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0.5 x, and 0.9 χ for the curves corre sponding to 1, 5, and 9% in Figure 4. If a standard deviation of 1% is accept able, the samples can be 100 times smaller than for 0.1%. An important point illustrated by the figure is that if the fraction of richer particles is small, and the leaner ones contain little or none of the sub stance of interest, large test portions are required. If a sample of gold ore containing 0.01% gold when ground to 140 mesh (0.1 mm in diameter) con sists, say, of only particles of gangue and of pure gold, test portions of 30 g would be required to bold the sam pling standard deviation to 1%. (An ore density of 3 is assumed.) Concluding Comments
tudent of Bunsen, co-Nobelist with Rayleigh, friend of Ostwald and Remsen and father of the noble gases, c o u l d Sir William Ramsay have wanted a n y t h i n g more? Why, only a c o p y of the Scott Specialty Gases Catalog! This d o c u m e n t is indispensable for workers in atmospheric chemistry. A m o n g its 160 pages you will find data not only on pure gases, but on CRM's — Certified Reference Materials — w h i c h are recognized by EPA and NBS as equivalent, to the letter's SRM's — Standard Reference Materials. Now available only in C O , they will soon include N O , S 0 2 and C 0 2 . UN MONOXlufc WTHOGEN 50 ppm Nominal
Also interesting reading is information about Scott Protocol Gases, used to establish NBS traceability for EPA at concentrations lying intermediate between C R M values. A n d tucked away on pages 94-96 is a description of the Scott collaborative gas analysis cross reference service, a sine quâ non for proving your standard of excellence in gas analysis. For a r g o n , for x e n o n , or for anything in between, look in y o u r copy of the Scott Specialty Gases Catalog. If y o u lack a copy, request one today.
Sampling is not simple. It is most important in the worst situations. If the quantities x,s,Ks,A, and Β are known exactly, then calculation of the statistical sampling uncertainty is easy, and the number and size of the samples that should be collected to provide a given precision can be readi ly determined. But if, as is more usual, these quantities are known only ap proximately, or perhaps not at all, then preliminary samples and mea surements must be taken and on the basis of the results more precise sam pling procedures developed. These procedures will ultimately yield a sampling plan that optimizes the qual ity of the results while holding down time and costs. Sampling theory cannot replace ex perience and common sense. Used in concert with these qualities, however, it can yield the most information about the population being sampled with the least cost and effort. All ana lytical chemists should know enough sampling theory to be able to ask in telligent questions about the samples provided, to take subsamples without introducing additional uncertainty in the results and, if necessary, to plan and perform uncomplicated sampling operations. It is the capability of un derstanding and executing all phases of analysis that ultimately character izes the true analytical chemist, even though he or she may possess special expertise in a particular separation or measurement technique. References
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(1) W. J. Youden, J. Assoc. Off. Anal. Chem., 50,1007(1967). (2) T. B. Whitaker, J. W. Dickens, and R. J. Monroe, J. Am. Oil Chem. Soc, 51, 214 (1974); Τ. Β. Whitaker, Pure Appl. Chem., 49,1709(1977). (3) Hazardous Waste Monitoring System, General, Fed. Regist., Vol. 45, No. 98, pp 33075-33127 (May 19,1980). (4) Staff, ACS Subcommittee on Environ mental Analytical Chemistry, Anal. Chem., 52, 2242 (1980).
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(5) See, for example, W. J. Dixon and F. J. Massey, Jr., "Introduction to Statistical Analysis," 3rd éd., McGraw-Hill, New York, 1969; M. G. Natrella, "Experimental Statistics," National Bureau of Standards Handbook 91, August 1963, U.S. Government Printing Office. (6) C. O. Ingamells and P. Switzer, Talanta, 20, 547 (1973); C. O. Ingamells, Talanta, 21,141 (1974); 23, 263 (1976). (7) S. H. Harrison and R. Zeisler, NBS Internal Report 80-2164, C. W. Reimann, R. A. Velapoldi, L. B. Hagan, and J. K. Taylor, Eds., U.S. National Bureau of Standards, Washington, D.C., 1980, ρ 66. (8) M. G. Natrella, "Experimental Statis tics," National Bureau of Standards Handbook 91, August 1963, U.S. Govern ment Printing Office, pp 2-13 and Table A6. (9) ASTM E-300 Standard Recommended Practice for Sampling Industrial Chemi cals, American Society for Testing and Materials, Philadelphia, 1973 (reapproved 1979). (10) J. Visman, Materials Research and Standards, November, ρ 8 (1969). (11) A. Benedetti-Pichler, in "Physical Methods of Chemical Analysis," W. M. Berl, Ed., Academic Press, New York, 1956, Vol. 3, ρ 183; W. E. Harris and B. Kratochvil, Anal. Chem., 46,313 (1974). (12) W. E. Harris and B. Kratochvil, "In troduction to Chemical Analysis," Saun ders, Philadelphia, 1981, Chapter 21.
Kratochvil
Taylor
Byron Kratochvil, professor of chem istry at the University of Alberta, re ceived his BS, MS, and PhD degrees from Iowa State University. His re search interests include solvent ef fects on solute properties and reac tions, applications of nonaqueous systems to chemical analysis, and methods for determining ionic so lutes. John K. Taylor, coordinator for qual ity assurance and voluntary stan dardization activities at the National Bureau of Standards Center for Ana lytical Chemistry, received his BS from George Washington University, and his MS and PhD degrees from the University of Maryland. His research interests include electrochemical analysis, refractometry, isotope sepa rations, standard reference materials, and the application of physical meth ods to chemical analysis.
