Mr Searle, Apparatus for Measuring the Extension of a Wire. 319 



while if the wire be first strained and then heated under strain 



I = l ( 1 + — V(l 4- a T 9) approximately 1 . 



The products of small terms being neglected, the equality of these 

 two expressions gives us 



T T 



Hence 



^ " a = ¥ U; ~ w = " :p ■ — r - ' a PP roximatel y- 



Now the experiments of Mr G. A. Shakespear (Phil. Mag., 

 Series v., vol. 47, p. 539) give the following values for dEjEdO : 



M f i ldE 



Metal ^ M . 



Copper - -00041. 

 Hard brass - '00035. 

 Iron - -00019. 



Steel - -00038. 



Taking the case of copper we have approximately a = 00001 G, 

 E =1'2 x 10 12 dynes per square cm., and thus we find for copper 



a _rZ« = 2xl0-"xr. 

 a 



For a wire 1 square mm. in section a load of 2 kilos gives 

 approximately T = 2 x 10 8 dynes per square cm. We thus find 



a T — a. 



= 4 x 10~ 3 . 



Hence if two copper wires each 1 square mm. in section and 

 3 metres long carry loads differing by 2 kilos, the expansion 

 of either wire due to 1° rise of temperature will be about 5 x 10~ 3 

 centimetres, and the more heavily loaded wire will lengthen by 

 5 x 10~ 3 x 4 x 10 _3 = 2 x 10 -5 cm. more than the other wire. This 

 quantity is hardly appreciable by the apparatus described in this 

 communication, and thus the method may be considered to be 

 satisfactory. 



The simplest method of determining the relative displacement 

 of the lower ends of the two wires consists in attaching a scale 



1 These expressions are only approximate since the changes in the area of the 

 section of the wire have been neglected. 



