of the Modulus of Longitudinal Elasticity of Steel. 445 



On the other hand, if E is measured at 20° intervals for the 

 purpose of observing the variation in E, we have 



*5~=260f. 



6 E 



It is evident, therefore, that if reasonably good values of e 

 are to be obtained, E would have to be determined with an 

 extremely high degree of precision. It is doubtful if in any 

 of the investigations under review the precision of individual 

 determinations of E has been higher than one per cent. In 

 fact Harrison, who gives the sources and the magnitudes of 

 the errors involved in his measurements, finds that the error 

 of individual determinations of E was two per cent. This 

 makes errors of individual observations of e over 100 per 

 cent. 



There is an indirect method by which the temperature 

 coefficient of the modulus of elasticity can be determined 

 far more accurately than with the direct methods we have 

 described. In this method the effect of temperature upon 

 the period of a tuning-fork (made of the substance to be 

 studied) is observed, and from the results e is computed. 

 Apparently former investigators have not appreciated the 

 great advantage of this method, for very few have tried it, 

 and then only as an interesting digression from their main 

 line of research. 



In a previous paper by the present writer * it was shown 

 that the following expression for the period of vibration of a 

 bar holds good for a tuning-fork between the temperatures 

 — 26° 0. and 57° C. 



p=^V^ ^ 



r A a V lli 



where L is the length (in case of tuning-forks the pro- 

 jection of the median line of the prongs upon the geometrical 

 axis of! the fork), a the thickness, E the modulus of elas- 

 ticity, and r ( = 1*287011) the root of the following equation : 



(e' + e-O sin 2^ + 2=0 |. 



Let P , E , and L denote, respectively, the values of P, E, 

 and L at 0° 0. Then since all linear dimensions are affected 

 by temperature in the same manner, equation (5) gives 



b^Lo iy (6) 



E L*P 2 { 



* Phys. Rev. xiii. pp. 337-359 (1919). 



t Poisson, Traite Mcchanique, ii. p. 390. 



