Effect of Temperature upon Modulus of Elasticity of Steel. 443 



obtained for the temperature coefficient are too great and 

 the results too contradictory to be explained on this ground. 

 We must therefore look into the experimental conditions 

 under which these results were obtained in order to account 

 for the discrepancies in a satisfactory manner. 



In all the experiments under review the temperature 

 coefficient was computed from values of the modulus of 

 elasticity of a piece of wire determined at different tempera- 

 tures by the usual method of stretching the wire and observing 

 the corresponding elongation. In two of the experiments 

 (those of Shakespeare, and Gray, etc.) the wire was suspended 

 vertically and was stretched by adding weights to a scale- 

 pan attached to its lower end. In other cases the wire was 

 mounted horizontally, and the desired tensile force was 

 applied to the wire by adding weights to a scale-pan 

 connected to the wire by means of a string which passed 

 over anti-friction pulleys. Harrison found this method of 

 stretching the wire unsatisfactory and used an especially 

 designed spring balance for that purpose. 



With the exception of Shakespeare all the observers 

 mentioned obtained the elongation by means of two micro- 

 scopes focussed on two points on the wire. Shakespeare 

 used an optical method in which the elongation of the wire 

 produced a change in the lengths of the paths of two beams 

 of light and caused interference bands to move across the 

 field of his observing apparatus. Some observers heated the 

 wire by passing an electric current through it, some by 

 enclosing it in a heating-jacket, and others by both methods. 

 The temperature was obtained either by measuring the 

 change of the electrical resistance of the wire, or by means 

 of mercury thermometers. 



An analysis of the results of these researches shows that 

 we may consider the errors in the measurement of the 

 elongation as one of the major factors contributing to the 

 discrepancies mentioned. It is noteworthy that, with the 

 exception of Shakespeare's case, the change of sign of 

 the temperature coefficient was observed when the wire was 

 relatively long, mounted horizontally, and stretched by means 

 of small loads. This suggests that the effect might have 

 been caused by the sag of the wire. It may be shown that 

 the apparent increase in the length due to taking up the sao- 

 of a horizontally stretched string is given bv the following 

 expression to a first order of approximation. 



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