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ELECTRIC TIME.

By M. LIPPMANN.

The unit of time universally adopted, the second, undergoes only very slow secular variations, and can be determined with a precision and an ease which compel its employment.  Still it is true that the second is an arbitrary and a variable unit—­arbitrary, in as far as it has no relation with the properties of matter, with physical constants; variable, since the duration of the diurnal movement undergoes causes of secular perturbation, some of which, such as the friction of the tides, are not as yet calculable.

We may ask if it is possible to define an absolutely invariable unit of time; it would be desirable to determine with sufficient precision, if only once in a century, the relation of the second to such a unit, so that we might verify the variations of the second indirectly and independently of any astronomical hypothesis.

Now, the study of certain electrical phenomena furnishes a unit of time which is absolutely invariable, as this magnitude is a specific constant.  Let us consider a conductive substance which may always be found identical with itself, and to fix our ideas let us choose mercury, taken at the temperature of 0 deg.  C., which completely fulfills this condition.  We may determine by several methods the specific electric resistance, [rho], of mercury in absolute electrostatic units; [rho] is a specific property of mercury, and is consequently a magnitude absolutely invariable.  Moreover, [rho] is an interval of time.  We might, therefore, take [rho] as a unit of time, unless we prefer to consider this value as an imperishable standard of time.

In fact, [rho] is not simply a quantity the measure of which is found to be in relation with the measure of time.  It is a concrete interval of time, disregarding every convention established with reference to measures and every selection of unit.  It may at first sight, appear singular that an interval of time is found in a manner hidden under the designation electric resistance.  But we need merely call to mind that in the electrostatic system the intensities of the current are speeds of efflux and that the resistances are times, i.e., the times necessary for the efflux of the electricity under given conditions.  We must, in particular, remember what is meant by the specific resistance, [rho] of mercury in the electrostatic system.  If we consider a circuit having a resistance equal to that of a cube of mercury, the side of which = the unit of length, the circuit being submitted to an electromotive force equal to unity, this circuit will take a given time to be traversed by the unit quantity of electricity, and this time is precisely [rho].  It must be remarked that the selection of the unit of length, like that of the unit of mass, is indifferent, for the different units brought here into play depend on it in such a manner that [rho] is not affected.