46 ELECT 11 ICI T Y [ELECTRIC CURRENT. KL is a platinum -iridmm wire, DK and HL are stout copper terminals to which it is soldered, DAE, EGF, FBH are stout copper pieces with binding screws and terminals for mercury cups, by means of which resistances R,T,U,S can be inserted at D,E,F,H. A, B, and G are binding screws for the battery wires and one end of the galvanometer wire. The other end of the galvanometer wire is screwed to a spring contact piece fixed to a sliding block at P ; when the button of this block is depressed, contact is made with KL, at a spot which is definite to an eighth or tenth of a millimetre. Platinum indium is chosen for KL, because it is hard and tough, not liable to be scratched or abraded by the con tact piece, does not oxidize or amalgamate with mercury, and changes very slightly in resistance when the temperature alters. The wire must be calibrated to find what correction, if any, must be applied for variation of resistance per unit of length at different parts ; for methods of doing this see Matthiessen and Hockin ; Brit. Assoc. Reports on Electrical Standards, p. 117 ; or Foster, Journ. of Society of Telegraphic Engineers, 1874. Foster s Kirchhoff s arrangement may be used in the ordinary method. V r av after we have made special experiments to determine the resistance of the connections, &c. Professor Foster (I.e.) has given a very useful method, by which the differ ence of two resistances can be got independently of the resistances of the connections. Suppose we wish to find the difference between R and S, which we suppose so near each other that, with the arms T and U approximately equal, there will be a balance when P is somewhere on KL. Let the reading for the position of the block be x, taken from left to right. Interchange R and S, balance again, and let the new reading be x (we suppose the difference between R and S so small that P is still on KL); then, if p. be the resistance of unit length of KL, R - S = fi(x - x). For, if a represent the resistance of the connections in DK, the same for the other end of the wire, and if T and U include the resistance of the invariable connections, then we have n + a+ux T where l~ length of KL. Hence Similarly therefore Methods of Mat- t.hiessen and Hoc- kin and of Sir W. Thom son. If we have to find the resistance of a thick cylindrical body, what is really wanted is the ratio of the current strength to the difference of potential between the two ends, when the current flows parallel to the axis at every point. The last condition is not generally fulfilled. It is obviously not so in the case where the cylinder is joined up with a thin wire. In cases where we wish to compare the specific resistance of two metals which we possess in cylindrical pieces, we get over the difficulty by observing the potential at a point at some distance from the end of the piece, where the flux is parallel to the axis at all points of the section. Matthiessen and Hockin used the following method for this pur pose (fig. 25). The two pieces XZ, YZ are soldered together and con nected in circuit with two resistance coils A / - 1*- and 0, and a graduated wire Pit as before. S, S are two sharp edges, at a measured distance apart, fixed in a piece of ebonite or hard dry wood, and connected with mercury cups. T, T is a similar arrangement for YZ. The galvanometer is inserted between S and Q, and the position of Q is found for balance ; then the terminal is shifted to S , and if necessary the resistances A and C altered, so as to keep their sum constant, until balance is again found. The same is done for T and T. Then, XS denoting the resistance between X and S, and A u Cj the values of A and C in the first case, and so on, we have Fl - where Hence Similarly Therefore XY XY XY This gives us the ratio of the resistances between SS and TT. The nlethod does not depend for its success on the goodness of the contacts at SS , &c. Another ingenious arrangement for effecting a similar purpose is due to Thomson, and will be found described in Maxwell, vol. i. 351. In measuring very large resistances, such as the insula- Resis tion resistance of a telegraph cable, it is convenient to use ance the quadrant electrometer. One end of the cable is con- nected with one electrode of a condenser, the other end with of the cable is insulated, and the other electrode of electi the condenser put to earth. The condenser is charged, met(;1 and the difference of potential between its electrodes measured by means of the electrometer. If E 1S E 2 be the value of the difference at the beginning and end of. an interval of t seconds, and if S be the capacity of the condenser in electromagnetic measure, then the resistance of the cable is in electromagnetic measure. If the condenser itself leaks, we must determine its resistance by insulating the electrodes and operating as before. Then, regarding the circuit in the first experiment as a multiple arc, composed of the insulation of cable and the dielectric of condenser, the true conductivity of the cable envelope is the difference of the conductivities obtained in the two cases. Several other methods might be used to compare metallic resisistance but they are of small importance compared with those we have now been describing. The reader who desires information concerning the ap plication of Ohm s law to condustors other than linear will find the sources sufficiently indicated in Wiedemann s Galvanismus; some of them have been alluded to in the Historical Sketch. Application of Ohm s Law to Electrolytes. In our discussion of Ohm s law, we have hitherto had in view principally the metallic part of the voltaic circuit. We now turn our attention more particularly to the fluid parts. It is of no importance in the present connection whether the fluid forms part of the "battery" or "elec tromotor," or whether it is inserted outside the battery ; the only difference in these two cases is, as we shall here after see, that in the former case energy is being absorbed by the current, and in the latter it is being evolved. In many respects the properties of the metallic and fluid parts of the circuit are alike : the electromagnetic action is the .j| same for both ; heat is also developed in the body of the conductor, whether metallic or fluid, according to the same law. But there is one peculiarity about a large class of Electj fluids which has no analogue in purely metallic conduction, b ^ . viz., that in them the passage of a steady current of elec tricity is invariably accompanied by chemical decomposi tion, definite in kind and quantity. To such fluid sub stances Faraday gave the name of electrolytes. For example, suppose we fill a small beaker with a solution of zinc chloride (ZuCl. 2 ), and suspend in the liquid two strips of pla tinum foil (called electrodes), at a moderate distance apart. Let a current enter at one of these strips, which we shall call the anode,
and leave at the other, which we shall call the cathode. It will be