the velocity of light is independent of the direction of motion of the observer. Thus we have:
C. Theorem. The velocity of light in free space as measured by any observer is independent of the direction of motion of that observer.
We are thus led to inquire further as to whether the velocity of light in free space is independent of the absolute value of the velocity of the observer. It appears to be impossible to prove that it is so independent; and yet one is unable to conceive of any way in which it could be dependent on the absolute value without at the same time depending on the direction of the velocity also. But, accepting A and B, we prove C which asserts that such dependence does not exist. There seems, then, nothing left to do but to assume that dependence on absolute value does not exist; and this is what is done in the theory of relativity. In the absence of experimental information in contradiction to this assumption it is undoubtedly the natural one to make. Any other procedure would be out of harmony with the usual methods of science. This assumption, therefore, is one which we make as the most natural teaching of experimental facts; and as such we treat it as a "law of nature" so long as fresh experiment does not invalidate it. This law may be stated as follows:
D. The velocity of light in free space as measured by any observer is independent of the absolute value of the velocity of the observer.
The law which we have stated as A above is often referred to as the first postulate of relativity. B, C and D taken together constitute the second postulate of relativity. We have broken this postulate into parts in order to state clearly just how it depends on experiment. Combining the parts we may state its essential content as follows:
E. The velocity of light is independent of the relative velocity of the source of light and the observer.
The theory of relativity consists of those conclusions which can be derived by logical process (that is, mathematically) from A and E in conjunction with certain principles which are universally accepted in the classical mechanics — at least, this may be taken as a tentative definition of the theory of relativity. If one agrees that experiment has been properly generalized in A, B and D one has therefore the alternative of accepting the conclusions of relativity or of giving up almost the whole of the usual system of mechanics. That one should take the first horn of the dilemma hardly admits question.
III. Fundamental Conclusions of the Theory of Relativity.
For the sake of convenience in stating some of the fundamental conclusions of the theory of relativity let us suppose that we have two observers
