August, 19511 GRIDGEMAN 449 Observations on the Spectrophotometric Assay of Vitamin A by Geometric Correction of Absorption Curves BY N. T. GRIDGEMAN The accuracy of the spectrophotometric assay of vitamin A by geometric correction of absorption curves depends on the valid scope of two assumptions, viz., that the absorption curves of natural forms of the vitamin are indistin- guishable from that of pure all-trans vitamin A, and that the ultra-violet absorption curves of materials other than vitamin A in natural oils have three linear points a t certain wavelengths. There is evidence that these assumptions are not always correct, and it is shown that comparatively small departures from these conditions may be associated with appreciable loss of accuracy. An attempt is made to quantify degrees of departure in terms of the accuracy of the result.The influence of the normal observational errors of spectrophotometry on the precision of the result is also considered. The application of the method to cod-liver oil, as originally proposed, appears to be more firmly based than its application to richer oils. IN 1946, Morton and Stubbsl described a geometric method of “breaking down” compound spectrophotometric absorption curves into two parts, the major part being the established and characteristic curve of the compound in the original mixture whose quantitative analysis r E” i S S r Fig. 1. The geometry of correction S is sought and the minor part being the remaining “irrelevant” absorption about whose shape certain simple assumptions must be made.The method was applied in particular to the estimation of vitamin A in cod-liver oil. Later, the same authors extended their work to the analysis of other liver ~ i l ~ . ~ ~ ~ OseI“‘ and McGillivray6 have also published papers on the application of the method to oils containing vitamin A. The’present paper records some observations on the theory and on the reliability of the method as applied to the analysis of vitamin A in fish-liver oils and concentrates; in this context, reliability includes both precision (reproducibility of results) and accuracy (approximation to truth).460 GRIDGEMAN : OBSERVATIONS ON THE SPECTROPHOTOMETRIC ASSAY OF [VOl. 76 DERIVATION OF METHOD Consider three vertical parallel lines, as shown in Fig. 1, of length EL, EM and EH, rising from a horizontal base at distances apart r and s.Suppose these verticals to be the sum of the two lower sets, about which we know, first, the values a and b in set I, and secondly, that the tops of the three verticals in set I1 fall on a straight line. Given EL, EM and EH, Y , s, a and b, we are required to find X. I t can easily be shown that- and the expressions for ax, b X , P and Q and 12 readily follow. Applying this to spectrophotometry we can see that, given (2) the optical densities (verticals) at any three wavelengths (horizontals) of a solution of a mixture, (ii) the relative optical densities at those wavelengths of one component (a) of the mixture and (iii) the fact that the optical densities at the same wavelengths of the other component, or the sum of the other components (p), lie on a straight line, WE: can calculate for each wavelength the exact and unique partition of the original optical density between the contributions of cc and p.Further, knowing the cell thickness, the streng1:h of the solution and the light absorption by pure cc at the three wavelengths, we can transpose our results into quantitative analysis. In practice this means working in terms of EiZa. It is important to note that there is no assumption of linearity of the optical densities of the irrelevant component /3 at wavelengths other than the specified triad; in between them the optical densities may take any value. In practice we can simplify things by so choosing r and s in equation (1) that a = b = (say) k. Then- To apply this equation to the assay of vitamin A, Morton and Stubbs determined the relative optical densities in various solvents over a wide wavelength range for vitamin-A, acetate (assumed to have precisely the same curve as the fatty-acid esters of vitamin A existing in fish-liver oils) and for vitamin-A, al.coho1 (assumed to have the same curve as the free vitamin A that is split off into the unsaponiiiable matter of fish-liver oils).They then assumed that, in most fish-liver oils, “the irrelevant absorption ‘curve’ is linear over the approximate range 310 to 340mp, i.e., that no impurity or artefact shows a maximum very close to that of vitamin A,” adding that “a good deal is now known concerning the spectra of vitamin A, and oxidation products of vitamin A, and it can be said that over the range 310 to 340 mp their absorption curves are at least approximately linear.”S With this in mind they chose, for vitamin-A acetate in cyclohexane, Y = 15 and s = 10.5 on either side of A,,,.= 328 mp. So in the present notation, EM = E at 328 mp, EL = E at 313 mp, and EH = E at 338.5 mp, where E is an abreviation for E:& These fixation points give k = 6/7, and the equation becomes- = 7 [E at 328 mp - 0.4118 :E at 313 mp - 0.5882 E at 338-5 mp], . . (3) X, of course, being E at 328 mp (.net), or (cow.), i.e., “corrected” to eliminate all absorption other than that due to vitamin A, in contradistinction to the E at 328 mb in the brackets, which is gross, i.e., as recorded on the original sample. cyclohexane, Morton and Stubbs find- Other, very similar, equations hold for other conditions.For vitamin-A X = 7 alcohol in = 7@ at 326 mp - 0.4 E at 311 mp - 0-6 E at 336 mpj.August, 19511 451 Oser-4 finds that the above Morton - Stubbs equation for vitamin-A acetate in alcohol applies equally to the same compound in isopropanol. For vitamin-A alcohol in isopropanol he uses the equation- VITAMIN A BY GEOMETRIC CORRECTION OF ABSORPTION CURVES 5 EH] X = 7 E M - - E L - iI l2 = 7[E at 326 mp - 0.4167 E at 312 mp - 0,5833 E at 336 mp], but the U.S.P. Assaye of Vitamin A specifies, for vitamin-A alcohol in isopropanol, the slightly different equation- = 7[E at 325 mp - 0.375 E at 310 mp - 0.625 E at 334 rnpu], the constants being based on a 23-laboratory co-operative examination of the U.S.P.Standard Vitamin-A acetate via the unsaponifiable matter. The recently published 1951 Addendum (Appendix XV, p. 92) to the B.P. 1948 specifies “6/7” correction formulae based on A,,,. = 327.5 mp, with r = 15 and s = 10-2, for the esterified vitamin, and on Amax. = 326.5 mp, with r = 14 and s = 10.2, for the alcohol form. No worker appears to have considered any value for k other than 6/7. From the Morton - Stubbs curve for vitamin-A acetate we can derive numerous equations geometrically no less valid than the “6/7” ones, although, of course, there may be dispositional objections to them. Some examples are- Both refer to cydohexane solutions. k 1/(1 - k) L, mp HJ mp s I ( y + 4 y / ( y + s) 9/10 10 316 336 0.4 0.6 5 310 341 0.4194 0-5806 4 308 343 0-4286 0.5714 4/5 3/4 Morton and Stubbs remark that the “only significance of the ratio 6/7 is that it is empirically appropriate in relation to the wavelength range covered, and to the performance of the spectrophotometer.JJ3 They had principally in mind high-potency oils, to which the formula originally devised for cod-liver oil was then being applied.There was in practice a special reason for the choice of the 313-mp fixation point on the absorption curves of cod- liver oil: it seemed least likely to disturb the mathematical assumption of %point linearity on the absorption curve of the irrelevant material. Some of the curves obtained by sub- traction of the vitamin-A curve from the gross curves of cod-liver oil exhibited small but distinctive peaks at about 305 mp and 320 mp associable with conjugated tetra-ene acids, and the trough in between usually reached a minimum at 313 mp.A comparison of the results from the standard “6/7” equation with those from the equations corresponding to the sets of constants tabulated above is made later in this paper. McGillivray6 uses the correction procedure in principle, but adopts a slightly different geometry that “lends itself to a simpler calculation.” Instead of taking fixation points at which the two “shoulder” absorptions are equal (ie., a = b = k), he prefers two points equidistant in wavelength from the point of maximum absorption (k, Y = s). He chooses 310mp and 340mp for vitamin-A alcohol and the equation is- X = EM - 2.611 (EL + EH) = 2Eat325mp -2.611 (Eat310mp+Eat340mp). SOURCES OF ERROR OBSERVATIONAL ERRORS- A result that is a function of three E values will clearly have wider limits of error than it result depending on one.To solve the complex problem of how much wider the limits of error are, it must be recalled that what is normally described as “error” in spectrophotometry can be ascribed to several variables, such as the effect of temperature and solvent, and the accuracies of the optical density scale, of the make-up of the test solution, and of the cell dimensions; all these will have in common an exactly parallel influence on the three E values, so that the corrected E value, being a function of the three, will be, as far as these and simiIa.r452 GRIDGEMAN : OBSERVATIONS ON THE SPECTROPHOTOMETRIC ASSAY OF [VOl. 76 sources of variation are concerned, in error to exactly the same extent as the uncorrected value.On the contrary, the reproducibility of the d a t i v e optical densities at the three wavelengths-covered by the term “residual error” in the analysis of variance-has necessarily an inflated influence on the error of the corrected E value. This residual error, therefore, independently affects the three readings, and its inflationary influence can be calculated. Let us assume that EM, EL and EH have a common coefficient of variation e; in other words, that the standard deviations of the three values are, respectively, eE@00, eEL/100 and eEH/100. Now, if we write the correction formula as- it follows from the theory of errors that the standard deviation of X will be- X = 7 [EM - CIEL - CZEH], - If we take the constants C, and C, appropriate for vitamin-A ester in cyclohexane (equation 3, above) and if, for simplicity, we suppose that the irrelevant absorption has zero slope over the three wavelengths (b., EM - X = EL - 6X/7 = EH - 6X/7), then the coefficient of variation, which is the percentage standard deviation of X, can readily be derived.It is- This means that the coefficient of variation of a corrected E value is greater than that of the original gross E value by a factor that depends on the amount of irrelevant absorption (EM - X) present at the central wavelength, 328 mp. If, for example, the amount is 10 per cent., then EM/X is 1.1 and the factor is 9.2. Some representative evaluations are as follows- Irrelevant absorption at 328 mp, yo .. .. 6 10 16 20 This special case of equality of irrelevant absorption at the three wavelengths is in practice very representative geometrically; it is obvious that within the range of slopes of the irrelevant contribution likely to be encountered the difference between (EL - 6X/7) and (EM - X) will be very close to that between (EM - X) and (EH - 6X/7), and the corresponding differences introduced into the error equation will almost compensate. So that, as far as this point is concerned, we can assume that t.he factors given above hold for all normal circumstances. The assumption that EL, EM arid EH have equal coefficients of variation is not wholly justified; in practice EL and EH can be expected to have slightly higher coefficients; this means that the given factors may be very slightly low.It appears, then, that for every 1 per cent. of observational error in a gross reading, an error of the order of 8 to 10 per cent. is to be expected in a corrected reading. Let us now reconsider the total error of variation of an E value, made up of the residual coefficient of variation e, and the summated variation due to the factors discussed above and whose effect is not magnified by correction: let us call its coefficient d. A duplicate E value from one laboratory will have an effective coefficient of variation of 2/(# + e 2 / 2 ) . If three E values are determined and two of them are used to “correct” the third, the resultant corrected E value will have an effective coefficient of variation of d ( d 2 + e2f2/2), where f is the error factor derived as shown above and whose value is here, say, 9.Typical values for e and d are, respectively, 1-5 and 2; hence, on evaluation it is found that the expected coefficients of variation of results of the type described are 2.3 for normal, uncorrected, E values and 9-8 for corrected E values. A recent co-operative trial designed t o ascertain the error of corrected E vaIues has yielded evidence not inconsistent with this theoretical derivation.’ Error factor .. .. .. .. . . 8.7 9.2 9.7 10.4 ASSUMPTIVE ERRORS- Assumptive errors are those introduced by departures from the basic assumptions of the shapes and positions of the tWQ absorption curves, that of vitamin A and that of the irrelevant material. Let us first consider departures from the assumed characteristics of the curve for vitamin A.Suppose, to begin with, that the true position of the vitamin A is displaced, without distortion, along the wavelength scale. (Such a shift might be artificial, caused by unknown solvent effects or maladjustnient of the wavelength scale or, alternatively, natural; in thatAugust, 19511 VITAMIN A BY GEOMETRIC CORRECTION OF ABSORPTION CURVES 463 the particular esterified vitamin A in the oil might be slightly different chemically or stereo- isomerically, and therefore spectrophotometrically, from vitamin-A, acetate.) It can be shown that the resulting displacement errors are as follows- Displacement of vitamin-A curve from assumed position Corrected E a t 328 mp as percentage of true value -2 mp 98-3 -1Illp 98.7 zero 100 104.1 2mCL 108.6 It appears that the errors so introduced are small if the vitamin-A curve reaches a maximum at a wavelength one or two millimicrons less than that of the assumed maximum, but appreciable if the displacement is in the other direction. Robeson and BaxterS have evidence that suggests that the vitamin A of the common fish-liver oils is two- thirds vitamin A, and one-third neovitamin A,, the two forms being equally potent.The The presence of neovitamin A may appropriately be considered here. I 1 I12 I I I I I I I I I I I 1 I I I L w \ 1 300 328 340 Wavelength, m l (4 I I 90.5 I I I : 21.5 1 , I ‘ 1 I I 1 * & I 1 300 328 340 Wavelength, mp (c) Fig. 2. correction of its absorption curve. as shown a t (c) How a hypothetical mixture of vitamin A and “irrelevant” material responds to 3-point The 3-point correction of the curve shown a t (b) partitions it absorption curve of the neovitamin seems to be similar to that of the ordinary (all-trans) material, but shifted 3 mp further up the wavelength scale, while its absorption at A,,,.is 10 per cent. lower than that of the ordinary vitamin A at its Amax.. Suppose that a 2 to 1 mixture of the two forms, uncontaminated and saponified, is assayed according to U.S.P. XIV.6 At the fixation points the true breakdown would be- E at 310 m p E at 325 mp E at 334 mp Vitamin A . . . . . . .. 59.5 69.4 59.5 Neovitamin A . . . . .. 25-5 30-6 28.1 Totalobserved . . . . . . 85.0 100.0 87-6454 GRIDGEMAN : OBSERVATIONS ON THE SPECTROPHOTOMETRIC ASSAY OF [VOl.76 and on applying the correction formula to the observed values the assay would be 93.6 per cent. of vitamin A, instead of the true (biological) value of 100 per cent. Let us now consider “distortion,” i e . , the possibility that the fixation points of the particular sample of vitamin A under test are not quite those assumed in the fonnula. To set out all the possible kinds and degrees of distortion would be impracticable, but a repre- sentative selection is shown in Table I. TABLE I EFFECT OF FIXATION-POINT DISPLACEMENT ON E AT 328mp (CORR.) OF VITAMIN-A ACETATE IN CYCZOHEXANE “Corrected” observed values when the true value is 100 If the higher 6/7 point, assumed to be a t 338-5 mp, is actually at 336.6 337.5 338.5 339.5 340.6 106.0 11 11.2 117.0 123.3 128.8 98.2 1LO3-4 109.2 116.5 121.0 to be at 313 mp, 314 80.9 86.1 91.9 98.2 103.7 is actually a t II; 315 73.5 78.7 84.5 90.8 96.3 f A \ point, assumed 313 89.1 94.3 100 106-4 111.9 Finally, there are possible faults to be reckoned with in the assumption of effective linearity of the curve of the irrelevant material.The term “effective” is used because, as already pointed out, the assumption concerns the E values a t the fixation points only, the contour of the curve between and beyond these points being immaterial. Curvilinearity of the three E values, as of any three points in a plane, can, of course, theoretically cover great distributional variety, ‘but fortunately for the present purpose all distributions can be considered as vertical displacements of the centre point, Le., values of E a t 328 mp greater or smaller than those interpolated from E at 313 mp and E a t 338.5 mp of the irrelevant material.It can readily be shown from the fundamental formula that one unit of departure from linearity in this measure (IZ at 328 mp) will result in an error of 7 units in the estimation of E at 328 mp (net) by correction. A hypothetical example is shown in Fig. 2 and in the following- If the lower E a t ,313 mp E a t 328 mp E a t 338.6 m p Vitamin A .. .. .. . . 85.7 100.0 85.7 Irrelevant . . .. .. .. I. 8.5 12.0 9.8 Sum .. .. . . 104.2 112.0 95.6 The three E values for the irrelevant material fall on a curve, which may be considered Correction as a 1.4-unit middle-point displacement from the straight line 18.5, 13.4, 9.8.of the summated E values yields the following analysis- E at 313 m p E a t 328 mp E at 338.5 m p Vitamin A .. .. .. :I 7.2 90.1 77-2 Irrelevant . . .. .. .. 27-0 21.9 18.3 Sum. .. .. . . 104.2 112.0 95.5 in which E at 328 mp for the vitamin-A fraction is 9-9 units (k., approximately 7 x 1-4) too low. This is not, it may be mentioned, an exaggerated example: if, as in Fig. 2, the curve through the three points, E at 313 mp = 18.5, E at 328 mp = 12-0 and E at 338.5 mp = 9-8, is plotted, its shape will be found not implausible for the irrelevant material likely to occur in fish-liver oils. Yet there would be a 10 per cent. error if such a mixture were analysed by 3-point correction. ALTERNATIVE FIXATION POINTS I t is useful at this stage to consider the effect of using correction formulae based on fixation points other than the customary ones, i.e., based on values of k (in formula 2) other than 6/7.Constants for the equations corresponding to k = 9/10, 4/5 and 3/4 have already been given; to compare their corrective values to typical curves for oils containing vitamin A the equations have been applied to the absorption data of five samples described and discussed by Adamson et aZ.’ Of the seven sets of data (one from each of seven independent laboratories) three had for this purpose to be excluded, because one did not include detailed curves andAugust, 19511 456 two included curves insufficiently detailed to permit interpolation of the new fixation points. The mean results from the other four laboratories are set out in Table 11, the normal k = 6/7 values being included for comparison.VITAMIN A BY GEOMETRIC CORRECTION OF ABSORPTION CURVES TABLE 11 PERCENTAGE OF IRRELEVANT ABSORPTION AT 328 mp CALCULATED FOR (Mean values for four laboratories) VARIOUS FIXATION POINTS OF FIVE SAMPLES Sample A r \ Halibut-liver Hake-liver Cod-liver k Concentrate* oil oil oil Blend t Mean 9/10 16.2 21.9 16-7 17.8 15-3 (17-7) 17.6 10.9 14.2 10.7 12.6 8.0 (11.5) 11.3 10.5 13.3 9-3 18.9 7.2 (1 1.0) 11-8 9.5 12.4 11.8 16.6 5-9 (10.1) 10.2 617 4/5 314 Mean 11-8 16.6 16.5 12.1 8.1 * A processed high-potency fish-liver oil concentrate. t A mixture of the first four samples. The bracketed figures are the expected values calculated from The 80 values condensed into Table I1 have been analysed for variance with the results the known composition of the blend.shown in Table 111. TABLE I11 ANALYSIS OF VARIANCE OF DATA SUMMARISED IN TABLE 11 Source of variation Mean Variance Significance D.F. square ratio (at P = 0.05) Between laboratories . . .. .. 3 80.3 1-29 not significant Between samples . . .. .. 4 142.4 2.29 not significant Between formulae . . .. .. 3 188.6 19.36 significant Laboratories x samples . . .. 12 6 2 4 6.40 significant Laboratories x formulae . . .. 9 3.0 < 1 not significant Samples x formulae . . .. .. 12 16.7 1.71 not significant Interactions- Laboratories x samples x formulae 36 9.74 1 From Tables I1 and I11 the following inferences can be drawn- (i) There is no significant over-all difference between the four laboratories. (ii) No significant differences are shown between the quantities of irrelevant absorption in the five oils.Nevertheless, there is a tendency for the halibut- and cod-liver oils to give higher, and for the blend to give lower, values than the average. (iii) Laboratories differ in their relative placing of the oils: it is only when the results of all laboratories are pooled that these differences are submerged. (iv) The quantities of irrelevant absorption indicated by the four formulae differ. This is almost wholly accounted for by the high “9/10JJ corrections. But the figures for cod-liver oil can be specially treated: with k = 6/7 the yield of irrelevant absorption is markedly less than that given with the other values of k . This difference does not quite reach significance at P = 0.05, but is still noteworthy.(v) The values calculated from the absomtion curves of the blend, and those calculated from the curves of the component oils, appropriately weighted, show discrepancies. Those for k = 9/10 are least discrepant. (vi) Except perhaps for cod-liver oil, where there is some chemical evidence for the suitability of the k = 6/7 points, there is nothing on which to base a decision as to which of the four sets of fixation points is best. MECHANISM OF CORRECTION Analytically, attention can be confined to the E values at the three specified wavelengths. But, having calculated the partition, we may plot the gross absorption curve in extertso, subtract from it the vitamin-A curve and so obtain the presumptive curve of the irrelevant material.456 GRIDGEMAN OBSERVATIONS ON THE SPECTROPHOTOMETRIC ASSAY OF [VOl.76 Morton and Stubbs have published a number of such curve partitions in illustration of the results of %point correction. The irrelevant components usually slope down gradually and unevenly, froq the region of low to that of high wavelength. Sometimes, however, the slope is in the other direction and accompanied by slight peaks on the higher wavelength side: the presence of vitamin A, (Amax. = 350 ‘rip) or of anhydrovitamin A (Amax. = 350, 370 and 390mp) can often be inferred in irrelevant-component curves of this type. The Wavelength, mp (0) CONCENTRATE I O( >c w 0 L I I I l r I 250 300 350 Wavelength, rnp (c) COD i $ 1 1 1 00 - I oc s W 0 Wavelength, mp (6) HALIBUT 250 300 350 wavelength, my (d) HAKE Fig.3. Absorption curves for the four oils. Upper curves, whole oils; lower curves, “irrelevant” absorptions assumed in %point correction at fixation points shown by vertical broken lines a t wavelengths of 313, 328 and 338-5mp. partitioned curves of cod-liver oil come into a special category because of the low vitamin-A potency of the oil: this means that the ultra-violet absorption of the fatty acids is large in relation to that of the vitamin and plays a big part in shaping the irrelevantwomponent curve. In Fig. 3 the absorption curves of the four main oils analysed in the co-operative study reported by Adamson et a1.’ have been partitioned on the basis of ordinaxy (K = 6/7) 3-point correction (the fifth sample, a blend, was not included as it was too heavily weighted withAUWSt, 19611 VITAMIN A BY GEOMETRIC CORRECTION OF ABSORPTION CURVES 467 the high-potency concentrate to be illustratively useful in this context).The irrelevant components clearly resemble those described elsewhere. To understand the mechanism of the correction procedure, it is necessary first to realise that any given gross curve can be partitioned into an infinite number of pairs ranging from 20 ,\“ UJ 10 ol ’ I I 250 300 350 Wavelength, rnp. (0) CONCENTRATE 250 300 350 Wavelength, (b) HALIBUT Fig. 4. Theoretical breakdown of whole-oil curves into vitamin-A ester portions (not The curves labelled M-S are those assumed in the 3-point correction because the marked E:L& a t 328 m p of whole-oil curve = 100 The figures a t the right of the curves indicate the possible percentage of “irrelevant” shown) and “irrelevant” portions points &it 313, 328 and 338.5mp) fall on a straight line absorptions at 328 mp a certain upper limit (particular to each curve) downward.For example, a curve exhibiting E at 313 mp = 98.0, E at 328 mp = 100.0 and E at 338.5 mp = 79.7 cannot (on the basis of the standard vitamin-A acetate curve) “contain” more vitamin A than that represented by458 GRIDGEMAN : OBSERVATIONS ON THE SPECTROPHOTOMETRIC ASSAY OF [Vol. 76 E at 328 mp = 93 and E at 313 mp = E at 338.5 mp = 79.7 If this maximum is expressed as 93 per cent. of vitamin A and 7 per cent. irrelevant material, this is but the first of an infinite series of theoretical partitions of the original curve ranging down to no vitamin A and 100 per cent.of irrelevant material. Obviously, the h;t is highly improbable and perhaps the first is unlikely, but somewhere in the range is the tnie partition, and adjacent to it, and on either side, are numerous theoretical partitions that on graph paper would look equally plausible. Among them is that selected by the correcticln procedure, viz.- E at 313 m p E a t 328 mp E a t 338.5 m p Vitamin A . . . . . . .. 76.6 89.3 76.6 Irrelevant . . . . . . . . 21-4 10.7 3.1 Sum . . . . . . 98-0 100.0 79.7 whose only distinctive feature is the linearity of the three points on the lesser curve. Let us now return to the partitioned curves in Fig. 3. Any one of these lesser curves selected by the correction procedure can be set in its appropriate place in a representative selection of the companion curves whose theoretical existence is discussed above.This has been done for the concentrate and the halibut-liver oil in Fig. 4, where the arbitrariness of the selection made by the correction procedure is reflected in the similarity of the other curves in the vicinity-and even although the extremes in these sets can be rejected as constitu- tionally improbable, there remains a wide range of possibilities. Another feature emphasised in Fig. 4 is the not inconsiderable discrepancy between the spectroscopic assumption of linearity and the mathematical requirement of linearity of the fixation points, for in between these points the curve is far from smooth. If these curves are examined further, the similarity in general shape of the two sets is particularly noticeable. Roughly the same absorption peaks and troughs occur, apparently, in the curves of the irrelevant material in two oils of very different natures-one a natural oil and the other a processed concentrate.What the two oils do contain in common is vitamin A and, as the most marked irregularities of the curves of the irrelevant material lie at about the same wavelength as the irregularity near the peak of the vitamin-A curve, the possibility must be considered of some degree of error in the assumption, in the correction method, that the absorption curves of the vitamin-A fatty-acid esters in these oils are identical with the published vitamin-A acetate curve. Graphically it can be predicted that a slight shift of the vitamin-A curves along the wavelength scale would tend to smooth the comple- mentary curves of irrelevant absorption.In Fig. 5, this is done for three representative members of the family of curves of irrelevant absorption from the halibut-liver oil in Fig. 4. Not only does this trial amendment of the assumption smooth the curves, but it materially alters the general slopes. An obvious and simple explanation of the peculiar shapes of the curves as left by the original subtractions woilld be that the wavelength scale was instru- mentally in error. This is unlikely, as the curves are averages obtained from several instruments in different laboratories, all agreeing on the position of Amax.. Moreover, there is evidence that the absorption curve of the vitamin A chromatographically separated from the concentrate was positioned 2 mp further up the scale than that of ordinary vitamin-A alcohol.What could cause the postdated differences between the accepted curves and those encountered in certain-for it is not possible, o:E course, to say all-oils? First, it is at least conceivable that the acid radicals of vitamin-A esters should slightly influence the contour of the absorption curve, i.e., that the curve for vitamin-A acetate, for instance, was not the same, spectrophotometrically, as that for naturally-occurring esters. Secondly, there may be differences between the absorption curves of the four geometric isomers of vitamin A whose occurrence and characteristics have not yet been fully established.Robeson and Baxters have distinguished between two isomers that occur together in fish-liver oil, and it is significant that they appear to have absorption curves similar in shape but 3 mp out of step (vide supra). VALIDITY OF RESULTS The previous section bears on the question of the validity of results in that it deals with the assumptions fundamental to 3-point correction of vitamin-A absorption curves. What is further needed is some direct evidence, i.e., comparisons between correction estimates and estimates by physico-chemical methods. The literature is not rich in information of thisAugust, 19511 VITAMIN A BY GEOMETRIC CORRECTION OF ABSORPTION CURVES 469 kind. Morton and Stubbs have discussed three samples of tunny-liver oil with this in mind, but there is not enough range among the samples to give the evidence great strength: it can be concluded that the corrected results are indeed of the same order as the physico- chemical results, but as they are also similar among themselves we cannot be sure that other 20 s u1 10 0 s w 1 I I I I 300 3 10 320 330 340 (4 Wavelength, mp 20 I 15% I I I I 0 300 3 10 320 330 340 Wavelength, mp (4 Fig.5. The curves labelled M-S are those selected by 3-point correction Ei& at 328 mp of whole-oil curve = 100 (a) Typical trio of the family of Halibut “irrelevant” curves, re-scaled from Fig. 4 (b) Comparable curves derived after assumption of a 3-mp upward shift of the complementary vitamin-A ester curve Effect of assumed wavelength shift on shape of postulated “irrelevant” absorption curves samples containing greater or less irrelevant material would respond in proportion.No information on sensitivity therefore emerges. Data on the 3-point corrected E at 328 mp values of several fish-liver oils, a distilled ester and vitamin-A acetate have been given by Coet~ee,~ but they contribute little to the460 GRIDGEM AN [Vol. 76 present problem. They turn on biological assays against /3-carotene, so that the precision and accuraey are insufficient to show up critical differences. The apparent percentages of irrelevant absorption in the samples are 0.6 per cent. for the acetate, 3.4 per cent. for the distilled ester, and 6.6 to 12.3 per cent. for the fish-liver oils, but the bio-assays correlate almost as well with the gross as with the corrected values (if., the coefficients of variation for the gross and corrected “conversion” factors are, respectively, 11 and 9).More interesting is Morton and Stubbs’s collection of assays on cod-liver oil given in their original paper.l Each sample was assayed by correction of the whole-oil absorption curve and by determination of the E value via the unsaponifiable matter (it has long been observed that most of the irrelevant material irz cod-liver oils can be removed by saponifi- cation). Morton and Stubb’s own tabulation of their results does not make it clear whether the correlation between the two methods is good or bad. In fact it is good, as can be seen from the summary in Table IV. TABLE I’V CONDENSATION AND REARRANGEMENT OF E AT 328mp DATA ON COD-LIVER OILS FROM MORTON AND STUBBS’S TABLE 111 (A?Za&d, 1946, 71, 355) The 20 samples are grouped in five equal sets and arranged in order of percentages of E at 328 mp due to vitamin A “Irrelevant” E at 328 mp Mean E at 328 m.p (gross) 1st set of 4 samples . . . . 1.086 2nd 9 ) .. . . 0.899 3rd 19 .. . . 0.832 4th 99 .. . . 0.836 6th 99 .. . . 0.609 , by 3-point correction, Yo 9.1 14.4 20-8 23-6 42-5 1 by determination of unsaponifiable matter, 10.4 14.5 19-5 21.6 34.6 % These figures suggest that the ultra-violet absorption of cod-liver oil fatty-acids is linear at the fixation points, and therefore, that the method has some validity for this oil. Evidence of a similar kind is needed before the application of the method to other oils can be established. At present its reliability is sub judace and its use requires caution. I . 2. 3. 4. 5. 6. 7. 8. 9. REFERENCES Morton, R. A., and Stubbs, A. L., Analyst, 1946, 71, 348. -- , Ibid., 1948, 42, 195. Oser: B. L., Anal. Ckem., 1949, 21, 529, McGillivray, W. A., Ibid., 1950, 22, 494. “United States Pharmacopoeia XIV,” Mack Publishing Co., New I’ork, 1950, p. 785. Adamson, D. C. M., Elvidge, W. F., Gridgeman, IX. T., Hopkins, E. H., Stuckey, R. E., and Taylor, Robeson, C. D., and Baxter, J. G., J . Anzer. CIzen2. SOC., 1947, 69, 136. Coetzee, W. H. K., Biochem. J., 1949, 45, 628. I , Biochem. J., 1947, 41, 525. -- R. J., Autalyst, 1951, 76, 445. LEVER BROTHERS & UNILEVER LIMITED FOOD RESEARCH DEPT., COLWORTH HOUSE SHARNBROOK, BEDFORD Janzcary, 195 1