is added,and a blue solution is obtained in the presence of a surface-activeE. L. Colichman’s modification202 Amer. Dyestuff Rep., 1915, 34, 245. 203 Soap and Saii. C h e w . , 1926, 22, 12.5.204 I d . Eng. Clzem. Anctl., 1945, 17, 744. 205 Ibid., 1943, 15, 492.2oc lbid., 1944, 16, 739. 2oi Anal. Chein., 1947, 19, 430.408 J . Assoc. Off. Agric. Chem., 1946, 29, 310. ?09 Ibid., p. 311.210 “ New and Non-official Remedies ”, 1946, p. 165 (ferricyanide method).2 1 1 Anal. Chent., 1947, 19, 886.213 Anter. J . Pub. Health, 1940, 30, 341.214 R. S. Shelton, J . Anter. Chem. Soc., 1946, 68, 753; I?. A. Reck, H. J . Hnrwood,and A. W. Ralston, J . Orq. Cheni., 1947,12, 517.2 1 5 Proc. Inter. Assor.. Milk Dealers, 1939, 31, 197.2 1 2 Proc. Ro!J. Sor., 1938, A , 168, 424.I n d . Eng. CJLeitz. Anal., 1043, 15, 234.J . Assoc. Off. Agric. Chew?., 1945, 28, 399.t J . Anier. Oil Chem. SIoc., 1947, 24, 54SEXTON OTT,S, FATS, ANn SURFACE-ACTTVR AGENTS. 301caonipouncl. The method is suitable for the anionic, cationic, and non-ionic:types.Certain cationic surface-active agents form st,oicheiometric salts withanionic types. This fact has been used as the basis of t,wo titrimetricmethods 212j 219 which, according to S. R. Epton,220 are not entirely satis-factory. He titrates the alkyl sulphate in water-chloroform mixture withcetylpyridinium bromide solution using a methylene-blue indicator solution ;when the colour in both layers is of the same intensity the equivalence pointhas been reached. T. Barr, J. Oliver, and W. V. Stubbing< 221 confirmEpton's findings and claim that their own method is an improvement on thetnethylene-blue method.The estimation of mono- and di-alkyl phosphates and free dodecyl alcoholin the presence of free acid is described.222 A Hintermaier 223 givesqualitative tests for detergent mixtures, and K. M. Linsenmeyer's scheme 224separates wetting agents into eight classes. H. B. Goldstein 225 describes thequalitative analysis of surface-active agents, and A. Parisot 226 gives indetail the analysis of some wetting agents. A. Steigmann227 gives twocolour tests for anionic wetting agents. G. E. W. S.H. J. DOTHIE.J. R. NICHOLLS.6. E. W. SEXTON.I<. (:. MTOOI,." I y 6. M. Preston, J . SOC. 1)yer.s Vd., 1045, 61, 163.220 Nature, 1947,160, 795.2"3 Fette u. Seifen, 1945, 51, 10.225 Amer. Dyestug Rep., 1947, 36, 629.22i J . Sor. Chenz. Id., 1947, 66, 356.s29 W. J. Harper, P. 13. Elliker, and W. I<. Moseley. J . Dairy Sci., 1047,30, 536.621 {bid., p. 909.134 Melliand. l'extilber., 1940, 21, 468.226 Corps gras et savons, 1943, 1, 11.428 Anzer. Dyestuff Rep., 1947, 36, 457.S. B. McFarlane, jiinr., Oil and ~Tonp, 1946, 23, 337..I. -4fner. Oil Chemz. h'oc., 1947, 24, 14.3