136 : REPORT—1862. 
Arrenpix A.—On the Variation of the Electrical Resistance of Alloys due to 
Change of Temperature. By Dr. Marruressen, PRS, 
It has been shown* that the influence of temperature on the electric conduct- 
ing power of the metals amounts to 29-3 per cent. on their conducting power 
between 0° and 100° C.: an exception to this law has been found in iron, the 
conducting power of which decreases between those limits 38:2 per cent. It 
was, therefore, useless to try any of the other pure metals, as they would, in all 
probability, have decreased by the same amount, as well as from the fact that 
the metals which would have suited the purpose had already been tried. I 
therefore turned my attention to the alloys, and, in conjunction with Dr. C. 
Vogt, have made a long series of experiments respecting the influence of 
temperature on their electric conducting power. After having determined 
the conducting power of a few of them at different temperatures, together 
with the help of the few experiments which have already been made by 
different observers, it became obvious that the percentage decrement in 
their conducting power stands in some relation to the fact that, when a solid 
metal is alloyed with another (with the exception of lead, tin, zine, and 
cadmium amongst each other), a lower conducting power is observed than the 
mean of that of the components+. The law which we found to regulate 
this property was with most alloys the following, viz. :— 
“* The percentage decrement between 0° and 100° in the conducting power of 
an alloy in a solid state stands in the same ratio to the mean percentage 
decrement of the components between 0° and 100° as the conducting power of 
the alloy at 100° does to the mean conducting power of the components at 100° ;” 
or, in other words, “ the absolute difference in the observed resistance hetween 0° 
and 100° of an alloy is equal to the absolute difference between the means of 
the resistance of the component metals between 0° and 100°.” 
For example, the conducting power of the hard-drawn gold-silver alloy 
was found equal to 15:03 at 0° (taking silver equal 100° at 0°), and de- 
creases 6-49 per cent. between 0° and 100°. The mean decrement of the 
components between 0° and 100° being 29-3 per cent., the conducting power 
of the alloy is 14:05 at 100°, and that of the mean of the components is 62:58 
at 100°. If we now calculate the percentage decrement in the conducting 
power of the alloy between 0° and 100° from the above data, we find it equal 
to 6°58 per cent., and by experiments it was found equal to 6:49 per cent. 
Or, taking the resistance of silver at 0°=100, and that of gold at 0°=128-3, 
we find the resistance of the alloy at 0°=665-3, and at 100°=711:-7, and 
that calculated from a mean of the volumes of its components at 0°=113-2, 
and at 100°=159-°8 ; therefore the absolute difference between the observed 
resistance at 0° and 100° is 46-4, and that between the calculated at 0° and 
100°=46°8. 
Knowing already, from my experiments on the electric conducting power 
of alloys§, that when two metals are alloyed together in any proportion, if the 
alloy is merely a solution of the two metals in one another, its conducting 
power may be approximatively foretold, and that, from the above law, it is 
necessary that if the conducting power of an alloy should vary between the 
limits of 0° and 100° to a minimum extent, the alloy itself must have a 
minimum conducting power as compared with that calculated from. its 
* Phil. Trans. 1862, pt. 1. 
+ Matthiessen and Vogt, unpublished researches. 
t{ Assuming that the conducting-power or resistance of an alloy is equal to that of 
parallel wires of the components forming it. 
§ Phil. Trans. 1860, p. 161. 
