50 ELECTRICITY [ELECTKJC CURRENT. to a common temperature, were, for the H 2 S0 4 , 141-73, 141-64, 141-52, 141-53, 141 55, and, for the NaCl, , l 366-27, 366-23, 366-25, 366-21 Siemens units, with the driving weights 5, 7 5, 10, 15, 20 kgr. respectively. (2) The resistance of a solution of zinc sulphate was found, first, in Beetz s manner with constant current and amalgamated zinc electrodes ; secondly, using alternating currents and the same electrodes as before ; thirdly, with alternating currents and the platinized electrodes; the three results reduced to a common temperature gave 53 7 49, 537 41, 537*20. The greatest divergence from the mean might have been caused by an error of -^ degree in the temperature measurement. The agreement may therefore be pronounced complete. We think that it must be con ceded that the experimental methods just described have solved in a satisfactory manner the problems involved in the determination of electrolytic resistance. We have dwelt on them so long partly because nearly all the in formation on the subject we possess has been obtained by their means, and partly because they present points of great theoretical interest. Another method has been employed by Ewing and Macgregor. 2 The electrolyte was inclosed in a narrow tube with wide ends, in which were set platinum electrodes. This arrangement was inserted in a Wheatstone s bridge, and its resistance measured in the usual way. The precautions against polarization consisted in operating with currents of very short duration, sent through the bridge by means of a "rocker" worked by hand ; the resistances in the arms of the bridge were also made large, in order to reduce the rate of polarization as much as possible ; another essential feature of the method is the use of a " dead beat" galvanometer with a mirror of very small moment of inertia. The paper of Ewing and Macgregor has formed the subject of a somewhat bitter criticism by Beetz, 3 to which Macgregor has replied. 4 Battery Battery Resistance. If the electromotive force and iti- resist- ternal resistance of a battery in action were the same, ancet whatever the external resistance, there would bs no diffi culty in finding the internal resistance by Ohm s method. We have simply to give two different values to the external resistance, and measure the current in the two cases. The electromotive force does not appear in the ratio of the two current measures; hence, knowing this ratio, we can find the internal resistance. Or we may use an electrometer, and measure the difference of potentials between the two poles of the battery, first, when the external resistance is infinite, secondly, when the external resistance is R. Then, if r be the internal resistance, the ratio of the first electrometer ing reading to the second is = , by Ohm s law ; hence r can be found. Difficul- Unfortunately, however, the electromotive force of a ties in battery is not independent of the external resistance. In
- " general, when a battery is circuited through a small resis
tance, its electromotive force is much smaller than when the external resistance is very great. This arises from the polarization set up by the passage through the battery of its own current, and possibly in some degree from other causes as well. There is also reason to believe that the internal resistance of the battery is a function of the cur rent. This being so, it is clear that a theoretically satisfac tory determination of battery resistance cannot be arrived at by such methods as we have described. Since, however, the increase of the electromotive force is very slow after the external resistance has reached a certain value, and since the alteration of the internal resistance takes some time, we can get in many cases measurements sufficiently accarate for practical purposes. A variety of methods have been devised with this object, and applied mostly to the so-called constant batteries. It must be remembered, however, that there is something indefinite in the term in- 1 No observation made for NaCl in the first case.
- Tratis. K.S.E,, 1373. _ Pogg, Ann., cliv. 4 Proc. R.S.K, 1875.
ternal resistance, unless the circumstances be given under which it is found. In the method of Von Waltenhofen, the battery is " compensated " by another battery so ar ranged that no current passes through it ; and then this arrangement is slightly altered, so that a very small current passes through the battery. This amounts to finding the internal resistance for very small currents. The method of Beetz also involves the principle of compensation ; two batteries are used, but the one whose resistance is to be found is compensator and not compensated. The circuit of the compensator is joined for an instant, and then the compensated battery is thrown in. The assumption in the method is that the electromotive force is the same in the first instant whether the battery is closed through a resistance R or a resistance R . The results seem to justify the assumption, and to establish the practical value of the method ; but there are clearly limits to its application which it would not be very easy to define. Beetz himself shows that the electromotive force of a battery is greater when it is compensated than when it is compensating. A similar objection may be urged against the method of Siemens, which again gives good results when properly used. We refer the reader interested in this matter to the sources of information already quoted (see Historical Sketch), and content ourselves with an accountof Mance s method, which, Manci although subject to the same objection as all the others, is m ethc very convenient for rough purposes, and is much employed in this country. Let A, 13, C, D be four resistances arranged in circuit, B being the battery whose resistance is required. Insert a galvanometer between AB and CD, and a circuit which can be closed and opened by means of a key between AD and BO. We thus have an ordinary Wheat- stone s bridge, with a key in place of a battery, and a battery in. place of the ordinary resistance to be measured. Owing to the pre sence of the battery, there will be a current through the galvano meter, which will deflect the needle ; this deflection is compensated by means of a magnet, and the needle brought back to zero. Then the resistances A, C, D are arranged so that tlie galvanometer is not affected when the key circuit is opened or closed; when this is so the key and galvanometer circuits are conjugate, and we have AC- BD = 0, from which we can find B, since A, C, D are known. In practice, however, it is impossible in the great majority of cases to fulfil the direction printed in italics. Suppose for a moment we had arranged the resistances so that AC - BD is very nearly but not quite zero, and suppose we close the key circuit, which had been formerly open, then, since this is not conjugate to the battery circuit, the external resistance opposing the battery is reduced ; hence its electromotive force falls, the current through the galvanometer is altered, and the deflection of the needle alters. At the same time there is a current owing to the fact that AC - BD is not exactly zero. These two effects may either conspire or oppose each other. No data, so far as we know, have been obtained which would enable us to tell how quickly this fall in the electromotive force of any given battery comes on. In practice we see a sudden jerk of the galvanometer, and then a slow swing. The former is due to the deviation of the bridge from balance, and the latter to the alteration of the electromotive force. It is easy to decide which is which, for the direction of the former can be changed by making AC - BD positive or negative, while the direction of the latter is not affected in this way. This disturbing effect is very great with one-fluid batteries ; it would, for instance^ be a hopeless undertaking to measure in this way the resistance of a cell of Smee while sending a large current. The effect is not so great with a Daniell s cell, and can be reduced ad libitum, by intro ducing metallic resistance into the battery circuit. The effect having been thus reduced within reasonable limits, we operate thus: Arrange the bridge until the deflection owing to deviation from balancers opposite to that due to the change in the electromotivo force; then, by gradual adjustment, work down the initial jerk to nothing, so that the needle appears to start off on its slow swing without any perceptible struggle. When this state of matters is AC reached, there is a balance, and B = - . Then subtracting from B D the resistance put into the battery circuit, we get the resistance of the battery. Of course this does not solve the problem of finding tho resistance of any battery sending any current ; but we believe that as much can be done in this way as in any other. Various modifi cations of Mance s method have lately been proposed, but their practical advantages over the original method have scarcely as jet
been established.