Consider, for instance, the length of an object, or again the comparison of two lengths situated in different parts of space. We have seen, when discussing mathematical space, that according to our measuring standards, which were conventional, these lengths might be equal or unequal; and it was this aspect of relativity which expressed the fundamental mathematical relativity of length. But we also saw that although in theory the definition of congruence was conventional, in practice, if we wished to define congruence so as not to enter into conflict with our sense perceptions, a definite type of congruence (practical congruence) was imposed upon us by nature. We saw further that bodies which were thereby defined as congruent constituted what are known as Euclidean solids, and that these were assumed to remain absolute in length, regardless of the observer’s motion. Under these circumstances, when a physicist such as Einstein, in contradistinction to a mathematician, asserts that length is relative, he is referring to the actual length measured out by a so-called rigid body; and he wishes to imply that this length will turn out to be indeterminate and to depend essentially on our conditions of observation. We see, therefore, that the relativity of the physicist is not inevitable, as is that of the mathematician. It is not an a priori type of relativity expressing a trivial relativity to [Pg 100] standard. It is essentially an empirical type of relativity, always subject to proof or disproof by precise empirical tests. The two following illustrations may be helpful: Consider a telegraph pole rising vertically from the ground. The visual angle under which this pole will appear to us is essentially relative, since it varies in value with the distance of the observer from the pole. Of course, this visual angle is fundamentally relative, since its value depends on the system of geometry we may adopt, but we are no longer discussing this mathematical aspect of relativity. We are assuming that our system of measurements has been fixed according to the requirements of practical congruence, i.e., that our measurements are performed with ordinary rigid rods and hence are Euclidean. In this event the visual angle under which we perceive a given pole is perfectly determinate when our distance from the pole is specified. But, on the other hand, it is relative, inasmuch as it is not immanent in the pole; it varies with our relative distance and thereby reduces to a mere relationship between the pole and our distance therefrom.