THE MEASUREMENT OF STRESS BY THERMAL METHODS, 241 
and @ is the observed value D,. Hence the observations for the ascending part of the 
curve must be corrected by the formula 
De D,(1 i + 
The value of k is determined in each case by the second part of the curve; and in the 
example shown and in all others described in this paper, it is of the exponential type. 
In the present example the value of the deflection D at any time after the loading 
ceased was found to be 
— -0045¢ 
D=9'8e 
where ¢ is the time in seconds from the cessation of the load. The curve showing the 
readings corrected for the radiation loss during the loading is shown dotted in fig. 5. 
There is also a correction for the change in resistance of the galvanometer coil and 
leads, owing to the change in the temperature of the room. The testing laboratory 
was very favourably situated in this respect, as its temperature rarely varied more 
than two or three degrees, and hence this correction was unnecessary. A further 
correction might be made since the current strength 7 in the thermopile circuit, and 
therefore the deflection of the galvanometer, =e and where ¢ is the angle turned 
through by the moving coil, but in all cases the deflection was so small in comparison 
with the distance of the scale from the moving coil and mirror attached thereto that 
the correction was negligible. 
5. THe RELATION OF STRESS TO STRAIN AND THERMAL CHANGE IN 
TENSION MEMBERS. 
The variation of strain with regard to tension stress follows a linear law very 
approximately over a certain range in the case of most metals, and in the case of iron 
and steel this linear relation holds for a considerable part of the whole range of stress 
up to rupture. This is easily shown by delicate extensometers, such as those devised 
by Unwin, Ewine, Martens and others. It becomes of importance to determine what 
is the relation of the thermal change to stress and to strain. The only previous 
experiments of which I am aware are those of TuRNER,* who has experimented upon 
the relation of thermal change to stress; and from the known properties of iron and 
steel as regards strain, he has deduced from his results that ‘the thermal limit of 
proportionality is lower than what is considered the true primitive elastic limit of the 
metal.” He suggests that there exists from the thermal point of view a well-defined 
range of almost perfect elasticity, beyond which “there is a considerable, in fact nearly 
equal, range of imperfect_elasticity, before reaching the limits of apparent elasticity of 
shape.” This is a matter of considerable importance in regard to the question of 
repeated stress, since if this is so, it may have an important bearing on the results of 
WOHLER and others. 
* Loc. ctt., ante. 
