Latimer-Clark's Potentiometer

In contrast to 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:

Let E₁, E₂ be the two E.M.F. to be compared, E that of a third battery, producing a current between the two points A and B; E must be greater than E₁ or E₂. Connect the three positive poles of the three batteries to A, the negative pole of E to B, and the negative poles of E₁ and E₂, through two galvanometers G₁ and G₂, to two points P₁, P₂ on AB; adjust the positions of P₁ and P₂ separately until no current flows through either galvanometer. It will be found convenient to have two keys, K₁, K₂, in the circuits for the purposes of this adjustment. Thus, positions are to be found for P₁ and P₂, such that on making contact simultaneously with the two keys there is no deflexion observed in either galvanometer. Let R₁, R₂ be the resistances of AP₁, AP₂ respectively, when this is the case. Then, C being the current in AB, we have

By this method of procedure results are obtained entirely independent of the battery used to give the main current through AB.

The differences of potential actually compared are those between the two poles of the batteries respectively, when neither is producing a current

A convenient experimental arrangement for carrying out the comparison of electromotive forces on this method as described by Latimer-Clark, has been called a 'potentiometer'.

The use of the two galvanometers is sometimes inconvenient, as it involves considerable complication of apparatus. In practice the following method may be adopted:

Connect the three positive poles of the batteries to A and the negative pole of E to B (fig. 76). Choose for the battery £ one which will give a fairly constant current through a large resistance, such as AB. Connect the two negative poles of E₁ and E₂ respectively to K₁, K₂, two of the binding screws of a switch. Connect K, the third screw of this switch, to one pole of the galvanometer G, and the other pole of the galvanometer to P, some point on AB. Make contact between K and K₁ and find a position P₁ for P, such that the galvanometer is not deflected. Turn the switch across to make contact between K and K₂, and find a second position P₂, such that the galvanometer is again not deflected. Then, if we assume that E has not altered during the measurement R₁, R₂, being the resistances of AP₁ and AP₂, we have E₁/E₂ = R₁/R₂.

To eliminate the effect of any small change which may have occurred in E, reverse the switch again, putting K and K₁ into connection, and observe a second position P₁' for P₁; the two will differ very slightly if the apparatus be correctly set up. Let R₁' be the corresponding value of R₁; the mean (R₁+R₁')/2 will give a value Corrected for the assumed small alteration in E.

For the resistance AB a long thin wire is sometimes used. This is either stretched out straight or coiled in a screw-thread cut on a cylinder of some insulating material. Contact is made at P by means of a sliding piece of metal. If this plan be adopted, it is somewhat difficult to get sufficient resistance between A and B for very accurate work. It is preferable, if possible, to use resistance boxes. Since the resistance AB is to be kept the same throughout the observations, two boxes are necessary. One of these forms the portion AP, the other the portion PB, the point P being the junction of the two. Having settled the total resistance AB, plugs are taken out of the two boxes to make up this total. The required adjustment is then attained by taking plugs, as may be needed, out of the one box AP, and putting plugs of the same value into the other box PB, or vice versa by putting plugs into AP and removing them from PB. In this way the total resistance AB remains unchanged.

In order to ascertain if the measurement be possible with the three given batteries, it is best to begin by making AP large and noting the direction of the deflexion; then make it small; the deflexion should be in the opposite direction. If this be the case, a value can be found for the resistance AP, such that the deflexion will be zero.

Experiment - Compare by means of the last arrangement given above the E.M.F. of the two given batteries.

Enter results thus:

Battery used for main current, two Daniell cells.
E1 = E.M.F. of a Leclanché.
E2 = E.M.F. of a Daniell.
Total resistance of AB, 2000 ohms.
R1 = 1370 ohms
R2 = 1023 ohms
R1 = 1374 ohms
E1/E2 = 1.342