232 PROFESSOR E. G. COKER ON 
If a be the coefficient of expansion of the bar for unit increase of temperature, we can 
write this in the form 
dp St, 
and for small changes of pressure and temperature we can write the equation in 
the form 
Jt 
Ap= At —2 
P tal 
where the sign of At depends upon the signs of a and Ap, since all the other quantities 
are essentially positive. 
For metals a is in general positive, and hence a compression stress will raise the 
temperature, while a tensional stress will lower it. Strictly speaking, the equation only 
holds for infinitesimal changes of p and ¢, and it is therefore essential to show what 
limitations, if any, are to be imposed in its application to bodies under great ranges 
of stress. The effect of a varying load upon the specific heat of a body has not been 
determined, so far as | am aware, but it is unlikely to differ by an appreciable amount 
from the specific heat at atmospheric pressure. The coefficient of expansion when the 
stress is varied may change to a small extent, and experiments were made by JouLE* 
to examine the effect of stress upon the expansion of various timbers, and he found 
an increase of expansibility with tension. As far as ] am aware, there are no 
experiments showing what effect stress has upon the thermal expansion of metals; 
and as the coefficient of expansion enters into the fundamental equation, a special investi- 
gation was made of the thermal expansion of brass and steel under different tension loads. 
3. Tort THERMAL EXPANSION OF BRASS AND STEEL UNDER TENSION STRESS. 
The general arrangement of apparatus adopted is shown in fig. 1, in which A is 
the standard of a small single-lever testing machine provided with a weigh-beam B 
and shackles CD for securing the test-piece E in position. The loading of the 
specimen is effected by suspending dead weights F from the end of the beam, and the 
maximum load which could be safely applied was 175 pounds. ‘The ratio of the arms 
of the lever was 20 to 1, and hence the maximum stress obtainable was 3500 pounds. 
In order to carry the experiments past the elastic limit, it was necessary to have 
a specimen of very small section; and on account of the difficulty of maintaining a 
solid specimen at a uniform temperature, and at the same time observing the change 
of length, the specimens were chosen of seamless drawn tube, very uniform in diameter, 
thereby permitting the outside being turned in a lathe to a manageable section. The 
ends of the tube were soldered into thick ferrules G, having side tubes H for the 
insertion of thermometers, and inlet and outlet tubes II’ were provided, connecting 
to a pipe system J, in which water could be circulated at any desired temperature. 
The circulation was effected by a small centrifugal pump K driven by an elegtrie 
* “On some Thermo-Dynamic Properties of Solids,” Phil. Trans., 1859. 
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