\Item{(b)} The track of a moving particle or light-pulse under specified initial conditions is unique, and it does not seem to be possible to specify any unique tracks in terms of intervals only other than those given by equations \Eq{(15.7)} and~\Eq{(15.8)}. \Item{(c)} We may arrive at these laws by induction from experiment. If we rely solely on experimental evidence we cannot claim exactness for the laws. It goes without saying that there always remains a possibility of small amendments of the laws too slight to affect any observational tests yet tried. Belief in the perfect accuracy of \Eq{(15.7)} and \Eq{(15.8)} can only be justified on the theoretical grounds \Item{(a)} or~\Item{(b)}. But the more important consideration is the universality, rather than the accuracy, of the experimental laws; we have to guard against a spurious generalisation extended to conditions intrinsically dissimilar from those for which the laws have been established observationally. We derived~\Eq{(15.7)} from the equations~\Eq{(15.5)} which describe the observed behaviour of a particle moving under no field of force. We assume that the result holds in all circumstances. The risky point in the generalisation is not in introducing a field of force, because that may be due to an attitude of mind of which the particle has no cognizance. The risk is in passing from regions of the world where Galilean coordinates $(x, y, z, t)$ are possible to intrinsically dissimilar regions where no such coordinates exist---from flat space-time to space-time which is not flat. The \emph{Principle of Equivalence} asserts the legitimacy of this generalisation. It is essentially an hypothesis to be tested by experiment as opportunity offers. Moreover it is to be regarded as a suggestion, rather than a dogma admitting of no exceptions. It is likely that some of the phenomena will be determined by comparatively simple equations in which the components of curvature of the world do not appear; such equations will be the same for a curved region as for a flat region. It is to these that the Principle of Equivalence applies. It is a plausible suggestion that the undisturbed motion of a particle and the propagation of light are governed by laws of this specially simple type; and accordingly \Eq{(15.7)} and \Eq{(15.8)} will apply in all circumstances. But there are more complex phenomena governed by equations in which the curvatures of the world are involved; terms containing these curvatures will vanish in the equations summarising experiments made in a flat region, and would have to be reinstated in passing to the general equations. Clearly there must be some phenomena of this kind which discriminate between \PageSep{41} a flat world and a curved world; otherwise we could have no knowledge of world-curvature. For these the Principle of Equivalence breaks down. \index{Equivalence, Principle of}% \index{Principle!of equivalence}%