-f-44 Prof. H. M. Dadouiian on the Temperature Coefficient 



where L is the length, w the weight per unit length, and T 

 the tension of the string. Thus the apparent increase in 

 length due to taking up the sag varies inversely as the square 

 of the load and directly as the cube of the length. It is to 

 be expected, therefore, that the errors due to the sag would 

 be relatively large in the case of long wires stretched hori- 

 zontally under low tension. While errors from this source 

 must have been considerable in some of the experiments and 

 must have contributed to the general irregularities of the 

 results, they cannot account for the discrepancies among 

 results obtained at different temperatures but otherwise 

 similar conditions. 



As has been already stated, most of the peculiar results 

 were obtained when the specimen was heated electrically. 

 This is to be expected, for unless the wire is perfectly homo- 

 geneous, of uniform cross-section, and of uniformly smooth 

 surface, there would be differences of temperature due to 

 non-uniform resistance and unequal radiation. 



The real explanation of the divergence of the results 

 under consideration is to be found, however, not in the rela- 

 tive precision of the measurements involved in the determi- 

 nation of the modulus of elasticity, but in the fact that the 

 methods used by previous investigators do not yield modulus 

 values of a sufficient degree of accuracy. This becomes 

 evident from the following analysis of the dependence of 

 the accuracy of the temperature coefficient upon that of the 

 modulus. 



Denoting the modulus of elasticity by E and its tempera- 

 ture coefficient by e, we have 



E = E [l + e(i-*„)], (2) 



where t and t represent the temperatures at which E and E 

 are determined. It may be shown from (2) that the per- 

 centage error in e is given bv the following expression : 



The first term under the radical sign may be neglected in 

 comparison with the second term on account of the presence 

 of e in the denominator of the latter 3 and (2) put in the 

 form : 



6 -e(t-t )- E ( ' 



If we put e = 2-7xl0" 4 and t — «„=100, we obtain 

 he _ , SE 



7 =o2 E- 



