Now introduce the condition that the velocity~$u$ is very small, remembering that $t_{2} - t_{1}$ will then become very large. Neglecting $u^{2}/c^{2}$, \Eq{(4.82)}~becomes \begin{gather*} \int_{t_{1}}^{t_{2}} dt \left(1 + \frac{\alpha}{c}\, \frac{dx}{dt}\right)\rlap{\qquad\text{approximately}} \\ = (t_{2} - t_{1}) + \frac{\alpha}{c} (x_{2} - x_{1}). \end{gather*} The clock, if moved sufficiently slowly, will record the correct time-difference if, and only if, $\alpha = 0$. Moving it in other directions, we must have, similarly, $\beta = 0$, $\gamma = 0$. Thus \Eq{(4.6)}~is the most general formula for the interval, when the time at different places is compared by slow transport of clocks from one \index{Transport of clocks}% place to another. I do not know how far the reader will be prepared to accept the condition that it must be possible to correlate the times at different places by moving a clock from one to the other with infinitesimal velocity. The method employed in accurate work is to send an electromagnetic signal from one to the other, and we shall see in \SecRef{11} that this leads to the same formulae. We can scarcely consider that either of these methods of comparing time at different places is an essential part of our primitive notion of time in the same way that measurement at one place by a cyclic mechanism is; therefore \PageSep{16} they are best regarded as conventional. Let it be understood, however, that although the relativity theory has formulated the convention explicitly, the usage of the word \emph{time-difference} for the quantity fixed by this convention is \index{Retardation of moving clocks}% in accordance with the long established practice in experimental physics and astronomy. Setting $\alpha = 0$ in~\Eq{(4.82)}, we see that the accurate formula for the clock-reading will be \begin{gather*} \int_{t_{1}}^{t_{2}} dt (1 - u^{2}/c^{2})^{\frac{1}{2}} \\ = (1 - u^{2}/c^{2})^{\frac{1}{2}}\, (t_{2} - t_{1}) \Tag{(4.9)} \end{gather*} for a uniform velocity~$u$. Thus a clock travelling with finite velocity gives too small a reading---the clock goes slow compared with the time-reckoning conventionally adopted.