THE MEASUREMENT OF STRESS BY THERMAL METHODS. 231 
heat by a direct application of the Thomson formula. In a recent valuable paper by 
TuRNER * the methods of Jour and Ep.iunp are substantially followed, and a detailed 
account is given of experiments on tension stress for metal bars of a size needing a 
modern testing machine for the stressing agent. 
2. Toe THERMAL EFFECT OF 'l'ENSION AND COMPRESSION STRESS. 
In the present paper the main object of inquiry is tension and compression, and 
for these stresses it is easy to deduce a’ simple form of the relation between the change 
of temperature and the stress from the equations of thermo-dynamics. 
If 2 be the length of unit mass of a rod subjected to a compression stress of 
intensity p, which shortens the bar by an amount d/, and E be the initial intrinsic 
energy of the bar and dH the amount of heat developed by the compression, 
we have 
dE + p-dl=Jdh- 
=3} (=), ap+(). “at } 
=F} pedp + tyadt ne RED 
: a oH 
where 7” is written for the more cumbersome symbol (al 
Now the alteration of length is a function of the pressure and temperature, and 
hence we have 
al al 
=~ d It . 
5 dp see 
ol al 
d= (ap, = ») dp+(St,-p 2 dt 
a perfect differential, whence 
BEE ny ®) 
ot Pi~P oy =a p— Po}? 
uae ig 2) peck 
op at ot 
Equation (1) can be written in the form 
— Peay 4 git 
Therefore 
giving 
a perfect differential also, from which we obtain 
aes ie Op _ 1a, 
PaNep et a) 
Now if a body be compressed adiabatically 
tat + pydp = 0 
cs a jo GE il 
Te uname 
* “Thermo-Electric Measurement of Stress,” Trans. Amer. Soc. C.H., 1902. 
