The value 21 of the resistance of the Daniell element for one square decimetre of mean surface, refers to the case in which the zinc cylinder is immersed in a mixture of one part sulphuric acid to ten parts

water.

The numbers given for the Stöhrer element refer to the same liquid, and the number opposite b to Leipsic cells; that opposite c to red clay cells. The resistance of Daniell's battery holds good for the same strength of sulphuric acid, and for red cells.

With equal surface and like liquid, the resistance of the Deleuil element a is to the Stöhrer element as 21 12; thus the discrepancy is purely in the dissimilarity of the clay cells.

By using red clay cells (c) instead of white, (b,) the resistance to conduction is increased in the ratio of 12: 43, or 3.6 times greater. Thus it may be expected, that, by using Leipsic clay cells, the resistance of the zinc and copper battery will be 3.6 times less than by using earthen cells, or for one square decimetre of mean surface, 78_

3.6

=21.6.

The Wollaston element was immersed in a liquid composed of one part sulphuric acid to twenty parts water. When one square decimetre of zinc was used, the mean resistance was 6.8. But since each surface of the zinc is effective, 6.8 is the resistance for an effective zinc surface of two square decimetres; thus, for one square decimetre the resistance is 13.6; for stronger acids the resistance would naturally decrease considerably.

§ 10. Electro-motive force.-By means of the two equations, (1) and (2), the resistance R of the element, as well as the electro-motive force E, can be computed. From the measurements already given above, we get the values of the electro-motive force of the zinc and carbon batteries of Stöhrer and Deleuil, and of the zinc and copper batteries, as they are presented in the tables under E, namely: For the zinc and carbon battery of Deleuil

The values of the electro-motive force of one and the same battery are very nearly equal, although the nature of the liquid, and with it the resistance to conduction, may change. In fact, the electro-motive force of the Stöhrer zinc and carbon battery differs only 0.1 part from the force of that constructed by Deleuil. This fact has already been mentioned more at length above.

It is now to be explained what we are to understand by these numbers. The electro-motive force is that force which sets the current in motion. We can of course measure this force, as well as that of the current, by its effects.

The electro-motive force of the voltaic pile is proportional to the electrical tension of the pole in the open circuit; we could, therefore, apply this tension as a measure of the electro-motive force, if the electrical tension were not so very small at the poles that it cannot be determined with much accuracy in batteries of a few pair of plates or elements. But Ohm's law teaches us that the force of the current of the closed battery is also proportional to the electro-motive force; and since the power of the current can be measured with great accuracy and reduced to a definitive unit, it is better to use the force of the current as a measure of the electro-motive force. We have

E
S=
W

in which W denotes the entire resistance which the current has to overcome; when W = 1, we have

S = E.

E is here the force of the current which the battery would give if the resistance to conduction were 1. In establishing our units of force of current and resistance, let us consider the value of electro-motive force, or the value of E, as the quantity of detonating gas which the current of a battery would give if the whole resistance were equal to the resistance of a copper wire 1 metre long and 1 millimetre thick; thus if we have found the electromotive force E of Daniell's zinc and copper battery to be 470, it means that the current of Daniell's battery would give 470 cubic centimetres of detonating gas per minute if the sum of all resistance were equal to the above-mentioned unit of resistance.

I consider it a great advantage of the chemical unit of force of current recommended above (= that current which yields one cubic centimetre of detonating gas per minute) that in adopting it the values of the electro-motive force are not barely proportional numbers, but that each has for itself a perfectly distinct and easily comprehended signification.

Although Jacobi was the first, to my knowledge, to attempt the reduction of the data of the galvanometer to the chemical effect, he did not make any further use of this chemical unit of the force of the current-that is, he did not apply it to the computation of the electro-motive force.

§ 11. The electro-motive force is proportional to the tension of the open circuit. It has been already mentioned that the electrical tension at the poles of an open battery may be considered as a measure of the elec

tro-motive force. The correctness of this assumption has been tacitly received by most physicists, although a direct experimental confirmation had not been attempted on account of the imperfection of the apparatus. Kohlrausch has at length supplied this omission. He converted the exceedingly sensitive electrometer of Dellman into a measuring instrument of great accuracy. By combining this instrument with a condenser (Pog. Ann. LXXV, 88) he succeeded in determining the electroscopic tension at the poles of an open, simple battery, with such exactness that there can be no longer any doubt of the correctness of the above-mentioned principle.

Kohlrausch has, at the same time, proved by this investigation that Dellman's electroscope, as it comes from his hands, is adapted to the most delicate electrical researches. For a more detailed description of the instrument and its use, we refer the reader to the excellent treatise already cited. The comparison of the electromotive force with the tension of an open battery may be found in a third memoir in volume LXXV of Poggendorff's Annalen, page 220. To render the results of this investigation comprehensible, we must first give the modus operandi more fully by which the values of the electroscopic tension can be derived from the measurements made by the instrument.

Kohlrausch's electrometer can be used as a measuring instrument in two ways, namely:

1. By placing the upper divided circle, which we shall term the torsion circle, at 90°, the movable needle will form an angle of 90° with the fixed metal strip. The needle and strip are now brought into communication, the electricity to be measured communicated to them, and then the connexion between needle and strip broken. The torsion circle being now turned back to 0, the needle will form an arc with the strip as much greater as the electrical charge is stronger.

The electrical charge which produces a deflection of 10 being denoted by 1, the strength of the electrical charge belonging to each angle of deflection can be determined. For the details of this computation I refer the reader to Kohlrausch's memoir in volume LXXII of Pogg's Ann. On page 385 he gives a table, indicating the corresponding electrical tension for each angle of deflection, which holds good, of course, only for his own instrument. For clearer comprehension of the matter we will present an extract from this table ;

Thus if the charge which produces 10° of deflection be denoted by 1, the electrical charges, which produce 40°, 60°, and 80°, are respectively equal to 4.39, 8.30, and 18.33.

Kohlrausch's table gives results for whole degrees.

2. The instrument can be applied in a second manner for measuring electrical charges. If after placing the needle and strip at right angles, both being in communication, electricity is imparted and the connexion then broken, we are able, by turning the torsion circle, to make the angle of deflection a constant quantity, say 30°. According to well known principles the electrical charge is then also proportional to the square root of the torsion necessary to maintain the needle at the deflection of 30°.

Fig. 10.

Kohlrausch determined the tension at the poles of different simple batteries by both methods; the batteries being arranged as follows: The two metals were soldered together; one was immersed in the liquid of the vessel A, (Fig. 10,) the other in the liquid of the vessel B; in each vessel a brass wire was placed, forming the poles. One of the wires was connected with the ground, the other with the collector-plate of a condensing apparatus. The tension of the positive as well as of the negative pole was determined for each battery by many experiments, and the mean of all taken.

100

A B

The electro-motive force of the different galvanic elements Kohlrausch determined according to Wheatstone's method, which will presently be mentioned. The following table contains the results of his measurement:

1. Zinc in sulphate of zinc; platinum in nitric acid of density 1.357....

2. Zinc in sulphate of zinc; the nitric acid of 1. 213 sp. gr..
3. Zinc in sulphate of zinc; carbon in nitric acid of 1. 213 sp. gr.
4. Zinc in sulphate of zinc; copper in sulphate of copper-
5. a. Silver in cyanide of potassium-common salt; copper in
sulphate of copper..

b. The same, later.

c. The same, still later

12.35

12.36

12.26

The tension of the open battery is determined by the above-described methods. The numbers under I and II were obtained by the first and second methods respectively.

Since the square roots of the torsions, as well as the numbers of the table on page 385 of volume LXXII of Pogg. Ann., denoting the tensions corresponding to the different angles of deflection, and also the number expressing the electro-motive force, are all measured by different units, Kohlrausch, in order to make the data comparable,

has multiplied the roots of the torsions by 1.0239, the values determined by the angle of deflection by 1.8136, by which means the results by the first experiment are rendered perfectly accordant. But since the rest of the corresponding numbers accord very closely, these experimental series prove that the electro-motive force is proportional to the electroscopic tension at the poles of the open battery.

This principle might be proved with less sensitive electrometers, by determining the tension at the poles of a battery of 30, 40, or more, elements.

Kohlrausch's instrument is also very well adapted to solve a disputed theoretical question, to which allusion has been made above. If a strip of zinc and one of platinum be immersed in a vessel of water without touching each other, according to Schönbein's view, the upper end of the zinc must indicate free negative electricity-the upper end of the platinum, free positive; while according to the contact theory the reverse should be the case. It is very desirable that Kohlrausch himself should investigate this, because he not only possesses an excellent instrument of the kind, but has attained great skill in manipulating with the apparatus.

§ 12. Indirect methods for determining the constants of the battery.The process given above, derived from formulas (1) and (2), for determining the resistance and electro-motive force of a galvanic battery, and that for determining the constants, which we will call Ohm's method, is as simple as it is accurate, if a suitable measuring apparatus is furnished, and a battery sufficiently constant be used. Both, however, were wanting at the time of the publication of Ohm's law, and it thus happened that complicated methods had to be used to obtain only tolerably accordant results. By degrees only, simplicity was attained in this instance, as is often the case in the history of physics.

First, there was wanting an instrument adapted to measuring the force of current; then the multipliers used were objectionable in two particulars: they were suited for weak currents only, and there was no simple law, showing the relation of the angle of deflection and the force of the current.

Several physicists have proposed very ingenious methods for graduating a galvanometer; that is, to determine empirically what relation the different degrees of deflection have to the force of current; yet since they do not appear to be very well adapted for general use, and only yield useful results in the hands of skilful experimenters, I may be pardoned for not going into the details of these methods of graduating. The method which Poggendorff has given for converting the galvanometer into a measuring instrument, is found in volume LVI of his Annalen, page 324. There is also in this paper a short collection of the methods recommended by other physicists for the same purpose, with indications of the sources, to which I must refer those who wish to enter into the details of this subject.

Fechner did not use the deflection of the needle for determining the force of current, but the period of oscillation of the needle about its position of equilibrium, for the case in which the coils of the multiplier are parallel to this position.