with B and B’ values, those of R’ have therefore been slightly overestimated and those of R more so, especially a t the 20-mpmole level. For these reasons, and apart from the facts t h a t near-white instead of monochromatic light was used and t h a t the solute might not have behaved ideally, close accordance of the data with Equation 4 could not be expected. The variability comparisons, however, are not vitiated. Table 11, Simple Semiempirical Relationship. T h e failure of the d a t a for p-aminoisobutyric acid t o accord well with Equation 4 (k” = 42.1 a n d 60.0 a t the 2- and 20-mpmole levels. rwpectively, and slightly more dirergent if corrected for substance residue effects) mas repeated by the data for the other four substances chromatographed. It is of interest that the restoration of reflected light would have tended to correct the departure of k’’ from constancy. Examination of the data for all five substances a t levels of 2, 4, 10, and 20 nipmoles showed close linear regressions betn-een & and 1/T values. Similar findings have been made with chromatograms of sugar mixtures ( I O ) . Equation 5 is derived from these facts, the function, a, satisfying the conditions that it tends to zero with Q and increases continuously with &.
+
+
+
where a = A A2 d 3 etc. = A/(1 - A ) = 9 / T = ( I / T ) - 1 = (BR’/RB’) - 1,,4 being the absorptance of the band-vis., 1 - T. Mean values of a (and the ranges) a t the 2- and 20-mpmole levels for each substance are shonn in Table 11, together with an analysis of their variances, coefficimts of variation (cv, and cct) for within-e\periment and total variabilities, and standard deviations (errors) of means of within-experiment triplicates. Clearly, values of k’” ( = & / a ) for any one substance are very similar at both levels. There is no evidence of consistency in skewness in the distributions of a (and hence k’”) values. The coefficients of variation are usually much larger at the 2- than a t the 20-mpmole level. The extent to which the coefficients would have been increased by using instead of 1/T to compute a, the variate R’/R which, like 1/T corrects for background but, unlike it, not for irregularities. might be assessed adequately from the p-aminoisobutyric acid data. -4t the 2- and 20-mpmole levels, respectively, and adjusted for substance residue effects, mean (R’IR) - 1 = 0.1177, 1.1573; s i = 0.00124, 0.0098; s: = 0.00117 (use 0.00124), 0.0106; cum = 28%, 8.470; cut = 2870, 8.8%. As expected, the means agree closely with
those of a, but the variances are much greater and the differences are of high statistical significance [F (14 d.f.) = 5.2, 3.0; P‘, 0.002, 0.024; F (20 d.f.) = 5.2, 2.8; P’, 0.001, 0.0131. The high eou. and cut values are unaffected by the residue adjustment, and at the 2-mpmole level those of a are only 46YGas large and a t the 20-m,uniole level only 60y0 as large; these very substantial reductions in variability result from a single refinement (correction for sheet textural irregularities) in the photometry. K i t h this refinement, the mean of triplicate assays is as reliable as the mean of about twelve replicates lacking it, as in the method of Block (1) and siniilar methods nhich do not zero the instrument on bleached band in the same position. The authors realize that time is consumed in the bleaching process, but this is short and the position for a measurement after bleaching is fixed by predetermined stage-scale settings instead of time-consuming trial and error. Let i Y = number of bands. For 12 1 measurements are replicates, 12 S required by other methods. For three replicates, 3 X 2 ( N 1) = 6 S 6 measurements are required n-ith this method for comparable precision. The advantage is already realized n-ith this method when S = 1, and increasingly so for larger A-.
( 7 ) Consden. R.. Gordon. A. H.. Martin.
work. (11) McEvoy-Bowe, E., Lugg, J.
IT. H., Australian Patent .Ippl. 44466 iIS%), 51256 (1959). (12) McFarren, E. F., Mills, J. A , -4s.~~. CHEM.24, 650 (195%). (13) Martin, A . J. P., ”Partition Chromatography,” Symp. Bzochem. Soc., So. 3, p. 4, (,l949). (14) Martin, 8.J. P., Synge, R. L. l f . , Biochem. J . 35, 1358 (1941).
(15) Pearson, E. S., Hartley, H. O., “Biometrika Tables for Statisticians.” Vol. 1, Cambridge Univ. Press, Cambridge, Eng., 1954. (16) Redfield, R. R., Barron, E. S. G., Arch. Biochem. Biophys. 35, 443 (1952). 1171 Salander. R . C.. Piano. ?*I..Patton. A.R., A N ~ LC. H E 25, ~ 1532 (1953). RECEIVEDfor review August 17, 1959. Resubmitted November 14, 1960. Accepted Kovember 14, 1960.
+
+
+
Correction Alternating Current Voltammetry with Controlled Alternating Potential
ACKNOWLEDGMENT
The authors are indebted to Lim Yen Hing, University of Nalaya, and Alan Mitchell, Lniversity of Western Australia, for technical help, especially in constructing the instrument; to S. E. Williams, J. E. Alderson, R. S. Crisp, and G. A. Rooke, University of Ifrestern Australia, for certain optical measurements; and to K. S. Stenhouse and staff, Commonwealth Scientific and Industrial Research Organisation Regional Laboratories, Kestern Australia, for statistical calculations. This n ork embodies part of a thesis submitted by E. NcEvoy-Boa-e for the Ph.D. degree in the University of Rfalaya.
LITERATURE CITED
(1) Block, R. J., AXAL. CHEM.22, 132T (1950). (2) Block, R. J., Durruni, E. L., Zweig, G., “A Manual of Paper Chromatography and Paper Electrophoresis,” 4cademic Press, S e w York, 1958. (3) Boissonnas, R . A., Helz;. Chim. Acta. 33, 1975 (1950). (4)Brimlev. R. C.. Suture 163. 215 ” , (1949). (5) Bull, H. B., Hahn, J. W., Baptist, V. H., J. Am. Chem. SOC.71, 550 (1949). (6) Clarkson, T. W.,Ilench, J. E., Biochem. J . 62,361 (1956).
I n this article by D. E. Kalker, R . S. Adams, and J. R . Alden [ ~ K A L .CHEN. 33, 308 (1961)], on page 309, column 3, the following Acknonledgment should be added: K o r k supported by Grant 3476 5038 of the General Research Funds of the University of Kansas and partially by the L-,P. Atomic Energy Commission through Contract AT(111)686, and this support is gratefully acknodedged.
Correction Recorder-Integrator Errors in Gas Chromatography Area Measurements I n this article by Charles H. Orr [ANAL.CHEW33, 15s (1961)] Equation
15 should be changed from P,
=
( X 100) = 100
to P, = ( R
x 100) -
100
VOL. 33, NO. 4, APRIL 1961
541
