serviceable. A few modifications had to be introduced. In the place of the two needles originally employed for obtaining contacts at fixed distances apart, and which if submerged in water would have introduced the disturbing effects of loose contacts, two fine copper wires were tightly wound around the extreme parts of the steel rod under experiment, and fastened in a way that made sliding impossible. The rod was then alternately placed in two vessels containing cold and warm water respectively, care being taken not in any way to strain the copper circuit wires. The short-circuiting through distilled water from one fine copper wire to the other is obviously negligible.

The temperature of the cold bath was approximately that of the room, and very constant; that of the warm bath varied during a single measurement not more than a few tenths of a degree. Temperature being read before and after the resistance measurement, the mean value could be regarded as a very satisfactory datum. The steel rod examined was placed first in the cold, then in the warm, and finally again in the cold bath. The mean of the measurements 1 and 3 was therefore to be combined with 2, 4 and 6 with 5, etc. The degree of approximate equality of the results of these distinct sets of observations, and the agreement between the measurements 1, 3, 4, 6, etc., give a good estimate of the accuracy of the work.

Material. Resistance-value of oxide tints.—The material used was that employed in all our researches, English "silver" steel in rods 0.15 cm. in diameter. After having been suddenly chilled in great numbers, certain of them were annealed by the electrical current, in this way: Having carefully polished the hard rod, it was introduced into the circuit of a dynamo-electric machine. As the temperature of the wire increased the oxide-tints appeared in a strikingly perfect manner, and it was only necessary to regulate the current cautiously and stop the operation at a given moment to obtain any oxide-tint desired almost uniformly over the whole length of the wire. The observations of this paragraph therefore give in an approximate way the temper-value of the oxide-tint appearing in air on a bright hard steel rod, in terms of electrical resistance.

Results. The following table, 1, contains a perspicuous comparison of the data of observation as obtained with six steel rods in different states of temper. For the diameter 2 p (cm) of the rod and the length 7 (cm) direct measurement showed the resistance w (ohm) at the temperature to (C.). Also the resistance W (ohm) at To. This is sufficient for the calculation of w, for 00 and a, the required coefficient. The known dimensions then enable us to deduce the specific resistance s (cm/cm2 0°). Finally, we give the specific gravity 4 of the wires, calcu lated for the known dimensions and the known weight. Our object in computing this constant was primarily that of checking the values for the sections of our rods as measured by the aid of the microscope. But they furnish a satisfactory corroboration of the general increase of dens

ity of steel on passing from the hard to the soft state, conformably with the results of C. Fromme:

If for a we take mean values, and compare these with the degrees of hardness of steel, characterized by 8, we obtain more clearly: TABLE 2.-Oxide-tint, specific electrical resistance and electrical temperature-coefficient of

steel.

Soft..

The electrical temperature-coefficient of steel, therefore, decreases in proportion as its specific resistance or its degree of hardness increases, at a rate diminishing as we pass from soft to hard steel.

The following little table interpolated from the above values, for practical purposes, may be put on record here:

TABLE 3.-Specific electrical resistance and electrical temperature-coefficient of steel. Prac

WROUGHT IRON.

Digest of earlier results.-The relation between electrical resistance and temperature in case of iron has been studied by a large number of observers, among whom Lenz, Becquerel, Arndtsen, Mousson, and others, are to be mentioned. But the most comprehensive and accurate data are unquestionably those given by Matthiessen and Vogt." These will therefore be discussed here.

Matthiessen and Vogt assume the quadratic formula

for 1, the conductivity of any given metal, relatively to hard-drawn silver (A ̧=100). Their results for a and b, in case of fifteen samples of iron, conveniently abbreviated, are contained in Table 4.

TABLE 4.—Electrical temperature-coefficient and electrical conductivity of divers samples of

Description of sample.

iron.

For the sake of facilitating a comparison of these results with our own, we reduced them, as nearly as possible, to absolute values of

cm

Ꭶ 0° microhm, by accepting for "silver hard," for which Matthiessen

cm2

and Vogt put λ=100,

8=1.574.

Moreover, the values have been arranged, commencing with pure iron, in the order of the values for resistance, the coefficient of quadratic t being discarded and only linear d introduced. The interpretation to be given to "a interpolated" will be explained presently.

"Matthiessen and Vogt: Pogg. Ann., CXVIII, p. 431, 1863.

12 Probable value for pure iron, hard, deduced from the observations with impure metal, from an inspection of the respective temperature-coefficients,

(612)

TABLE 5.-Specific electrical resistance and electrical temperature-coefficient of different kinds of iron.

Resistance-temperature equations of iron and of steel.-The first line of these data, showing the mean value of a number of observations with pure iron, is the most reliable. If this be added to our results for steel (Table 2), the whole series of results may be compared graphically, by representing specific resistance, 8, as abscissa temperature-coefficient, a, as ordinate. The points lie satisfactorily on a locus of definite character, which in its turn may be utilized for purposes of interpolation. In this way the last column of the foregoing table ("a interpolated") has been deduced, the temperature-coefficient for each value of specific resistance for the sample of iron cited being selected. The discrepancies or differences between observed and calculated results are not larger than a combination of observations made on the great variety of material by different observers, together with the wide range of possible errors incident to all, would lead us to anticipate. Even the position of soft steel with reference to the curve is, in every respect, satisfactory. It is in this way, finally, that the practical results in Table 3 were derived.

Benoit finds the following relations between resistance and temperature for soft iron and soft steel, respectively:

and

8,=0.1272 (1+0.00452 · t+0.0000058 · 12),

s=0.1149 (1+0.00498 · t+0.0000074 · ť2),
(Hg=1 mmm2).

These results referred to microhms and cm/cm2 are

for iron, and

8=12.1
8=10.9

a=0.00452

a=0.00498

for steel. Both sets of values are in good accordance with our graphic representation. We obtain by means of this:

and

For 8=12.1, the value a=0.00457,

For 8-10.9, the value a=0.00485.

13 Benoit: Comptes rend., LXXVI, p. 342, 1873. Wiedemann, 1. c., p. 525. The small value 8=10.9 obtained by Benoit for soft steel is remarkable and exceptional.

CAST-IRON.

Anticipative results. Of particular interest in connection with this discussion is the behavior of the most highly carburized of commercial iron-products, cast-iron. Observations for pairs of the electrical magnitudes under consideration, for this material, are not in hand. Elsewhere we will describe certain experiments, made in some number, with reference to the thermo-electric and galvanic properties of cast-iron. Here we need only mention, that the specific resistance of this metal is very decidedly larger than the largest attainable results for glass-hard steel. If, therefore, a relation between electrical conductivity and electrical temperature-coefficient of the kind premised, actually exists, then this latter quantity must, in like manner, be smaller than the smallest results arrived at in case of steel.

To test this inference, three samples were selected from our supply of cast-iron rods, Nos. 13, 14, 15, each about 25 cm. in length, and their resistance in the soft or thoroughly annealed state (annealed at red heat and cooled very slowly) determined at different convenient temperatures. But this resistance, in view of the comparatively large section of the said rods (about 0.4 cm2) being as small as 0.004 ohms, the measurement had to be made even with greater precaution than was necessary in the case of steel.

Method of measurement.-The method of measurement was, however, essentially identical in the two sets of experiments, being Matthiessen and Hockin's. The terminal wires of copper, wherever necessary insulated by glass tubes, were wrapped around and soldered to the castiron rods; these, together with the insulated terminals and a good thermometer, introduced into a wide glass tube. Through the latter, closed at both ends by suitably perforated corks, securing tubes of influx and efflux, vapor at the boiling point of the respective liquids continually circulated. Methyl alcohol vapor, and steam were especially convenient. The tube itself, thickly jacketed with felt and cloth, showed a desirably constant temperature throughout the course of the work. All these precautions were necessary, for the ulterior reason of excluding possible thermo-electric action at the junctions of cast-iron and copper. Such currents are otherwise readily evoked in intensity sufficient utterly to vitiate the accuracy of the measurements.

Results. The following table will show that the experiments conducted with this care were satisfactorily succeessful. Here a and b denote the sides of the approximately rectangular section of the castiron rods; 7, the effective length in the resistance measurements. From an inspection of the resulting errors, the linear relation assumed to exist

14A detailed discussion regarding the electrical effects of the strain accompanying hardness and of carburation, respectively, will be given in Chapter III.