uated, subject to assumptions, for da, dp, and dR in Equations 15, 16, and 17, while the previous paper (50) gave those for dP,, du, dcl, and dcz, except that for arbitrary scale ends, R/100 must be replaced with ( E - p ) / ( a - p). Means have been suggested for making errors due to temperature, wave length, source, photocell, or cuvette changes insignificant, so t h a t these need not be considered as zi. T h e size of any error sets a limit on the precision attainable, whether or not the other errors are known-for example, the readability of the Beckman D U scale is about + O.lyo. T h e error coefficient in the ordinary method reaches a minimum value of e. Thus no analysis carried out in the ordinary way on a Beckman D U can hope to have a concentration error less than + (O.l)e or f 0.27%. Many reported analyses come close to this limit. APPLICATIONS
Differential absorptiometry has been applied to alumjnum (6), beryllium (69) , chromium ( I C ) , copper ( I I ) , erbium (IO), manganese (14, 60), molybdenum ( 4 ) , neodymium (9, IO), nickel ( l a ) ,niobium (47), platinum (3), plutonium (@), praseodymium ( I O ) , samarium (IO), tantalum (4?‘), titanium (17, 43, 45), uranium (5, 23, 56), and zirconium (26, $9) among the metals, and also to cyanide (46), fluoride (85), and phosphate (27). Aspects of precision absorptiometry other than the differential technique are less easily indexed, and no search for their applications has been made. ACKNOWLEDGMENT
The author thanks Charles V. Banks, P. G. Grmes, and R. I. Bystroff for helpful correspondence, and P. E. Rouse for helpful discussion, concerning the ideas of this paper. H e is grateful also to the Los Alamos Scientific Laboratory of the University of California for permission to publish the work, which was performed under the auspices of the U. S. Atomic Energy Commission. LITERATURE CITED
(1) Allen, E., Steams, E. I., ANAL. CHEM. 24,2009 (1952). (2) Ayres, G. H., Zbid., 21, 652 (1949). (3) Ayres, G. H., Meyer, A. S., Jr.,Zbid., 23,299 (1951). (4) Bacon, A., Milner, G. W. C., Anal. Chim.Acta 15, 573 (1956).
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(5)^. B;won, A., Milner, G. W. C., Analyst 8 1 , 456 (1956). (6) Banerjee, D. K., ANAL. CHEM.29, 55 (1957). (7) Banks, C. V., Grimes, P. G., Bystroff, R. I., Anal. Chim. Acta 15,367 (1956). (8) Banks, C. V., Grimes, P. G., Bystroff, R. I., Iowa Stette College, Ames, Iowa, private communication. (9) Banks, C. V., Spooner, J. L., O’Laughh, J. ANAL. CHEM. 28, 1894 (1956). (10) Ibid., 30,458 (1958). (11) Bastian, R.,Zbid., 21,972(1949). (12) Zbid., 23, 580 (1951). (13) Zbid., 25, 259 (1953). (14) Bastian, R., Weberling, R., Palilla, F., Zbid., 22, 160 (1950). (15) Berck, B., Zbid., 25, 1253 (1953). (16) Cahn, L., J. Opt. SOC.Am. 45, 953 (1955). (17) Carvalho, R. A. G. de, ANAL.CHEM. 30, 1124 (1958). (18) Cole, R., J. Opt. SOC.A m . 41, 38 (1951). (19) Committee on Balances and Weights, Anal. Chem. 26, 1190 (1954). (20) Committee on Nomenclature in -4pplied Spectroscopy, Ibid., 24, 1349 (1952). (21) Committee on Nomenclature, Division of Analytical Chemistry, Zbid., 24, 1348 (1952). (22) Crawford, C. hl. (Patterson, A. M.), Chem. Eng. News 33, 5262 (1955); 34, 1075 f1956). (23) Crbuthamel, C. E., Johnson, C. E., A N A L . CHEM. 24, 1780 (1952). (24) Freeland, M. Q.,Fritz, J. S., Zbid., 27, 1737 (1955). (25) Freund, H., Holbrook, R. F., Ibid., 30,462 (1958). (26) Gedansky, S . J., Gordon, L., Ibid., 29, 666 i19571 (27) Gee, A:, Deitz, V. R., Zbid., 25, 1320 (1953). (28) Gridgeman, N. T., Ibid., 24, 445 (1952). (29) Ibid., p. 2010. (30) Gridgeman, N. T., Photoelec. Spectrometry Group Bull. 8, 197 (1955). (31) Hamilton, R. H., ANAL. CHEM.25, 399 1953). (32) E! amilton, R. H., IND.ENQ.CHEM., A N A L . ED. 16, 123 (1944). (33) LeRoy, G., Ann. fals. et fraudes 10, 208 (1917). (34) Lindsay, R. B., “Physical Statistics,” Equation 59, p. 30, Riley, New York, 1941. (35) Lothe, J. J., ANAL. CHEY. 28, 949 (1956). (36) McBrvde. “ , W. A. E., Ibid.., 24,. 1639 . (i952). (37) Rlandel, J., Stiehler, R. D., Zbid., 29, l7A (April 1957, Part I). (38) Mandel, J., Stiehler, R. D., J . Research Natl. Bur. Standards 53, 155 (1954). (39) Manning, D. L., White, J. C., ANAL. CHEM.27, 1389 (1955). (40) Mellon, M. G., “Analytical .4bsorption Spectroscopy,” p. 110, Wiley, New York, 1950. (41) Zbid., pp. 111-12. (42) Ibid., p. 338. (43) Milner, G. W. C., Phennah, P. J., Analyst 79, 414 (1954).
w.,
(44) Rlueller, R. H., Kinney, G. F., J . Opt. SOC.Am. 25, 342 (1935). (45) Neal, W. T. L., Analyst 79, 403 (1954). (46) Ohlweiler, 0. A,, RIeditsch, J . O., ANAL.CHEM.30, 450 (1958). (47) Palilla, F. C., Adler, S., Hiskey, C. F., Ibid., 25, 926 (1953). (48) Phillips, G., Analyst 83, i 5 (1958). (49) Pollard, G. E. (Hallett, L. T.))ANAL. CHEW27, 7A (August 1955). (50) Reilley, C. N., Crawford, C. Al., Zbid., 27, 716 (1965). (51) Ringbom, A., 2. anal. Chern. 115, 332 (1939). (52) Robinson, D. Z., Cole, R., J . Opt. Soc. A m . 41, 560 (1951). (53) Rogers, .4.J., in “Polonium,” H. V. ?foyer, ed., Office of Technical Services, Dept. Commerce, Washington 25, D. C., T I D 5221, p. 288 (July 1956). (54) Snesarev, K. h., T r u d y Koinissii Anal. A k a d . Sauk S.S.S.R.,Otdel. Khirn. Nauk 4(7), 282 (1952). (55) Strong, F. C., ; ~ N . < L . CHEII.24, 338, 2013 (19521. (56) S
