Viewing the situation as it now stands, we may say that material rods, visually recognised as rigid, will be taken as norms of measurement in physical space. In other words, it will be assumed that rods which coincide when brought together will continue to remain congruent when transferred, independently of one another, to other regions of space. Of course, the physicist will guard himself as much as possible against local contingent influences, such as variations of pressure and temperature, which might influence the behaviour of his rods. But when all these elementary precautions have been observed, the geometry determined by our rods will automatically become the [Pg 48] geometry of space. This physical definition of congruence may be termed practical congruence, as distinguished from theoretical congruence, which is embodied by the mathematical types we have discussed. With his standard rigid bodies defined in this way by physical objects, the physicist can perform measurements in the space of his frame and in consequence obtains the numerical results of three-dimensional Euclidean geometry. Inasmuch as the more careful he is to guard against such contingent influences as variations of temperature, the more accurately will his numerical results approximate to those of pure Euclidean geometry, he feels justified in stating that rigid objects behave like rigid Euclidean bodies and that the space of our experience is rigorously Euclidean. We may also recall that his rigid bodies having been defined, the definition of a straight line as the axis of rotation of a revolving solid, two of whose points are fixed, or as the shortest distance between two points in space, follows immediately; and of course the straight line thus defined satisfies Euclid’s parallel postulate, since it is derived from the behaviour of Euclidean solids.