of the Modulus of Longitudinal Elasticity of Steel. 447 

 Making use of the relation 



P = P o [l + 0(*--«6)L 



we can express the first term under the radical sign in 

 terms of more directly measured magnitudes and put (16) 

 in the form 



-= /TM^ ~4~ /8P\ 2 «7S*\ 2 

 € V w v*-* ; + <9*(*-* ) 2 Viv + e\a)' 



On account of the factor I -A the third term under the 



radical sign of the last equation is negligible compared with 

 the other two. Neglecting this term we have 



Se_ / / St x 2 , 4 TSPx 2 " 



Comparing the last equation with (3) we observe that the 

 first term under the radical sign of each is or! the same form. 

 Therefore the relative error in e due to an error in t is 

 inversely proportional to the precision with which the tem- 

 perature is measured in the two methods. My experiments 

 were carried out in constant temperature rooms in which 

 the temperature was changed very slowly and was measured 

 to 0° '02 C. Consequently the error from this source was 

 very much smaller in my experiments than in those of 

 previous observers. The temperature term is negligible, 

 however, in both (3) and (17) ; therefore the relative 

 precision of the two sets of experiments may be determined 

 by comparing equation (4) with the following obtained by 

 omitting the temperature term from (17); 



T = ff(t^i'T (18) 



2 . a/2 



The factor ^ ? is about three times as large as 



e(t-t ) " e (t-t y 



but -p was about *0001 in my experiments, while -^r was 



about '01 in the experiments of previous observers. In 

 other words, the errors of individual determinations of e 

 were about thirty times smaller in my experiments. 



It may be remarked here that the observed effect of 

 temperature upon the modulus of longitudinal elasticity is 

 due to (a) a change in the elastic properties of the substance, 

 and (b) changes in the linear dimensions of the body. The 

 contribution of the latter to the temperature coefficient of 



