The Precision of Limiting Quantities

Needless to say, as one approaches the limit, T — becomes smaller and, for the exponents jS and S at least, so does 7 — 7 . Assuming that the precisions of T and 7 themselves are approximately constant, the uncertainties in In I r - r I and In 7 — 7 are growing as one gets closer to the desired limit. Moreover, as we shall see, the closer one gets to the critical point, the more serious the perturbations due to gravity become. 

Statements that an exponent has been determined with a precision (standard deviation) of, for example, a = 0.002 are suspect. Sometimes all this means is that the experimenter has plotted all the measured points, weighted them equally, and used a linear least-squares program to evaluate the best value of the slope and its standard deviation the reported is then not a limiting value, but an average value, and the a may be nearly meaningless. The actual uncertainty may be far larger, as more precise measurements and more careful analysis may show.f 

Today s experimentalists are more sophisticated and error analyses are now both more detailed and more circumspect. Fewer claims of high precision are being made estimates of exponents and their uncertainties are surely now more realistic, but the added caution leads to the superficial misimpression that the experimentalists have made no progress. 

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