polarization is greater in the combination of zinc and copper than in that of zinc and iron.

This galvanic polarization we will consider hereafter more at length; it is only mentioned here so far as is necessary to show the course of Poggendorff's investigation.

If the values found by Ohm's method for the electro-motive force do not accord with the tensión series, the cause, as above remarked, is purely in the modification which the original electro-motive force undergoes by polarization. Poggendorff endeavored to determine the value of their original electro-motive force before it was modified by polarization. We will pass by the earlier efforts by which this object was but imperfectly attained, and turn to the consideration of a method which Poggendorff has published in volume LIV of his Annals, page 161.

This method differs essentially from all others, in that not the current of a battery, but only the tendency towards a current, is measured. To avoid polarization, Poggendorff endeavored to prevent the current from coming into action, and to compensate it beforehand by another whose electro-motive force was constant and known.

The arranging and establishing of this compensating method is described somewhat diffusely by Poggendorff, and on that account is not perfectly clear; hence I have departed from his mode of presentation, since it has been an object in this report to make it as intelligible as possible.

In Fig. 13, C represents a constant element-say a Grove's, and I

Fig. 13.

another voltaic element, whose electro-motive force is less than that of C. The positive poles of both are connected by a conductor, and likewise the negative. In the connexion of two poles of like name a multiplier m is inserted; the connexion of the other two poles can be broken at a at pleasure, and renewed again. The conducting wire a db closes the constant battery C.

Suppose the element I is precisely equal to C, and the connexion at a is made, this combination, then, is in fact nothing else than two elements so connected that they constitute a single element with a double surface; but, if the electro-motive force of I is weaker than that of C, the actions of the currents are somewhat more complicated.

Denote by

1, The resistance of the element C, together with the conductors between a and b.

', The resistance of the element I with the conductors between a and b, the resistance of the multiplier included.

r, The resistance of the conducting wire a db.

E, The electro-motive force of C.

E', The electro-motive force of I.

The current of the element C divides at a and b into two parts; one of which passes through the conductor by d, the other through I. The resistance to conduction of the one branch is r, that of the other

is ; hence the resistance of the two branches together is

the undivided current which C produces is

In this we neglect the electro-motive force in I.

l'r

The part of the entire current which passes through I is—

Er

l (l' + r) + l' r'

and

(1)

The entire current which I produces, and which is divided between the branches a Cb and a db,

is

The two currents (1) and (2) pass through the multiplier in opposite directions. Since the denominators of the values (1) and (2) are exactly equal, the multiplier evidently will stand at the zero point, if

For given values of E E' and I a value of r can always be found which will satisfy equation (3); that is, there is a certain length of the conducting wire a db with which the multiplier indicates no current, when the wire coming from a is brought in contact with one of the poles of C.

If the resistance r be too great, the multiplier will indicate a current in favor of C; on the contrary, the current of C in the multiplier will preponderate if the resistance r is too small.

If the resistance r in the wire a db is precisely such that the multiplier remains at zero when the circuit is closed at a, or when equation (3) is satisfied, we get from this equation the following:

We can thus compute the value of E'; that is, the electro-motive force of I, when E, the electro-motive force of C, is known, and also the values of resistance l and r.

The exact length of the wire a db cannot be attained at the first trial; in general by closing the circuit at a the needle of the multiplier will be deflected to one side or the other, according as the wire is too long or too short. By a few trials, shortening or lengthening the wire a d bas may be necessary, it is easy to find such a length thatthe galvanometer will indicate no current, or at most a very feeble one.

This is to be considered as a first approximation to the correct ratio between r and 7. The battery I should now be left open for a time, that it may lose all polarization; or, what would be better, the negative plate should be taken out of the liquid, cleaned, and then restored to its place. If a deflection occurs again on closing the circuit, the length of the wire a db must be regulated until the exact proportion is obtained. The current which the electro-motive force of the element I, unmodified by polarization, tends to generate, is compensated, and the value of E' can be computed by equation (4).

Poggendorff proved his method by ascertaining with it the electromotive force of constant elements, which could be determined in another manner, and found perfectly accordant results. He obtained, by Ohm's method

The electro-motive force of Grove's element...
The electro-motive force of Daniell's element....

25.886

= 15.435

The Grove's element was then placed at C, and the Daniell's at I, (Fig. 13.) was 35.03. The equilibrium, above mentioned, took 52.68. For this case we have—

place when r

which accords very well with the value of E', determined by Ohm's method.

Poggendorff now used this method for determining the original electro-motive force in constant batteries. That of Grove's battery, adopted as the standard of comparison, was found by Ohm's method to be equal to 22.88, and he found for the original force of an inconstant battery, made of

Zinc and copper........
Zinc and iron..

Iron and copper

.....

13.79

7.40

6.00

These results prove that the original electro-motive force of these combinations very nearly satisfy the law of the tension series, since that of copper and iron, and that of iron and zinc, is nearly equal to the electro-motive force of copper and zinc; thus, 7.4 +6=13.4, nearly equal to 13.79.

If the current of the zinc and iron battery is stronger than that of the zinc and copper, and if, according to Ohm's method, the electromotive force of the former combination is found greater than that of the latter, it is solely because the current of the zinc and copper combination generates a stronger polarization, acting against the original electro-motive force, than the current of the zinc and iron battery.

§ 14. Comparison of different voltaic combinations. In the last paragraph we have seen how the constants of a voltaic combination can be determined and expressed in comparable values. None of the statements of the effects of batteries, as they are ordinarily presented

for comparison, are satisfactory. The want of accurate numerical determinations occasions great uncertainty in regard to the advantages and disadvantages of different galvanic combinations. If such uncertainty exists in the accounts of men of science, it is not at all surprising to find communications in technical journals, which betray entire ignorance of the principles here discussed.

Let us now examine the most important of the galvanic combinations somewhat more closely.

§ 15. The simple zinc and copper battery.-The Wollaston battery is a convenient form of the simple zinc and copper combination, with one liquid.

The batteries of Young and Münch may be considered as variations of Wollaston's, and therefore a description of them is not necessary.

The simple zinc and copper battery, it is well known, is not constant, because the electro-motive force is considerably modified by the polarization of the copper plate, which takes place in consequence of the current. Poggendorff found, as we have seen, the electro-motive force of the zinc and copper battery in dilute sulphuric acid, before being modified by polarization, to be equal to 13.8, while the electromotive force of Grove's battery is equal to 22.9.

Assuming the electro-motive force of Grove's battery to be 830, referred to the chemical unit, (see table §9,) the unmodified electro-motive force of the zinc and copper battery would be 500 of the same unit. But according to my experiments, when the current commences, the electro-motive force of the zinc and copper combination is only 208; thus, by polarization, the force is very soon reduced to of its original value, and this is also the reason that immediately after immersion the current is exceedingly strong, but then very rapidly decreases. The polarization having once reached its maximum, the current remains tolerably constant at least, so much so as to admit of accurate measurement. The numbers from which the values previously given (§ 9) of electro-motive force and of resistance to conduction of Wollaston's battery were computed were not immediately observed, but are the means of numerous readings. To form a correct idea of the action of this battery, I will give here the corresponding series of observations entire:

On closing the battery, a few moments elapsed before the needle came to rest, from very rapid oscillation; and even after the oscillation had ceased it went back slowly, and was tolerably stationary at 26°, which is the first entry in the table. A copper wire was then inserted, of which resistance, by previous experiment, had been found equal to that of 7.2 metres of the normal wire. The needle came to rest at 12°, but after a short time went back to 11.5°.

The copper wire was then removed from the circuit, when the deflection was 24°, &c., &c.

The brass wire, which reduced the deflection to 5o, had a resistance equal to that of 29.2 metres of the normal wire.

Thus we see that the current of this element, after the first oscillation, remains tolerably constant-at least, so much so that approximately accurate estimates can be made for computing the electromotive force and resistance to conduction. While, on the one hand, the electro-motive force is considerably weakened by the current, on the other the resistance is not great, even with very weak acid. Where it is not important to make exact measurements, and when a steady current is not required for a long time, the zinc and copper battery may be advantageously applied to many galvanic experiments. If elements with large surfaces are necessary, the form of Hare's spiral is to be preferred.

The force of the polarization is dependent, most probably, upon the strength of the current, though accurate researches on this subject are yet wanting.

The reason why batteries with one liquid are not constant is to be sought in the polarization of the negative plate, and this is obviated as much as possible in the so-called constant battery. Yet the strength of the current of the constant battery gradually decreases, by leaving it closed for a long time, because the liquid gradually changes the dilute sulphuric acid becoming converted, by degrees, into a solution of sulphate of zinc. A corresponding change in the nature of the liquid takes place in all batteries, without exception, and it is only to be avoided by renewing the liquid from time to time. An arrangement might be so made that the heavy solution of sulphate of zinc would flow off slowly from the lower part of the vessel, and the fresh acid flow in above at the same rate.

A circumstance which acts quite injuriously in all batteries without porous partitions is, that, in consequence of the current, the sulphate of zinc solution is decomposed, and metallic zinc deposited on the negative plate, whence, during a protracted action of the battery, its electro-motive force must decrease more and more.

The constancy of the battery current depends essentially upon its strength. Feeble currents, like those obtained by using very dilute acid, and with great resistance included in the circuit, remain constant for some time; while, by using stronger acid and less resistance, the strength of the current must necessarily decrease far more rapidly. Hence, if it be desired to compare different batteries, with reference to their constancy, equal resistance and like acid must be used. Negect of these conditions may have been the occasion of numerous rrors in regard to the constancy of single batteries.