unshielded value. The other terms are reduced to 1/61st, 1/101st, 1/141st, &c., parts of their unshielded values.

2n

In this case the potential inside is very little less than when there was no iron, A1 being-A/a," for all values of t until t is small; of course A1 is 0 when t is 0.

It is easy to extend the reasoning to several enveloping cylinders of iron, or to the case of any distribution of inducing potential which does not vary in a direction parallel to the axis.

XXXI. The Clark Cell when Producing a Current. By S. SKINNER, M.A., Lecturer at Clare College, and Demonstrator at the Cavendish Laboratory, Cambridge*.

THE A

§ 1. Introduction.

HE electromotive force of the Clark cell when not producing any current has been frequently determined, and has been found to be of so constant a value that it is now used as a standard. These values of E.M.F. are for the cell when its poles are not united by a conductor. In the following ar account is given of a series of experiments made on cell when producing currents, with the view of ascertaining, (1) how far the total electromotive force round the circuit differs from that of the open cell, and (2) how this new value for the E.M.F. changes when the current is maintained. If these quantities can be accurately measured, it follows that a cell might be used for producing currents of known value. Some experiments have been made on subject (2) by Threlfall and Pollock (Phil. Mag. November 1889), and their results are compared with mine in Sect. 8.

§ 2. The Cells.

The experiments were made on three cells, all much larger than the ordinary Board-of-Trade pattern of Clark cell.

Cell B, made July 1891, is the cell no. 90 described on p. 558 of the paper by Mr. Glazebrook and the author, Phil. Trans. 1892, A. The area of its exposed zinc surface is approximately 14-4 square centimetres.

Cell L, made November 1892, is a much larger cell fitted up in a cylindrical jar 22 centim. high and 13 centim. in diameter. The zinc plate exposes an area of about 95 square

centimetres.

Cell N, made July 1893, is intermediate in size and exposes about 29 square centimetres of zinc surface.

* Communicated by the Physical Society: read June 22, 1894.

In all three cells the zinc plate, a piece of common zinc sheet, is placed horizontally, and they have the same E.M.F. within 2 parts in 5000.

§3. The Effect of Uniting the Poles of a Cell.

rE

Let a cell of electromotive force E and internal resistance R have its poles joined by a wire of resistance r; then, providing R and rare constant, and there is no polarization, the potential-difference between the poles will be however, there is polarization, then this potential-difference where e is the value of the electromotive force

will be

re

R+r'

required to produce the observed current.

R+r

If,

The value of (E—e) is the electromotive force of polarization.

re

In the large Clark cells described above E and e are nearly equal when the current is not larger than 01 ampere ; this small difference is the subject of the following measurements. To obtain it, it is clearly necessary to find the value of the potential-difference and of the resistances R and r. The measurements for R are contained in Sect. 4 ; γ consisted of thick wire coils or of a special wire resistance immersed in a large tank of paraffin oil; and the measurements of the potential-differences are contained in Sect. 6.

R+r'

We shall now give an illustration, taken from an actual experiment, of what happens when the poles of a cell are united. On July 25th the cell L had an electromotive force, with its poles open, represented by 5009 on the compensator. The poles were then joined by a resistance of 1000 legal ohms, and their potential-difference, taken as quickly as possible, was then rather more than 4983 and rather less than 4984. Then a resistance of 500 legal ohms was substituted for the 1000; the potential-difference fell to 4959. Next, with 200 legal ohms the potential-difference was 4885. Lastly, the poles were opened, and the electromotive force of the cell was found to be 5009.

It is seen from these numbers that the cell recovered its electromotive force entirely after the various operations, and this is a typical instance of the behaviour of the cells. It should be mentioned here that these tests, as well as tests on two other cells, were made in the interval between the two sets of resistance observations recorded in the column of the table §4, headed "July 25th, Before After."

§4. Measurement of the Internal Resistance of the Cells. The important determination of the resistance of the cells was made by the method of Opposition, and by the use of an Alternating Current. By opposing any two of the cells, the resulting electromotive force was so small that, making them an arm in a Wheatstone's arrangement, there was no deflexion in the bridge-galvanometer. The bridge was fed with an alternating intermittent current by means of the commutator used by Mr. T. C. Fitzpatrick in his electrolytic measurements, B. A. Report, 1886, p. 328.

In this method the commutator is arranged to supply the currents in the galvanometer-circuit always in the same direction, so that an ordinary sensitive mirror-galvanometer can be used. The drum of the commutator has on each circular face eight insulated sectors of brass, those on one side being larger than those on the other. The larger sectors are connected by brushes to the battery-circuit, and the smaller to the galvanometer-circuit. They are arranged so that the battery connexion is always closed before that of the galvanometer, and is always broken after that of the galvanometer. A more complete description of the commutator, which works excellently, will be found in the paper already mentioned. Two or three Leclanché cells were used as the battery.

The method of connecting two cells together so as to have small resulting electromotive force is particularly applicable in the case of Clark cells, for they may be obtained of nearly equal electromotive force. In the case of the cells we are discussing, as mentioned in § 2, the greatest difference was never more than 2 in 5000.

The errors to which this method of measuring batteryresistance is liable are two: first, from self-induction, and second, from polarization at the electrodes. The only conductor containing self-induction of any magnitude is the galvanometer-coil, and as the method is a zero method this does not matter. The second error is eliminated by using an alternating current. However, following Fitzpatrick's method, tests were specially made for polarization by varying the ratio of the arms and by varying the speed of the commutator. For instance, on one occasion the resistance was between 11.0 and 11.1 with the usual speed for working; when the speed was more than doubled, the resistance retained the same value.

The three cells were measured in pairs, and the results in legal ohms are given in the following table, where C is the resistance of the connecting wires.

The words "Before," "After," refer to the relation of these measurements to those recorded in § 6.

L

N

B

From which are calculated the following values of resistance :

The temperatures are those of the water-bath in which the. cells stood; the cells were not moved during the whole of the measurements. It will be noticed that the resistance of the cells is lower at high than at low temperature. This agrees with the fact that electrolytes decrease in resistance with increase of temperature.

§ 5. The Resistances, and Apparatus for Comparison of

Electromotive Forces.

The compensating apparatus was the same as that described in §8 of the paper by Mr. Glazebrook and the author already quoted. However, in the place of the Leclanché cells there described to produce the main current, I used one or two large Clark cells. The reason for this change arose from the irregular behaviour of the Leclanché cells, when changes were made in the amount of current taken from them. The results of eleven series of observations were rendered useless on this account. When only one Clark was used in the main circuit, the standard cell for reference was a Helmholtz mercurous-chloride cell, $7. When two Clark cells were used, the standard was some other Clark cell which was kept at rest.

The circuits, through which the currents from the cells under test were taken, consisted of thick wire coils from a legal ohm resistance-box for the values 1000, 500, 200 legal ohms, and of a german-silver wire of 147 legal ohms wound on an ebonite frame, which was placed in a tank of paraffin oil. This german-silver wire was always used when the current was maintained for any length of time, as from its construction its temperature could be very accurately observed.

§ 6. Determination of the Electromotive Force of

Polarization.

By means of the method described in §5 the results in the following table were obtained. The units of electromotive

The simplest way to examine these results will be to calculate the electromotive force required to produce the observed current, when the cells are producing currents of different values. Using, then, the equation

with values of R from § 4 and of r from § 5, we have the following values of e:

From which we obtain the values for E-e, the electro

motive force of polarization being — (E—e).