THE ELECTRICAL RESISTANCE OF CERTAIN ALLOYS. 601 
TABLE I. 
Resistance. 
Temperature. 
Observed. Calculated. 
168° C. 12°33 12°340 
47-2 12°47 12-471 
65°4 13*55 12°543 
89°3 12:64 12:635 
104:2 12°685 12°689 
118:0 1274: 12:738 
127°6 UB ea LTT 
147°4 12:84 12°836 
These results are found capable of being very accurately represented by the 
following formula, in which R stands for resistance ¢ for temperature. 
R=12°265 + 00456257 — 00000468752. 
The numbers of the third column are calculated by means of this formula, and 
show a satisfactory agreement with those of the second. For a wire therefore 
whose resistance at 0° C. would be unity (7 representing the resistance of such 
wire, and the formula being supposed to hold at 0°), 
r=1+ °00037198¢— -0000003821772?. 
Hence, if & represents the conductivity of such wire, 
k=1—-00037198¢ + :000000520542?. 
With this result we may compare the formula which MaTrHressEN and Voct* 
give for an alloy of the same metals 10°96 per cent. by volume of which is iron. 
They find 
k=1—:000487452 + 000000103462’. 
It will be noticed that their coefficient of ¢ is greater than ours, our co- 
efficient of 7” greater than theirs. This may be partially accounted for by the 
fact that we carried our measurements to much higher temperatures than they. 
The rate of change of resistance with temperature decreases more rapidly at 
high than at low temperatures. We may here give a table of coefficients of the 
corresponding formule for iron and gold. A and B are the coefficients of ¢ and 
t? respectively in the formula : 
kor r=1+At+ Be’. 
* Phil. Trans. Roy. Soc. Lond., vol. cliv. (1864), p. 167. 
