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



Apparatus for Measuring the Extension of a Wire. By- 

 Mr G. F. C. Searle, Demonstrator at the Cavendish Laboratory. 



[Received 29 March 1900.] 



In the study of the effects of longitudinal stress upon the 

 length of a wire some accurate means is required for measur- 

 ing the elongation of the specimen. The simplest method of 

 magnifying the effects to be observed consists in using a wire 

 of a considerable length, which for convenience is hung from a 

 fixed support, the extension being produced by hanging weights 

 to the lower end of the wire. Two chief sources of error must 

 be avoided at the outset. These arise from the yielding of the 

 support and the change of length of the wire due to rise of 

 temperature. The latter cause may introduce a large error, for 

 a rise of 2° C. will produce an increase of length of yL mm. in 

 a copper wire 3 metres long. Both errors are practically 

 eliminated if, instead of finding the displacement of the lower 

 end of the wire relative to a fixed mark, observation is made 

 of the displacement of the end of the wire relative to the lower 

 end of a second wire of the same material, hanging from the 

 same support, stretched by a constant weight and serving as 

 a standard of comparison. It is here assumed that the coefficients 

 of expansion of the two wires are identical in spite of their differences 

 in stress. 



It may not be out of place to consider the amount of error due 

 to the failure of this assumption. 



Let the coefficients of expansion under zero stress and under 

 a stress of T dynes per square cm. be denoted by a and a T respec- 

 tively. Let E and E e denote the values of Young's modulus at 

 a standard temperature and at a point 0° higher \ Let l be 

 the length of the wire when free from strain at the standard 

 temperature. 



Then if the w r ire be first heated and then strained we have for 

 the new length 



I = l (1 + a.9) ( 1 + p -J , approximately ; 



1 The modulus E e is determined from observations on the elongation of a wire 

 by a load, at the constant temperature 0, without regard to the causes which may 

 contribute to that elongation. A similar remark applies to a ,. 



