52 ELECTRICITY [RESISTANCE. addition of larger quantities of the foreign metal lowers the con ductivity. (2.) The formulae for the temperature variation for alloys of the metals a among themselves agree very closely with the mean for- mulie calculated from the volume percentages. If P denotes the fraction of itself by which the_conductivity at exceeds that at 100 for an average pure metal (P = 29307), and P the same fraction, observed in the case of any alloy for which the observed and mean or calculated conductivities at and 100 are ^o> ^ioo> an( l ^o> "100 then, according to Matthiessen, the following relation holds for alloys of metals a among themselves, and metals B among themselves: P . p .. if . 1. f . 1 .. ft 100 . tjoO) or, which is the same thing, R , ke._, denoting resistances,
- 100 ~ -"9 -^100 ~~ **0
For alloys of a with B, the observed value of P is in general greater than that calculated by this formulae. Effect of Other Physical Conditions affecting tJie Resistance of Solid Bodies. physical Besides temperature, a variety of other circumstances affect the condi- specific resistance of metals. As a general rule, metals are worse tion. conductors in the hard than in the soft state. Tempering steel increases its resistance considerably, but subsequent heating and gradual cooling reduces the resistance again. The resistance of a wire stretched by a weight is increased more than can be accounted for by the mere decrease of the section. 1 Winding on a bobbin has the same effect. The finer a metal is drawn into wire, the greater is its specific resistance in the case of iron, the smaller in the case of copper. Magnetization has also in certain cases been found to affect the resistance. These effects were studied by Sir William Thomson ; the results of his researchas are given in his Bakerian Lecture, Phil. Trans., 1856. The experiments are very instructive, and many of them well worth repeating now that we have more delicate apparatus. The most curious case of alteration of resist ance is that of tellurium and selenium. We have already men tioned that selenium in the amorphous state is a non-conductor. After continued heating it passes into the crystalline state and con ducts. Sale found 2 that the conductivity of this crystalline form of selenium is greatly affected by light, and that, too, differently by light of different colours. Prof. W. G. Adams 3 has lately made a series of experiments on the subject, and concludes that there is an action of light, which varies as the square root of the illuminating power, and is distinct from any heating effect. He found the resis tance of selenium in one case diminished by a fifth when it was exposed to the light of a certain paraffin lamp ; the change in tellurium under similar circumstances was irJ 5 th. He found that the passage of a strong current through selenium sets up a kind of polarization, which opposes a current in the same direction as that which produced it, and aids a current in the opposite direction. This led him to suspect that the action of light might of itself start a current in the selenium, and he found that under certain circum stances this is the case. Fluids. The verification by the experiments of Kohlrausch and Nippoldt of Ohm s law for electrolytes, through a wide range of electromotive force, has greatly increased the interest of all data relating to the resistance of this class of conductors. We have no difficulty in working with electrolytes whose composition and physi cal state is perfectly definite, a thing next to impossible in the case of solids. Hence the resistance of an electrolyte has, far beyond the resistance of a solid metal, a value as datum for physical specula tions concerning the ultimate properties of matter, which underlie Ohm s law. We refer the reader to Wiedemann s Galvanismus for an account of the earlier results in this department of Pouillet, Hankel, Becquerel, Horsford, Wiedemann, Becker, Lenz, and Saweljew. We recommend to his notice particularly the careful experiments of Beetz on zinc sulphate (his temperature determinations are the most extensive of the kind), also the researches of Paalzow, who examined the conductivity of various mixtures of two solutions, the conduc tivities of which had been separately determined. He finds that if R and R be the resistances of the components, the resistance of the RR Speci resist ance temp* tuve ( effidt of ele rolvd mixture is not so that the current is not divided between R + R the liquids as if they were metals in multiple arc; nor is it the mean of R and R , but it lies nearer the smaller of the two. A similar result was arrived at by Ewing and Macgregor. 4 Kohlrausch and Grotrian 5 have made the most recent as well as the most extensive investigations ; and we shall best describe the present state of scientific knowledge on this subject by giving an analysis of their results and conclusions. Their experiments deal with the chlorides of the metals of the alkalies and alkaline earths. Kohlrausch has also examined a number of the commoner acids. For convenience we have transcribed the diagram given by Kohl rausch, which embodies certain of the results obtained by himself and Grotrian. Fig. 1 of the diagram gives the conductivities 6 (Ar lb ) at Diagram illustrating Electrical Conductivity. 18 C. ; the ordinates represent & 18 x 10 5 , except for acetic and tar- taric acid, where they represent fc, 8 x 10 7 and & 18 x 10 6 respectively, the abscissae represent percentages by weight in the solution of HC1, H,S0 4 , NH 4 C1, &c. In fig. 2 th values of the temperature 1 For recent experiments on this subject soe Proc. R. S., Dec. 1876. and June 1877. Authorities for some of the other facts stated will be found in Wiedemann, i. 207. 4 Prof,. R. ,<?., 1873. " 3 p rof p ^ volR xxjjj xxiv< xxv coefficient | for!8C. are given by the ordinates, .the abscissas being percentages as before. For convenience of drawing the coeffi cient of acetic acid is decreased by O Ol. The curves which appear in the diagram include all the distinct varieties ; and it will be seen that in all cases the conductivity varies 4 Trans. R.S.E., 1873. 5 Pogg. Ann., cliv., 1875, an.l clix., 1876.
f Mercury is the standard-