468 Royal Society : — 



resistances at 0° and 100°C. The formula, however, expresses the 

 fact that the absolute difference between 0° and 100° C. in the 

 resistance of an alloy is equal to the absolute difference between 0° 

 and 100° in the calculated resistance of the alloy. 

 Formula 2 may also be written 



f T —— f y 



100° 100° 0° 0°' 



which, if correct, leads to the expression 



r t~ r t =r o°~ r o° ; 

 that is, the absolute difference between the observed and calculated 

 resistances of an alloy at any temperature equals the absolute 

 difference between the observed and calculated resistances at 0° C. ; 

 or, in other words, r-r'=z constant. (3) 



After giving various examples to show the correctness of the above, 

 we prove that from the expression 



r t — r' t =a. constant 



we may deduce the formula for the correction of resistance or con- 

 ducting-power for temperature of an alloy as soon as we know its 

 composition and its resistance at any temperature ; for, as r'ioo° 

 r' 0O , and r' t may be calculated with the help of the formula given 



for the correction of conducting-power for temperature for most of 

 the pure metals, if the constant rt — r't be determined, then 



r ioo° =r y+ constant > 



r t =r't + constant, 



r o° =r 'o° + constant J 

 and from these terms the formula for the correction of resistance or 

 conducting-power for temperature may be calculated, which in most 

 cases will be found very near the truth. 



In the second part we show by a few experiments that most alloys 

 of three metals will probably be governed by the same law with 

 respect to the influence of temperature on their conducting-power as 

 alloys of two metals. 



In the third part we deduce 



P : F : : M : M' , (4) 



100° ioo° ^ ' 



(where P and P' represent the observed and calculated percentage 

 decrements in the conducting-power of impure and pure metals be- 

 tween 0° and 100° C, M 10QO and M' 10()O their conducting-powers at 



100° C. ; F is for most metals 29*307) from 



P O :Pc::X 100O :V 100O . .••... (1) 



For when we consider the last two terms of the proportion, and bear 

 in mind that a trace of another metal has very little or no effect 

 upon X' 6 (when it represents the conducting-power of an alloy 



consisting of one metal with only a trace of another metal), while it 

 alters X to a very marked extent, it is evident that X' 10QO may be 



replaced by M 10QO . 



