Specific resistance.-The following table contains our data for the specific resistance of the same alloys to which the foregoing tables (35-39) refer. The first two columns need no explanation. Column third contains the resistance in ohms per meter of wire at the temperature in column fourth. Under 2p the diameter and under s, the specific resistance in micro-ohms at the temperature t is given. The constant a, finally, whose signification is apparent from 8,8 (1+at), enables us to calculate 8, the specific resistance at zero centigrade, in micro-ohms.

It is to be remarked that all the measurements were originally made in Siemens' units (ohm=1.06 Siemens), and subsequently reduced. The temperature-coefficients used, a, are obtained from the results of Matthi. essen, C. Vogt, and v. Bose, by calculating with the aid of their formulæ, s, for 1000 and 0°, and then finding the mean coefficient (a) between these limits. This is obviously permissible in our case.

56 Matthiessen u. v. Bose: Pogg. Ann., CIII, p. 412, 1858.

The following table (41) contains results of Matthiessen and others; a and b here are Matthiessen's constants for his relation between electrical conductivity and temperature. By means of these A and A', the electrical conductivity at 0° and 100°, respectively, were calculated. But, according to Matthiessen, λ=100 for hard silver; λ=1.656 for mercury, (0°). Hence

=

100

1.656

λι 1.06

log 8=2.19375-log λ,.

From these values of st the constant a was then obtained, in the way already given, 8=8 (1+at).

TABLE 41.-Specific resistance of alloys of silver.

Digest. Diagram.-For the sake of perspicuity, the final results are tabulated again as follows.

TABLE 42.-Corresponding values of the galvanic and thermo-electric constants.

TABLE 42.-Corresponding values of the thermo-electric and galvanic constants-Cont'd.

The results contained in the last table (42) are given graphically in figure 13, specific resistance being represented as abscissa, thermo-elec

FIG. 13.-Specific resistance and thermo-electric constant: steel, silver-gold, silver-platinum, silver

zinc.

tric constant as ordinate. In order to facilitate comparison the linear relation which holds for steel (see chapter II, page 63) is also drawn,

and the interval of variation57 of the constants in question indicated by two small circles near the ends of the line. All the constants are given in microhms and micro-volts, respectively, and the thermo-electric position is referred to silver.

Discussion.-A mere glance at the curves tells us that the relations under consideration are by no means of a simple character. Both properties, as exemplified by the thermo-electric constant and specific resistance, pass through maxima or minima, in such a way, however, that the said singular points do not coincide-i. e., are not properties of one and the same wire as regards composition. Equally difficult is it to observe any perspicuous law for the direction of the line joining the extreme points (those corresponding to pure metals) of the curves. The very simple relations which obtain in case of steel would apparently lead to the anticipation of some result of this kind.

The given curves, however, apply only for fixed conditions of temperature; the galvanic constant 8 only for the temperature t=0; the thermo-electric constant a for the mean temperature (T+t)=0. But the temperature-coefficient, both for thermo-electric power as well as for specific resistance, varies in a marked degree as we pass from alloy to alloy. Hence it follows that for each temperature there exists a set of curves of the kind in question, characteristic of the said temperature. Change of temperature, therefore, involves a change in the curves both in figure and in position. It follows herefrom that a certain temperature must exist for which the figure of the curves is the simplest possible; our knowledge of the effects of temperature is, however, as yet insufficiently accurate to enable us to adduce further inferences. It is to be noticed that, at least as far as the above experimental matter is concerned, the magnitude of the given curves-i. e., the range of variation of the involved electrical constants-is qualitatively in the order of the differences of the specific volumes of the metallic components of the respective alloys. The very large loop, obtained in the experiments with silver-platinum alloys, corresponds to the marked increase of hardness which these materials experience with increasing additions of platinum to silver. On the other hand, in the case of silver-gold and silver-copper alloys, a very great difference in the extent of the loop is apparent, unaccompanied by corresponding differences in the degrees of hardness of the respective alloys. That the bulge in the different curves must be wholly to the right of the lines joining the extreme

57 In later researches the superior limit was found to be even above 50.

58 In reference to thermo electric power we consider the quantity 2b in the equation e=ar+bró as a kind of temperature coefficient, since the thermo-electromotive force e for a given difference 7, of temperature, increases linearly with the mean tem2' perature of the junctions.

5 We shall find below that hardness may also exist in iron-carburets without a marked electrical equivalent.