CORRESPONDENCE
An Approach to Numerical Differentiation of Experimental Data SIR: The article, “An Approach to Numerical Differentiation of Experimental Data,” by Stephen Whitaker and R . L. Pigford [IND.ENG.CHEM.52, 185-7 (1960)], fails to mention a pioneer reference, invaluable to the student of data treatment, “Graphical Calculus,” by Theodore R . Running, George Wahr, publisher, Ann Arbor, Mich., 1937. I was fortunate to take a course from Professor Running in this subject and ir has provided me with a point of view toward data that has proved itself over the years. The tendency of engineers to view numbers with an awe and reverence is discouraging in the face of the known difficulties of taking reliable data, and the difficulty of extrapolating even the best of such data to other cases. The desire to generalize is with us all and it takes a firm control to keep this desire in its place and treat data with the tough mindedness they deserve. The natural hope of discovering truth causes us to see in coincidence the gleam of eternal truth, and the later brutality of factual disagreement may likewise cause us xo seek carefully for error in these distasteftil later numbers. W h y is it we clutch attractive numbers so readily, and only ask for a check and verification when the apparently contradictory numbers are presented? Professor Running discusses in his thin text of only 81 pages the differentiation of data, both as to the first and the second derivative. H e considers both weighted and unweighted data, and illustrates his arguments with examples taken from several experiments. His procedures are ser forth concisely in statements such as the following, “By the graduation of experimental data is meant the process of finding from a set of observed values of y 5 corresponding to a set of values of x , a new set of values of y locating points on a smooth curve and whose residuals are consistent with the experimental errors.” I n essence, he uses the principle that many complex curves can be approximated by sections of parabolic curves, whose first derivatives are straight lines. If then, the first derivative of the data is approximated by a number of straightline sections, these can be used to smooth
the data and allow some examination ot consistency to be made. This note is submitted in the hope i r inay call attention to this little volume by Professor Running, which so concisely treats this fascinating subject.
JAMES€1. IJYIEG;\SD 4032 Las Pasas Way Sacramento 25. Calif.
Professor Running‘s brief book was not known to the authors who appreciate D r . i2’iegand‘s calling i t to their attention. The principal aim of our paper was to show the. simplicity of using staxistically sound formulas for differentiating numerical data and obtaining an estimate of the error of the differentiated quantity. STEPHEN IVHITAKER
\\-e \(.odd like to add the fol1ou.ing comment to that of Dr. Wiegand Procedures for numerical differenliation by an! one of several different methods are covered in many standard reference works on numerical analysis. SIR:
2401 Brae Road Arden, Del. R . L. PIGFORD Dept. of Chemical Engineering University of Delaware Newark, Del. AND
Correction
Nitric Acid ManufactureTheory and Practice
Sachsel (with the condensed article in IND.ENG.CHEM.52, 101-4 (February 1960)], Figure 7 and its caption, ap-
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F I G U R E 7 . R E A C T I O N R A T E CONSTANT A S A F U N C T I O N O F TEMPERATURE 2 NO 0, = 2 NO,
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