Note 21 — Chapter VII · GRAVITATION—THE EXPLANATION

In so far as these casual influences are not entirely eliminated by the selection of material and the precautions in using the rod, appropriate corrections must be applied. But the rod must not be corrected for essential characteristics of the space it is measuring. We correct the reading of a voltmeter for temperature, but it would be nonsensical to correct it for effects of the applied voltage. The distinction between casual and essential influences—those to be eliminated and those to be left in—depends on the intention of the measurements. The measuring rod is intended for surveying space, and the essential characteristic of space is “metric”. It would be absurd to correct the readings of our scale to the values they would have had if the space had some other metric. The region of the world to which the metric refers may also contain an electric field; this will be regarded as a casual characteristic since the measuring rod is not intended for surveying electric fields. I do not mean that from a broader standpoint the electric field is any less essential to the region than its peculiar metric. It would be hard to say in what sense it would remain the same region if any of its qualities were other than they actually are. This point does not trouble us here, because there are vast regions of the world practically empty of all characteristics except metric, and it is to these that the law of gravitation is applied both in theory and in practice. It has seemed, however, desirable to dwell on this distinction between essential and casual characteristics because there are some who, knowing that we cannot avoid in all circumstances corrections for casual influences, regard that as license to adopt any arbitrary system of corrections—a procedure which would merely have the effect of concealing what the measures can teach us about essential characteristics.