Let us have a rigid rod at rest; this has a length _l_, when measured by a measuring rod at rest; we suppose that the axis of the rod is laid along the X-axis of the system at rest, and then a uniform velocity _v_, parallel to the axis of X, is imparted to it. Let us now enquire about the length of the moving rod; this can be obtained by either of these operations.— (_a_) The observer provided with the measuring rod moves along with the rod to be measured, and measures by direct superposition the length of the rod:—just as if the observer, the measuring rod, and the rod to be measured were at rest. (_b_) The observer finds out, by means of clocks placed in a system at rest (the clocks being synchronous as defined in §1), the points of this system where the ends of the rod to be measured occur at a particular time _t_. The distance between these two points, measured by the previously used measuring rod, this time it being at rest, is a length, which we may call the “length of the rod.” According to the Principle of Relativity, the length found out by the operation _a_), which we may call “the length of the rod in the moving system” is equal to the length _l_ of the rod in the stationary system. The length which is found out by the second method, may be called ‘_the length of the moving rod measured from the stationary system_.’ This length is to be estimated on the basis of our principle, and _we shall find it to be different from l_. In the generally recognised kinematics, we silently assume that the lengths defined by these two operations are equal, or in other words, that at an epoch of time _t_, a moving rigid body is geometrically replaceable by the same body, which can replace it in the condition of rest. Relativity of Time. Let us suppose that the two clocks synchronous with the clocks in the system at rest are brought to the ends A, and B of a rod, _i.e._, the time of the clocks correspond to the time of the stationary system at the points where they happen to arrive; these clocks are therefore synchronous in the stationary system. We further imagine that there are two observers at the two watches, and moving with them, and that these observers apply the criterion for synchronism to the two clocks. At the time _t__{A}, a ray of light goes out from A, is reflected from B at the time _t__{B}, and arrives back at A at time _t′__{A}. Taking into consideration the principle of, constancy of the velocity of light, we have _t__{B} - _t__{A} = _r__{AB}/(_c_ - _v_), and _t′__{A} - _t__{B} = _r__{AB}/(_c_ + _v_),