The principle of relativity of classical mechanics is understood to signify the consequence, which arises out of Newton's equations of motion, that two systems of co-ordinates, moving with uniform motion in a straight line with respect to one another, are to be regarded as fully equivalent for the description of events in the domain of mechanics. For our observations on the earth this means that any mechanical event on the surface of the earth—for example, the motion of a projected body—does not become modified by the circumstance that the earth is not at rest, but, as is approximately the case, is moving rectilinearly and uniformly. Yet this postulate of relativity does not fully characterize the Newtonian principle of relativity, even if it expresses that experimental fact which constitutes the essence of the principle of relativity. The postulate of relativity has yet to be supplemented by those formulæ of transformation by means of which the observer is able to transform the co-ordinates
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that occur in Newton's equations of motion into those of a system of reference which is moving uniformly and rectilinearly with respect to his own and which has the co-ordinates