Properties, Specific Resistance and Hardness of Steel. 315 



dependent not only on its chemical nature, but also on its me- 

 chanical condition (hardness). Let us therefore put 



y=y +<9', y=y' o +0", 



where $' and $ f/ are to represent the (absolute) constants de- 

 pendent on the chemical nature of A' and A n respectively, 6' 

 and 6", however, varying with the hardness of the metals. 

 Thus the above equation becomes 



e t = {(y -y ) + {6'-6")\t(i +/( t) ). 



But suppose that A r and A" are not different metals, but 

 represent two rods to which different degrees of hardness have 

 been imparted, which were originally, however, cut from the 

 same wire. In this case ($' — ■& // )=0, whence 



E t =(0'-0")t(1+/(t)), 



dependent only on r and the difference of hardness of the 

 rods. 



It will be shown below that the electromotive force of an 

 element of soft and hard steel varies continuously with the 

 difference of temperature t and with the difference of hard- 

 ness of the rods. We will therefore put Q'' , the constant belong- 

 ing to the soft bar (i. e. one which has been heated above red- 

 ness and allowed to cool slowly in a badly conducting medium), 

 equal to zero, as it is in this that the molecules will most 

 probably have assumed normal positions. If, furthermore, we 

 replace 



E t =0't(1+/(t)) by E T = rtr + 6r 2 , 



a sufficient approximation for practice, we derive 



^=a + 2$T and RS^l =a 



LdT Jo 



This expression, i. e. the limiting value of the electromotive 

 force of a thermoelement composed of a . soft rod and one of 

 any degree of hardness to the corresponding difference of 

 temperature* when the latter converges towards zero, will in 

 the following be taken as the measure of the hardness of the 

 harder bar. I shall apply the term thermoelectric hardness to 

 it throughout the following paper (abbreviated T. E. H.). 



The relation between the thermoelectric properties and 

 hardness of steel, notwithstanding its comparative import- 

 ance, has never, to my knowledge, been made the subject of 

 detailed and exclusive study. All the experiments thus far 



* The colder end being supposed at 0°. 



