This procedure of ascribing discrepancies in our mathematical anticipations to the presence of contingent influences rather than to the falsity of our theory is only human. There is no inclination, merely because the hundredth case turns out to be an exception, to abandon a theory which has led to accurate anticipations in 99 cases out of 100. But we must realise that this procedure of appealing to foreign influences, while perfectly legitimate in a tentative way, must be applied with a certain amount of caution; in every particular case it must be justified by a posteriori determination of fact. Thus Leverrier was also the first to discover certain irregularities in the motion of the planet Mercury. As in the case of Uranus, he attempted to ascribe these discrepancies to the presence of an interior planet which he called Vulcan and which he assumed to be moving between the orbit of Mercury and the sun. Astronomers have, however, failed to find the slightest trace of Vulcan, and a belief in its existence has been abandoned. If contingent influences are to be invoked for Mercury’s anomalies, we must search for them in some other direction. In this particular case all other suggestions were equally unsatisfactory. Hence even before the advent of Einstein’s theory, doubts had been raised as to the accuracy of Newton’s law of gravitation. The procedure of patching up a mistaken theoretical anticipation with hypotheses ad hoc has not much to commend it. Yet when, as was the case with Vulcan and Neptune, the influence we appeal to is of a category susceptible of being observed directly, the method is legitimate. But when our hypothesis ad hoc transcends observation by its very nature, and when, added to this, its utility is merely local, accounting for one definite fact and for no other, it becomes worse than useless. This abhorrence of science for the unverifiable type of hypothesis ad hoc so frequently encountered in the speculations of the metaphysicians is not due to a mere phenomenalistic desire to eliminate all that cannot be seen or sensed. It arises from a deeper motive entailing the entire raison d’être of a scientific theory. Suppose, for instance, that our theory had led us to anticipate a certain result, and that experiment or observation should prove that in reality a different result was realised. We could always adjust matters by arbitrarily postulating some local invisible and unverifiable influence, which we might ascribe to the presence of a mysterious [Pg xv] medium—say, the ether . We should thus have added a new influence to our scheme of nature.