3 special ingredients of the alloy, and which depends only on the resistance-position of this alloy in the class. I venture to assert therefore that the arrangement of points is in accordance with a definite underlying law, with reference to which exceptional data are to be interpreted. The law in question appears to me particularly noteworthy as being among those which spe 1. FIGURE 1.-Showing the relation between temperature-coefficient (a) and electrical resistance (so), in case of platinum alloys. cially hold for the solid state. In his experiments on the conductivity of solid mercury, C. L. Weber found its resistance to increase fourfold in virtue of fusion. Simultaneously with this variation, the temperature-coefficient of solid mercury (0.00455) falls to the relatively very low value (0000927 between 30° and +45°) which holds for the liquid metal. Weber points out the close approximation of the temperature coefficient of solid mercury to that of the other solid metals, and infers even closer agreement at temperatures sufficiently below the melting point of mercury. It is in a similar sense that in §1 I referred the properties to be investigated in this paper to a class of alloys characterized by high melting points. * C. L. Weber, Wied. Ann., xxv. p. 245, 1885. The large variation of resistance at the melting point, observed in case of mercury and other metals and alloys (K, Na, etc.), suggests the striking adaptability of these substances for experiments on the relation between melting point and pressure; or in general on the continuity of solid and liquid state. Change of resistance is here the criterion of fusion. 7. Having thus obtained some general notions of the dependence of f'(0)/ƒ (0) on ƒ(0), it is in place to inquire more fully into the form of this dependence. I will proceed in a manner similar to that employed in §4, and postulate the hyperbolic equation (x+1)(y+m)=n. Availing myself of the chart, figure 1, selecting for preliminary computation a set of coördinates as carefully as possible from it, x=11.7 I find the constants l, m, n to be y=0·00300 l=−0·1360, m=0·0002548, 164 n=0·03764. The values found for l, m, n are exceedingly significant. Since a varies between 10 and 70, 7 is in general much less than one per cent of x. This observation at once suggests the assumption of a simpler form of equation in which 7=0. Again the positive character of m indicates that larger values of a10° would tend still further to simplify the equation (x+7) But aloo> a357 follows from the experiments; (y+m)=n. hence also α 100 and therefore the postulation of x(y+m)=n is altogether warranted. To obviate the necessity of a complete recalculation of a, I used the following method of passing from a100 and a357 to a. If the values s, s', s', correspond respectively to t, t', t", and if (s' — s) (st'' 2 — s''t2) — (s′′ —s) (st' 2 — s't2) α from which it is easy to deduce a-a100 in terms of a100-a357. Now st"'-s't=D" and st'-s't=D' are already known from the earlier computations; and when a correction only is sought s'te and s'te may here be neglected as compared with st" and st', respectively, t being small in comparison with t' and t". Hence 2 which equation, since the fraction (t'/t') is constant, is a convenient form, and much of the correcting may be done mentally. I may add that the three quantities aloo, a367, a357 0 0 α 1009 have similarly simple approximate relations to each other; for instance, a100-a357 (t"-t'/t"-t) (a100-a367), α and since the fraction_(t"-t' (t"-t) is constant, such reductions also are mental. I observe finally that the effect of these corrections is only a few units of the last figure. The methods are therefore sufficient. 8. Having made this preliminary survey, the data are available for the calculation of m and n by the method of least squares. It is expedient, however, before doing so, to put the postulated equation under the form f'(0)/f(0)=n. 1/ƒ(0)—m, where 1/f(0) is the zero value of the electrical conductivity of the alloy whose temperature-coefficient is a. This equation when operated on by the method of least squares does not give inordinate preference to high values of specific resistance; and since such high values can not be warranted with a greater degree of accuracy than the low values, the said equation may most expediently be made the basis of computation. The following table contains the results and is intelligible without further explanation. The alloys 10, 11, 12 which I insert for completeness, were added subsequently to the calculation. The probable errors of m and n indicate that the inaccuracy is largely incurred in the measurement of f'(o) /f(o). The constant ʼn is much more fully warranted. 9. Endeavoring to describe the platinum alloys as a class possessing generic electrical characteristics it is permissible to abstract from the minute and isolated behavior of the individual alloy. It appears that the electrical temperature-coefficient (ƒ'(0)/ƒ (0)),* varies as a linear function of conductivity (1: f(o)), throughout the whole of the enormous variation of electrical resistance (10 to 65 microhms, c. c.), presented by platinum alloys not too highly alloyed (<10 per cent). In other words, if at to, the specific resistance of a platinum alloy be denoted by f(x,t), where t symbolizes temperature and x is a variable parameter, then ƒ (x,0) (ƒ'(x,0) /ƒ (x,0)+0·000194)=0·0378. χ It is perhaps not superfluous to remark in passing that if instead of the arbitrary temperature 0° C., some other value more in keeping with the qualities of platinum alloys had been selected, the constants m and n would present different values; and it is conceivable that correlated values of f(t) and ƒ'(t) may exist for which the constant m is annulled, and for which the given equation takes the simple form xy = n'. TABLE IV.—Electrics of platinum alloys. Digest ƒ (0) (ƒ′ (0)/ƒ(0)+m)=n. 27 | + + + + | . | + | + + | | + | + | + | + + | | + 5 Fe + 9 Fe + 3 Steel +23 Steel 17 6 4 + 1 + 1 5 1 55558887 54 24.5 1.41 m=0·0001939±0·0000233 n =0.03778 +0.00054 3 10. It is desirable finally to give as graphic an exhibit of the results taken collectively, as possible. Unfortunately any scale which clearly presents the results for gold, silver and copper, will crowd the results for platinum and the iron-carburets; and vice versa. Perhaps the following chart, fig. 2, will FIGURE 2.-Diagram of the relation between temperature coefficient (a) and conductivity (20) for certain low 400 percentage alloys. |