Poggendorff's Method for the Comparison of Electromotive Forces

The method given in §76 for the comparison of electromotive forces is subject to a defect similar to that mentioned in §77, on the measurement of resistance; that is, it depends upon measuring the deflexion of a galvanometer needle, and assumes that the E.M.F. of the batteries employed remain constant throughout the experiment.

The following method, first suggested by Poggendorff, resembles the Wheatstone-bridge method for measuring resistances, in being a null method; it depends, that is to say, on determining when no current passes through a galvanometer, not on measuring the deflexion. We have seen (p. 422) that if a current C be flowing through a conductor, the E.M.F. or difference of potential between any two points, separated by a resistance R, is CR.

Let AB (fig. 75) be a conductor of considerable resistance, through which a current is flowing from A to B; let P₁ be a point on this conductor, E₁ the difference of potential between A and P₁. If A and P₁ be connected by a second wire AG₁P₁, including a galvanometer G₁ in its circuit, a current will flow from A to P₁ through this wire also. Let a second battery be placed in this circuit in such a way as to tend to produce a current in the direction P₁, G₁, A₁) the current actually flowing through the galvanometer G₁ will depend on the difference between E₁ and the E.M.F. of this battery. By varying the position of P₁ along the wire AB, we can adjust matters so that no current flows through the galvanometer G₁; when this is the case it is clear that the E.M.F. E₁ of the battery is equal to the difference of potential between A and P₁ produced by the first battery. Let the resistance AP₁ be R₁ and let R be the resistance of AB, and ρ that of the battery which is producing the current through AB, including, of course, any connecting wires, E being the E.M.F. of this battery. Then, if C be the current in AB, we have

or,

This equation gives us, if we know ρ, the ratio E₁/E; for R and R₁ can be observed.

This method will be satisfactory in practice if R is very great compared with ρ, for then an approximate value of ρ will be sufficient; or if R is sufficiently large, ρ may be entirely neglected, and we may write E₁/E = R₁/R.

This is Poggendorff's method of comparing the E.M.F. of two batteries. The following arrangement, suggested by Latimer-Clark, obviates the necessity for knowing ρ.