Critique of Critical Tables.

The need for critical tables has grown out of the spectacular fecundity of modern experimental research. Some fifty thousand scientific periodicals throughout the world present a wealth of material with which it is impossible for any one individual to come into mere physical contact, much less to digest and evaluate. A large part of the material thus published which is pertinent to critical tables comprises numerical data of various sorts, perhaps for the most part values of the various physical parameters which describe the properties of different materials, but also numerical values for fundamental constants such as the velocity of light or the intensity of gravity. This numerical material is subject to extensive duplication, for many measurements are made independently of each other. Furthermore, techniques are continually being improved so that continually better values are being obtained for ostensibly the same parameter. It is the primary function of a set of critical tables to subject this welter of numerical material to some sort of critical evaluation, which will enable the interested user to form a judgment as to the "best" value for any parameter, and also to make some estimate of the "probable" error of the value selected as the "best." It is the purpose of this introductory talk to inquire into some of the principles which should control any attempt to select a "best" value or to estimate how good the "best" value may be expected to be. This inquiry will be both general and also particular, in so far as special kinds of parameters demand special treatment. I cannot hope to give you anything philosophically profound, or to do more than to present considerations obvious to every one of you who is willing to give the matter a little thought. It is, I think, usually implied that not only should any critical tables endeavor to present the "best" values, but that they should also endeavor to find, within limits, the "correct" values. That is, the usual implication is that there is an "objective" background to all our measurement, and that the ultimate purpose of our measurements is to find the "objective" values of the various parameters, such as the velocity of light, which are true and correct independent of the measuring instrument or of the measuring agent. Now it may well be that something of this sort is an ideal, and a proper ideal of our measurements, but I think that examination of what we actually do when making measurements and determining the numerical values of our parameters will show that any such ideal is at best a limiting ideal which we never actually attain in practice and in fact never can attain. For it is obvious that the making of numerical measurements and the assessing of their probable excellence is unavoidably a human enterprise, and that all we can attain at any epoch is a consensus of the best opinion of qualified experts at that epoch. Now, with all due deference to my audience, the opinion of qualified experts is subject to the hazards of human frailty, and our evaluation of what can be accomplished by critical tables must take into account as one of the factors this element of human frailty. The importance of this factor may be compara-