Measuring constants of nature: Confirmation and determination in piezoelectricity

Exact measurements are a central practice of modern physics. In certain cases, they are essential for determining values of coefficients, for confirming theories, and for detecting the existence of effects. The history of piezoelectricity at the end of the nineteenth century reveals two different methods of exact measurement: a mathematical versus an "artisanal" approach. In the former, a scientist first carried out the experiment and later employed mathematical methods to reduce error. In the latter, a scientist physically manipulated the experimental apparatus to bypass possible sources of error before its performance. These two approaches were related to German theoreticians and to French experimentalists, respectively. However, affiliation with a particular school rather than nationality was the decisive factor in the differences between the two approaches. Despite differences, adherents of both approaches sought to attain high precision and to eliminate even small experimental errors.This history exhibits the complexity and flexibility of experiments and their analysis. It supports the claim of the "New Experimentalism" that theory does not supply complete directions for practical experimental decisions. An example for this is found in the way an experimental error was discovered (after incorrect results had already been published) only by a comparison to an earlier experiment rather than to a theory.