Principles of Precision Colorimetry Absorption Law Deviations in Measurements of Relative Transmittance C. F. HISKEY
AND
IRVING G.YOUNG'
Polytechnic Institute of Brooklyn, Brooklyn, A'. Y. the result of a study of the effects of absorptioii law deviations on the precision of colorimetric analyses, for absolute and relative concentration measurements, a simple method for estimating the maximum precision possible with any given absorber has been developed. In absolute measurements the precision is oaly slightly affected by absorption law deviations, but with relative measurements this effect may be considerable. .is
I
X QU-4XTITATIVE colorimetry or spectrophotometry thc precision of analysis may be materially improved if a relative rather than anabsolute concentration is determined. In this type of measurement a high absorbance standard is compared with a sample of similar but unknown concentration. The details of this general method have been extensively treated, as to both the theory involved (1,6-8) and some direct analytical applications (2,d, 9, 12-f4). If a high absorbance reference standard is used, it becomes necessary to operate with an increased light intensity in order to achieve a photocurrent sufficient to set the transmittance scale a t its normal value of 100%. With a monochromator of the type incorporated in the Beckman spectrophotometer, this is easily effected by opening the slits. A consequence of this manipulation is that the band of spectral energy passed by the instrument is broadened, causing absorption law dekiations which are particularly pronounced when the absorption band width is either narrower than, or comparable to, the pass band width. Such deviations lead to a loss of precision in colorimetric analysis. In this paper this problem is treated generally, not only for relative concentration measurements but for absolute ones as well. Techniques are described for selecting the reference standard concentration, so that maximum precision may be obtained in any given analysis. This study concludes with an examination of slit width effects when these high absorbance reference standards are employed.
1, is equal to A1 - a' X c,. I t can be seen from the geometrical construction that X will increase the more the response curve deviates from ideality. If the deviation were so great that in a limiting situation the response curve became parallel with the concentration axis, then X and the absorbance would become equal and the value of the product a' X c would be zero. In other words, a further increase in concentration would produce no measurable change in absorbance. I t is evident, therefore, that for such a situation the relative error, dclc, nould become infinitely large. To derive a function which would permit a computation of thc relative error in any system having an absorption law deviation. it is first necessary to remember that the absorptivity coefficient nill not be a constant but will be the integrated value of the slope of the response curve aver a concentration range from zero t o thv concentration of interest. Thcrefore,
A = -logZ/Zo
=
aav.bc
(1)
FORMULATION OF THE DEVIATION PROBLEM
In a previous paper (6) the effect of an absorption law deviation on the precision of a relative absorbance measurement was formulated in a preliminary fashion. It is now intended to develop that approach in a more explicit way, considering first the case of an absolute colorimetric measurement. For this purpose, suppose that the deviation case illustrated in Figure 1 is taken. In this instance the relation between the measured absorbance and the concentration (solid line) is linear a t low concentrations with a elope ( AA/Ac)equal to the absorptivity coefficient, a . At higher concentration values, however, the curve deviates considerably from a linear relation, so that a t some value c1, the absorbance hap a value given by A,. A tangent to the curve a t A1 will have a slope equal to an apparent absorptivity coefficient, a'. This absorptivity value obviously applies only for a very small concentration interval in the vicinity of c1. In this discussion b, the length of the light path in the absorption cell, is given the dimensions of unity. It is a8 though AI were made up of two parts, one being the product a' X c1 while the other part, represented by X in Figure
CONCENTRATION
Figure 1. Absorption Law Deviation
.It any particular concentration c1 where the absorbance is the absorptivity coefficient may be represented as
a'
=
-11,
(3,
Then the slope of the curve of transmittance versus concentration for any given concentration mould be
dc =
-
1
- d(l0g Z/Zo) a'b
a n d therefore the relative error would be
dc = 0.4343 -
Present address, United States Electric Co., 222 West 14th St.. New York 11, S. Y.
&,"'
a'
1
1196
x -
lo
d Ill0
log
-
I1
(3)
1197
V O L U M E 23, NO, 9, S E P T E M B E R 1 9 5 1 This differs from the relative error function in a nondeviating caw only by the term aav./a‘. If two solutions of identical absorbance and therefore identical transmittance were compared with itgard to the relative error of the concentration measurcment in each case, the relative crror of a deviating solution would be found to be a,,./a’ time.; I:trgvr than the relative crror of a nondeviating one Formulated in terms of the construction in Figure 1 it is seen that aaa.wiii equal Al/cl a t concentration c I rwhile the slope of the curve a t t h s t concentration will be a’. Al/cl thus appears as an average absorptivity coefficient. In a nondwiating case it will be a constant, but in the deviating cases it will vary with concentration. Initially it will have a maximum value, but as the concentration and therefore the dt3viation increase it will decrease. a’ is the slope of the tangent a t any point along the curve. Initially its value will be very nearly equal t o At/cl, but with incrrasing concentration it will decrease a t a faster rate than Aljcl I t might be considered as the absorptivity coefficient a t some particular point on the absorption curve and applicable for only an infinitesimal concentration interval on cither side. The= considerations show that
The effect of an absorption law deviation on the precision of an :ibsolutc absorbance mcasuirsment is therefore seen. If a ’ decreases to about half of its initial value, .41/(U’ X cl) may bts about 2, representing a doubling of the relative error over lvhat it would be if the deviation did not occur In practical work a deviation of this magnitude seldom will be obtained with a good spectrophotometer. With relative measurements, however, absorption law deviations are greater and therefore have a more pronounwd effect on precision
If the btariclard and unknown have nearly equal concentrations,
Z1/I1will nearly equal unity, log Iz/IIwill be practically zero, and consequently the value of the denominator will be about equal to A I - X = a’ X C I . It will be a matter of concern t o the analyst to have this latter quantity maximal, for only then will the relative error be minimal. Recalling that a‘ diminishes as the concentration increases, it is a t once evidenb that ehould this term fall at a faster rate than the rate of increase of the concentration, a’ X c would decline with increasing concentration. This would niean that the relative error would illcrease with increasing concentration of the reference standard rather than the opposite. The problem for the analyst is to discover (a’X c ) ~for ~ any . particular system, as this will allow the most preci.x analyses. EXPERIMENTAL EVALUATION OF MAXIMUM PRECISION
-4s shown in Figure 2, anthracene has a relatively sharp absorption pcak in the near ultraviolet with the absorption maximum a t about 350 5 nip ThiP spectrum was measured with the hydrogen lamp supplied with the Beckman DU spectrophotometer as the source of radiation. Superimposed on this spectrum is the effective band width in this region as taken from the calibration curve supplied by the manufacturer. It shows that the pass band is relatively large even for $he smallest slit width used-Le., the 0.25-mm. value. Deviations from the absorption law- may be expected therefore even in absolute measurements which would use the narrolvest slits. As the slits ale opened the deviations will become more pronounced. Consequently this substance \vas selected for experimental study.
0.5
S.W. QIVENIN M M .
r
I M M = 7.5m4 EFFECTIVE BAND WIDTH.
0.4.
PRECISION OF RELATIVE MEASUREllEhT
For a relative transmittance measurement using a standard nhose aksrbance is A1 and an unknown whose abqortiance is 1 1 2 and where a =
U‘C?
7is
a
CI
only slightly larger than unity, an evalua-
tion of the relative error may be made if the following relations RIP u..ed:
0.75‘
s W
(3
0
J
0.I
01
360
350
WAVELENGTH
and Figure 2.
I
370,
(m4)
Absorption Spectrum of Anthracene in Benzene 10 mg. per liter
By differentiating the last equation with respect to a (or c 2 ) and dividing this differential by 01 (or c n ) ,the relative error function is obtained.
(5)
Remembering that log I l l l o = - A l leads us to rewrite Equation 5 ae:
To determine the effect of the referencc standard concentration a t a’a t 359.5 mp, the following procedure was used: From a more concentrated stock solution of anthracene in benzene solvent various aliquots were taken and diluted to a constant volume with pure solvent. In this way a group of solutions was prepared whose concentrations varied from 0 to 100 mg. per liter with concentration increments of 2.5 mg. per liter. The absorbances of these solutions were first measured by comparison against the solvent. Sext a solution Those absorbance (log Z 0 / 1 l ) waa about 0.43, with a concentration of 10 mg. per liter, was taken as a reference standard and the other more concentrated solutions were compared with it to obtain absorbance differences-Le., log 1 1 / 1 9 . The samples taken ranged in concentration from 10 to 20 mg. per liter. I n order to set the transmittance scale at 100% when the 10 mg. per liter solution was
1198
ANALYTICAL CHEMISTRY
graph. 111the third colunin the values of a’ x c are given; they rise to a maximum of 1.08, after which a further increase in concentration has little effect. This indicates that a reference standard having a concentration in the range of 30 to 40 mg. per liter will gilre masimum precision. Higher are to be avoided, as there Tvouldbe further loss of resolution without any advantage. Indeed, errors due to The data obtained in this way are summarized in Figure 3 overlapping absorption bands might often be introduced. Under where the absorbance differences are plotted as a function of the certain circumstances it night even be advantageous to work with a standard whose concentration is only 20 mg. per liter, since concentration. As each reference standard mas used for a conthere is only a small increase in the value of a’ X c beyond that centration interval of 10 mg. per liter, there are ten curves plotted point. For a colorimetric determination in which the unknown in this composite graph. and standard concentrations are equal, the relative error in the first four cases would be about 1.0, 0.56, 0.47, and 0.40 times the value of A(Zz/Zj), so that beyond the 20-mg. standard very lit,tle precision is gained for the resolution which is lost,. The considerations presented above indicate the procedure to be followed by the analyst when using a monochromator instrument of this sort for the determination of other substances. Operating with the instrument in its most sensitive setting-Le., with the smallest value of A(Z2/11) possible-the absorption spectrum of the substance under consideration should be nieasured. From a knowledge of the dispersion of the instrument in the wave-length region of the IO 20 30 40 50 60 70 80 90 100 absorption maximum it can then be decided n-hether a pronounced deviation will occur when C, =CONCENTRATION OF REFERENCE STANDARD(MG./LITER the slit aperture is given the largest possible value Figure 3. Absorption Law Relations for Different Concentrations for the system under study. If it appears that of Anthracene in Benzene at 359.5 mfi the deviation may be serious, the maximum apparent absorbance should be evaluated. This may be effected by preparing a series of solutions in n-hich The data of Figure 3 show a number of items of interest. In the concentrations vary according to the simple arithmetic series the first place, all the curves are very nearly straight lines or may 1, 2, 3, 4 . etc., choosing the first concentration so that its be represented as such to simplify the computations which folabsorbance will be about 0.43. In this way it will be necessary low. This permits an easy assessment of a’ for each reference to make only about five solutions to test a range of standard standard. For each 10-mg. interval it is only necessary to take densities from 0 to 1.74. If pronounced deviations occur around the maximum absorptivity difference and divide it by the con0.43, it will be advisable to make a new set of standards whose centration difference to obtain the corresponding approximate densities cover a smaller range. The proper standard may then value of a‘. be selected according to the technique described above. In general, it is not necessary to go to densities above 2, as the gain in precision beyond that point is small. A precision in exTable 1. Computation of Best Concentration for Reference Standard cess of 1 part per 1000 or 2000, which theoretically could be realConcn. of Reference ized a t densities of 0.4 and 0.8 respectively, if A ( I z / I l ) has a value Standard, Mg./L. a’ a’ X e of 0.001, is not easy to achieve because of difficulties with the 0 0,046 10 0.044 0.44 absorption cell optics. 20 0.039 0.78 Reference to Table I shows that after the apparent absorbance 30 0.031 0.93 40 0.027 1.08 reaches a maximum value, it does not stay fked as the concentra50 0.020 1.00 60 0.015 0.90 tion is increased further, but instead declines perceptibly. This 0.98 70 0.014 decline is real and very definitely outside the limits of experi80 0.012 0.96 90 0.011 0.99 mental uncertainty. The variation of a’ X c n-ith concentration is a function of the shape of the spectral band and of the instrumental response in the wave-length region being used. I t will I t can also be seen that profound changes of the apparent vary considerably from case to case, but can easily be determined absorptivity coefficient are occurring with increase in concentraby the technique outlined above. tion. These changes are reflected by the change in the maximum Occasionally a situation arises, as in the case of rare earth value on the ordinate which is obtained for each 10 mg. of conspectra, where the peaks are so sharp that the apparent absorbcentration difference. Even with the introduction of the very ance declines as soon as the most dilute reference standard is subfirst reference standard, the effect of opening the slits is perceptistituted for the solvent. In such circumstances little can be done ble for a spectrum such as this. Were there no alteration in the to improve the precision, unless the absorption band coincides value of the absorptivity coefficient, the slopes of all these lines with the wave length of some monochromatic source and that would be identical and therefore they would all terminate with source can deliver sufficient flus for the purpose in hand. Then the same ordinate value. by making a proper optical substitution of this source, the apTaking these data it is now possible to compute a set of a’ X c proach previously described may be applied. There is, of course, values for this system (Table I). the further possibility of using a more sensitive detector than that The concentrations referred to in the first column are those of supplied with the instrument. With such a detector it would be the reference standard. The values of a’ are taken from the possible t,o narrow the slits substantially and thus minimize the used as reference standard, it was necessary to open the slits somewhat and therefore suffer a small loss of resolution. The 20 mg. per liter sample was nest chosen as the reference Ftandard and the range of 20 to 30 mg. per liter was studied in a manner similar in every respect to that applied to the preceding standard. This process was continued until the last reference standard had a concentration of 90 mg. per liter and was used over the 90- to 100-mg. range.
. .. I
V O L U M E 2 3 , NO. 9, S E P T E M B E R 1 9 5 1
1199
apparrnt deviation. Photomultiplier circuits capable of doing just that arc currently available.
etc., have been obtained, a' may be computed approximately from any two successive sets of values for slits and concentrations, using the derived relation.
ALTERNATIVE METHOD OF SELECTISG BIAXIMUM ABSORBAKCE Ail altrrnat,iye method for determining the maximum absorbance to be used in the reference standard is based upon measurenicbnts of the slit xidth apertures required for balancing standards of various concentrations. The relat,ion between the slit width of the monochromator and the absorbance of the reference standard was treated in a previous paper (8). I n the course of that irivcxstigation a group of nondeviating absorbers was placed in the xbsorption cell, the transmittances n-ere determined, and then the size of the slit, opening required for balancing the spectrophotonieter a t 100% transniittance n-as determined. For the
I
idt.:il cases it,was observed that,lo =
(2)'
where
$I was the trans-
riiittance of the sample, So was the slit width required to balance the inst,rument a t loo'% when the abaorption cell contained solvent only, S was the slit width value when the absorber was placed in the beam, and r was the instrumental term whose value for a properly aligned monochromator having equal entrant and esit slits would be 2.0. In practice T may have some other value t,han 2, but this does not affect the method described here.
This method is somewhat ~implerthan that previously given, as feTver measurements are necessary. Some data taken on the anthracene spectrum with the Beckman DU spectrophotometer are preqented in Table I1 along r i t h the computations of a' and a' X c. AS the value of a' is computed from two successive slit values, it approximates the slope of the response curve a t the intermediate concentration-i.e., 5, 15, 25, etc., mg. per liter. The values of a ' X c are also for standards of intermediate values. Comparison of these data with those of Table I shows that the t\to methods give essentially the same values for the maximum effertive absorbance which may be obtained. The value of r in these computations mas 2.0. Had it been some other value, the a' x c values of Table I1 would have differed numerically by a constant fraction equal to the ratio of the two values of r. This would have no effect on the selection of thc, proper concentration of the reference standard. SLIT PROBLEM IN REL4TIVE ABSORBANCE
MEASUREMENTS
Table 11. Reference Standard Concentration Computed from Slit Width Data Concn. of Reference Standard, Mg./L. 0
s, M n r .
10
0 200
20
0 328
30
0 500
40
0.G83
50
0 890
60
1 080
0 116
0'
a' X e
0 Olh
0.23
0 013
0.65
0 037
0.93
0 028
0.98
0.023
1.04
0 Oli
0 94
The response curve, for relative absorbance measurenients in a spectrophotometer where balance is achieved by adjusting the slit width for each reference standard, differs from that obtained in absolute measurements whenever an absorption law deviation occurs. This is caused by the peculiar energv distribution across the pass band interval which occurs in such cases. I t may be helpful to the analyst, therefore, if this problem is examined in sufficient detail to provide at least a qualitative picture of the problem. For a finite pass band covering the wave-length interval Ah the absorbance as measured by a spectrophotometer is exactly given by the expression:
The absorptivity coefficient may be expressed in terms of these slit wttings and for the nondpviating case becomes:
a=- r
S
bc log &
(7)
Suppose that the group of reference standards referred to above were placed one a t a time in the light beam and the instrument m-as balanced a t 1 0 0 ~transmittance. o Because a deviation will result, it follows that the value of the absorptivity coefficient computed by Equation 7 will not be constant but will show the deviation characteristic of these relative measurements. The relation Fhown in Equation 8 will be observed:
a.v. =
A r S - = - log bc bc So
The tangent to this relation will, of course, be a' and experimentally it may be approximated in the following manner. After a group of reference standards of concentrations c1, c?, c3 , . . c7>,cn + I . . . etc., have been interposed in the light beam and the corresponding slit settings, S1, 82, 8 8 . . . S,, 8, + I . .
.
where E , &I, and S are, respectively, the intensity of the energy from the source, the transmittance of the monochromator, and the sensitivity of the receptor for an infinitesimal wave-length interval in the pass band. The correeponding transmittances for the solution and solvent are given as t i and to. A similar expression may be written for an absorbance difference measurement, except that te and t l , respectively, would be substituted, Now if in an actual measurement the wave-length interval AA could be reduced very nearly to zero, radiation would become nearly monochromatic and the absorbance or absorbance difference thus determined would be a true one equal to -log t i l t o or -log t2/tl, respectively. On the other hand, if the various terms in the integral could be correctly evaluated, the measured absorbance might be suitably separated into a true value and a number of deviation terms. Hardy and Young ( 5 )recently have obtained a general solution of thie problem, permitting in some caseP an easy experimental measurement of the important deviation terms. Eberhardt ( 4 ) and others (11) have developed some empirical equations for computing absorbances as a function of slit widths when these have small values.
ANALYTICAL CHEMISTRY
1200
In relative abForbance meaaurcbments the slit width problem is somewhat different, being complicated by the use of a reference standard which alters thc energy distribution in the pass band interval and necessitates the use of wider apertures Consequently there is a substantial difference between the type of absorption law deviation which occurs in the two kinds of photometric measurements listed above. The difference becomes immediately apparent when the absorption spectrum of a substance IS measured with different slit widths against a solvent and against reference standard solutions of the substance. Data on these two kinds of spectra have been assembled in Figures 4 and 5 for anthracene in toluene. In Figure 4 the spectra given were obtained when comparison was made against the solvent with the instrument set for its highest, intermediate, and lowest resolution. This was achieved by varying the sensitivity knob on the spectrophotometer. At the highest resolution the slits had their smallest values and therefore the sensitivity was least ( d , / Z o was a t a maximum). The reverse was true a t the lowest resolution. The measurements were made on a solution whose anthracene concentration was 10 mg. per liter. I t can be seen in Figure 4 that opening the slits produces a negative absorption law deviation in the region of the absorption peaks and a positive one in the region of the minima. At various intermediate wave lengths the deviations are practically absent. These results are exactly those to be expected, but different from those obwrved in Figure 5 .
with rmpect to both the character of the deviation and the 1 0 ~ 3 tion of the absorption peak. There are no regions of positive absorption law deviation such as occurred previously in the regions of the absorption minima, but instead these positions have become regions devoid of apparent deviations. In addition, the position of the :ibForption maximum shows a shift to shorter wave lengths as the reference wlution increases in concentration Were there no deviations in thew plots, all fi1.e curves would be identical.
I
340
1.0
350
360
WAVELENGTH(M
Figure 5 .
340
Figure 4.
360
350
370
WAVELENGTH (VI4 Slit Width Effects on Absolute Absorption
Spectra
Here the measurements were made by comparing a standard reference solution with one which contained 10 mg. per liter more of the anthracene. The instrument was set a t its lowest slit width or minimum sensitivity for these measurements. The uppermost curves in both Figures 4 and 5 are identical, comparison having been made against the solvent. Each lower curve in Figure 5 is for a solution whose anthracene concentration is 10 mg. per liter higher than the one above it. The results displayed here are qualitatively different from those of the previous figure,
370
4)
Slit Width Effect on Relative Absorption Spectra
The differences observed in thth relative absorbance measurements can easily be accounted for in terms of the changing energy distribution which results from interposing absorbers between the source and the receptor when the transmittance scale is being set. This may be indicated in a more explicit fashion by considering the changing intensities of a group of monochromatic rays distributed across the pass band as the concentration of an absorber is varied, as the slit width is varied, and then when both the slit width and the absorber concentration are varied in such a way as to maintain a constant receptor response. When the image of the entrance slit of the monochromator h a e the same width as the exit slit, then according to the investigations of Runge (IS) and Paschen ( I O ) the spectral transmittance, corrected for dispersion, Rill be triangular in shape. In other words, if the monochromator is considered as a narrow pass band filter and if a plot i s made of the intensities of the various monochromatic rays passed as a function of their wave lengths, this plot will be an isosceles triangle with a base twice the effective band width. The response will rise linearly with wave length, reaching a maximum a t the center of the band, and then fall back to zero. This is the behavior of the Beckman DU spectrophotometer when properly aligned ( 4 ) . In Figure 6, A , the triangle shown indicates the intensities of the various monochromatic rays a t wave lengths T,U,V ,W ,and X . It can be seen that T and X have zero intensity while V has a maximum intensity
1231
V O L U M E 23, NO. 9, S E P T E M B E R 1 9 5 1 Suppose that R I I .iboiber showing no deviation is placed in front of this beam. Then earh of the wave lengths being passed will be reduced a proportionate amount and, as shown in the diagram, carh will be rcduceti to ?.i'%*of its initial value. The inten-ity distribution across the wave-length i n t c r ~ i lwhich emerges from the sbsorber and passes to the photocell is that shown by the smaller tiiangle. The crowhatched area represents the light that has been absorbed. If the slit width is doubled, this same'type of intensity distribution persists, except that the res onse a t the peak has been doubled and the base of the triangpe is now twice as wide. The total energy passed by the slits will, of course, be four times greater than in the previous case. (If the instrument is properly aligned, the total energy changes as the cerond power of the slit uidth.)
T
U
V
W
X
T
A -
R
S
T
U
V
W
X
i
W
X
h-
U
AFigure 6.
V
W
X
Y
Z
R
i
i
U
nEnergy Relations across a Slit
Thus, changing the slit setting not only varies the band width but alters the relative intensity relations among the rays passed in such a way as to increase those a t the edge of the band relative to those in the renter. This fact must be recalled when the efrecta of varying F l i t and concentration are considered simultaneously. These new relations are diagrammed in Figure 6, B , where it is now seen that the intensity a t wave length T is just one half that of wave length V ,which still is the peak intensity. Thus relative to V , T has grown considerably as a result of doubling the slit width. The cross-hatched area still represents that fraction of the new pass band which has been absorbed by the ideal reference standard, while the area enclosed by the smaller triangle repres e n t ~the intensity distribution of the light which has passed through this absorbing solution. The area of this small triangle is obviously equal to the area of the larger triangle in Figure 6, A . This will be true if the photoelectric response is constant across the wave-length interval under consideration. Such an assumption is often justified by experimental data a t a good many wavelength positions and is used here to simplify the discussion. Now it d l be useful to consider the energy relations across the pass barid when an abqorber is used which show? apparent deviations. For this purposc it may be assumed that the center of the pass band coincides with thc ahhorption peak. On either side of that
wave length the absorptivity coefficients decrease. This will mean that as the concentration of the absorber is increased, the relative intenbity distribution in the pass band nil1 change. The center of the band \ d l be most strongly absorbed and thercforc a t any absorber concentration will be reduced proportionately more than the outer regions. Should the absorption band be a relatively sharp one as with the rare earth Fpectra, it xould be possible for the center of the band to 1~ completely absorbed with only the band edges being transmitted As the central ray diminishes the main c'nergy, absorption occurs a t wave lengths where the absorptivity coefficient is less and therefore a deviation becomes apparent. Such relations as these have been diagrammed in Figure 6, C, which illustrates the differences betlwen this case and the unknown deviating case. When the slit is opened t o compennate for the energy lost by absorption in the central region, the effect of a changed anergy distribution becomes much more pronounced, because the main source of radiant energy effective in rebalancing the transmittance scale comes from those portions of the pass band which have the smallest absorptivity coefficients. Proportionately, therefore, these wave lengths are enriched in the pass band used for measuring the absorbance diflfcrence. This situation is shown in Figure 6, D, where it can be seen that the most intense rays occur a t wave lengths T and X. The peculiar results of Figure 5 can be easily associated uith these changes of energy distribution-across the slit and it is thii aspect which makes this type of apparent deviation different from that of absolute absorptiometry.
Y t
ACKNOWLEDGMENT
The authors acknowledge the very considerable assistance given to this study by Willard P. Tyler and Donald W. Beesing, B. F. Goodrich Research Center, Brecksville, Ohio. They supplied the authors with a voluminous body of data on the anthracene system and thus made this study comparatively easy to effect. In addition, the critical assistance of R. 4.Harrington is gratefully acknowledged. LITERATURE CITED ( 1 ) Allen, E., and Hammaker, E. M., ANAL.CHEM.,22, 370 (1950). (2) Bastian, R., Ibid., 21, 974 (1949). (3) Bastian, R., Weberling, R., and Palilla, F., Ibid., 22, 160 (1950). (4) Eberhardt, W.H., J. Optical SOC.Am., 40, 172 (1950). (5) Hardy, A. C., and Young, F. hl., Ibid., 39, 265 (1949). (6) Hiskey, C. F., AN.~L.CHEM.,21, 1440 (1949). (7) Hiskey, C. F., Trans. JY. Y . Acad. Sci., 11, 223 (1949). (8) Hiskey, C. F., Rabinowita, J., and Young, I. G., ANAL.CHEM., 22, 1364 (1950). (9) Lykken, L., and Rae, J., Ibid., 21, 787 (1949). (10) Paschen, F., W i e d . Ann., 60,712 (1897). ( 1 1 ) Philpotts, A. R., Thain, Wm., and Smith, P. G., ANAL.CHEM., 23,268 (1951). (12) Robinson, D. Z., Ibid., 23, 273 (1951). (13) Runge, C., 2. Math., 42, 205 (1897). (14) Young, I. G., and Hiskey, C. F., ASAL. CHEM.,23, 506 (1951).
RECEIVED March 22, 1951. Prevented in part before the Second Meetingin-Miniature of the Metropolitan-Long Island Section of the A M E R I C A N CHEMICA SOCIETY, L Brooklyn, X. Y . , hlarch 1951. The nomenclature and method of approach used in this article are in conformity with those given in a previous paper (6). Reading of the above article will facilitate the understanding of niany points which are treated only briefly in this paper.
