An Electrical Method of Measuring Small Intervals of Time
F. C. Brown · Physical Review · 1912
W HEN it is desired to measure the time between two mechanical operations, we have found that it may be carried out quite accurately by the use of resistances, battery, ballistic galvanometer, condenser, and contact keys.The principle is based on the relation between the electro-magnetic and the electro-static systems of units, and if we define the ohm in terms of the dimensions of a mercury column, the method is an absolute one.Aside from the advantage of having an absolute measure of time in terms of length, or of length, mass and resistance, the advantages of the method are simplicity and ease of manipulation.The interval of time to be measured may be diminished to the limits of dependable electrical contact, no doubt less than o.ooi second.How large the interval may be varies from 0.4 second to several seconds depending on the period of the galvanometer.THEORY.The theory of the method is essentially the same as that given in a previous paper on a method of measuring fluctuating resistances, 1 but as Dr. Erich Schneckenburg, of Berlin, has kindly pointed out that the method of derivation of equation ( 1) in that paper is not obvious, I shall briefly review the essential steps.Suppose it is desired to know the interval of time, A/, between the making of electrical contact at /1, and the time of breaking of contact at fe.It is to be shown that this time interval varies directly as the throw of a ballistic galvanometer which has been connected, as shown in Fig. 1, in a Wheatstone's bridge circuit during the interval.Considering the battery resistance small compared to the other resistances, we obtain, by KirkehhofFs and Ohm's Laws, the current through the galvanometer to be ._ E(aR -bx) *-( kl x + k 2 y (I)where k x = Gb + aG + ab + aR + bR t h = aRG + bRG + abR.