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° C., which completely fulfills this condition. We may determine by several methods the specific electric resistance, ρ, of mercury in absolute electrostatic units; ρ is a specific property of mercury, and is consequently a magnitude absolutely invariable. Moreover, ρ is an interval of time. We might, therefore, take ρ as a unit of time, unless we prefer to consider this value as an imperishable standard of time.
In fact, ρ 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, ρ 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 ρ. 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 ρ is not affected.
It is now required to bring this definition experimentally into action, i.e., to realize an interval of time which may be a known multiple of ρ. This problem may be solved in various ways,[1] and especially by means of the following apparatus.
A battery of an arbitrary electromotive force, E, actuates at the same time the two antagonistic circuits of a differential galvanometer. In the first circuit, which has a resistance, R, the battery sends a continuous current of the intensity, I; in the second circuit the battery sends a discontinuous series of discharges, obtained by charging periodically by means of the battery a condenser of the capacity, C, which is then discharged through this second circuit. The needle of the galvanometer remains in equilibrium if the two currents yield equal quantities of electricity during one and the same time, τ.
Let us suppose this condition of equilibrium realized and the needle remaining motionless at zero; it is easy to write the conditions of equilibrium. During the time, τ, the continuous current yields a quantity of electricity = (E / R)τ; on the other hand, each charge of the condenser = CE, and during the time, τ, the number of discharges = τ/t, t being the fixed time between two discharges; τ and t are here supposed to be expressed by the aid of an arbitrary unit of time; the second circuit yields, therefore, a quantity of electricity equal to CE × (τ / t). The condition of equilibrium is then (E / R) τ = CE × (τ / t); or, more simply, t = CR.
C and R are known in absolute values, i.e., we know that C is equal to p times the capacity of a sphere of the radius, l; we have, therefore, C = pl; in the same manner we know that R is equal to q times the resistance of a cube of mercury having l for its side. We have, therefore, R = q ρ (l / l²) = q (ρ / l) and consequently t = pqρ.