A dilute solution of sulphate of zinc........... ...0.0223 ....0.0263 Hankel has published a more extensive series of experiments on this subject, (Pog. Ann., LXIX, 255.) He found the resistance of a concentrated solution of sulphate of copper (A) of the spec. grav. 1.17, at different temperatures, as follows: The resistance of 108.7 parts of the former solution (A) with 185 parts was, at 00 11 25 67.4 22.87 15.16 10.5 7.1 The resistance of a concentrated solution of nitrate of copper was, at The resistance of a concentrated solution (B) of sulphate of zinc was, at The resistance of a mixture of 71 parts of the solution (B) and 118 parts water was, at The unit to which these resistances were referred was arbitrary.. The construction of the vessel holding the liquids used in these experiments cannot be clearly understood from Hankel's description. On considering the result, we find that the decrease of resistance is not proportional to the increase of temperature, as Becquerel supposes. For the concentrated solution of sulphate of copper, we have on an. average the following for a rise of one degree of temperature: Thus for a given difference of temperature, the corresponding change in the resistance of the liquids is greater, the lower the temperature. § 34. Galvanic polarization varies with the magnitude of the force of the current. Many physicists, and among others Lenz, (Pog. Ann., LIX, 234,) have expressed the opinion that the electro-motive opposing force of a voltameter is independent of the strength of the current. In Daniell's memoir, mentioned above, (Pogg. Ann., LX, 387,) this opinion is adopted, and the attempt is made to establish it by a series of experiments with the voltameter. These measurements, however, are not exact enough for this purpose. Wheatstone also entertains this opinion, and is thereby led to a further false conclusion. He determined the electro-motive force of a battery of three Daniell's elements, then the electro-motive opposing force in a voltameter, which was inserted in the closing arc of the same battery. He found E=90 e = 69. E When batteries of four, five, and six elements were used, almost exactly the same value for e was found; hence Wheatstone inferred that the electro-motive opposing force may be considered as constant. E is here the electro-motive force of three combined cups, consequently the electro-motive force of one cup is 30, a value less than e. Wheatstone thinks that the phenomenon may be explained by supposing that a single element cannot effect the decomposition of water in a voltameter. 3 But this is erroneous. The electro-motive opposing force can never become stronger than the original cause which produces it; hence we must suppose that the electro-motive oppposing force is dependent upon the strength of the current. But then the current of a single element can certainly decompose water, though at a very small rate. For instance, when a voltameter was inserted in the closing arc of a Daniell's element, its plates being about two square inches, I obtained a very sensible development of gas. That the electro-motive opposing force in a voltameter actually depends upon the strength of the current, appears very strikingly in a series of experiments which I made for this purpose. As already mentioned above, I found the electro-motive force of a battery of six zinc and carbon elements to be E=4422, and the electro-motive opposing force, e = 1000. 737, The electro-motive force of each single element was 442 = thus decidedly less than the electro-motive opposing force in the voltameter. The electro-motive force of a battery of four such elements (zinc and carbon) was next determined; the result was E3124. After inserting the voltameter the electro-motive force was only E1= 2427; hence, e EE' 700. Here, with a weaker current, the electro-motive opposing force appeared sensibly less; indeed, in this case it is less than the electromotive force of an element. For a battery of two elements the result was No claim to great accuracy is made for the numbers just given, but that which is placed beyond doubt by them is what might have been foreseen; the electro-motive opposing force becomes gradually less with the decrease of the strength of the current. Hence it is a function of the current, though the force of this function must be determined by more accurate experiments. That the magnitude of the electro-motive opposing force is dependent on the strength of the current was first placed beyond doubt by Poggendorff.-(P. A., LXI, 613.) Buff also (P. A., LXIII, 497) found the electro-motive opposing force of a voltameter greater with the current of three zinc and carbon elements than with that of only two; he found, moreover, the magnitude of the polarization diminished by the insertion of a greater length of wire in the closing arc. Fig. 27. For the case in which the electrodes fill up the whole section of a trough like that of Fig. 27, the polarization appeared somewhat greater, according to Buff, when the decomposing cell is less full. If the electrodes are suspended in the surrounding liquid, without filling the whole section, the size of the electrodes has no influence on the magnitude of the polarization. § 35. Numerical determination of polarization.--Lenz and Saweljev have instituted a large series of experiments for determining galvanic polarization in different cases. (Bull, de la Classe Phys. Math. de l'acad. de Sci. de St. Peters, b. T. V., p. 1; P. A., LXVII, 497.) The process which they used to determine the magnitude of polarization in a decomposing cell was that of Wheatstone, viz: by determining the electro-motive force of a battery, first with metallic closing conductors, and afterwards with the decomposing cell inserted. The dif ference of these two numbers, gives the magnitude of the electromotive opposing force produced by the polarization in the decomposing cell. The following example will explain the mode of observing. To reduce the deflection of the compass-needle from 20° to 10° the following must be inserted: By this method the following values were found for the galvanic polarization of different decomposing cells: Copper-plates in sulphate of copper.. Amalgamated zinc plates in nitric acid.. 0.07 0.03 0,01 These experiments prove that polarization disappears when the escape of gas ceases at the electrodes; in all three cases no oxygen appeared at the positive electrode, because it oxidized the metal immediately on its evolution from the water; the escape of hydrogen at the negative electrode was prevented in the first case by attracting in its nascent state the oxygen from the oxide of copper, and precipitating metallic copper; in the other two cases the nascent hydrogen was immediately oxidized by the nitric acid. Thus here, where the electrodes are not covered with a stratum of gas, polarization does not take place; the small numerical values given above are not due to the polarization of the electrodes, but to the fact that they do not remain in the same state-one plate being attacked and the other not, and thus the pair of plates itself becomes a feeble electro-motor. Buff also (P. A., LXXIII, 497) found the polarization for copper plates in sulphate of copper, and for zinc plates in sulphate of zinc, very small. Lenz and Saweljev found further for the polarization of Platinum plates in nitric acid..... 2.48 5.46 1.00 2.15 1.45 0.33 1.26 Graphite in concentrated......". These numerical values are mostly the mean results of a number of experiments. In the first case, that of platinum plates in nitric acid, there is no escape of hydrogen at the negative electrode-the polarization shown in the value 2.48 is thus to be ascribed entirely to that at the positive electrode, where oxygen appears; 2.48 is consequently the magnitude of the polarization which a platinum plate receives from oxygen. In the second case, that of platinum plates in sulphuric acid, development of gas takes place at both electrodes; therefore 5.46 is the * Composed of 6 vols. of concentrated SO3 + 100 of water. sum of the polarization of both plates; the polarization of platinum by oxygen being 2.48; that of the same metal by hydrogen is 5.46 2.48 2.98, or nearly 3. In the four succeeding cases, (zinc, copper, tin, and iron, in sulphuric acid,) the positive electrode is attacked, and therefore the corresponding numerical values are those of the polarization of these metals by hydrogen. Arranging these results, we have for the polarization of If we introduce into the closing circuit of a battery a decomposing cell of unlike plates, this itself will act as an electro-motor, and the effect of its force will, according to circumstances, either favor or oppose the polarization. Suppose the electro-motive force of the decomposing cell, as well as its polarization, to oppose the electro-motive force of the battery, then the difference D obtained from the measurements of the electro-motive force of the battery, with and without the decomposing cell in the circuit, will be the sum of the electro-motive force of the decomposing cell, and of the polarization, or De + p; denoting by e the electro-motive force of the decomposing cell, and by p the polarization taking place in it. If we have determine the value of D for differently constructed decomposing cells, (say, for example, consisting of platinum in nitric acid, and zinc in sulphuric acid, platinum in nitric acid, and copper in a potash solution,) we can compute for these combinations the value of e by deducting the respective values of p. In this manner Lenz and Saweljev ascertained the electro-motive force of the following combinations: Platinum in nitric acid, combined with |