6 ROYAL SOCIETY OF CANADA 



If therefore the bar is suddenly compressed without gaining or 

 losing heat, i.e., at constant entropy <p , we have 



or 



Kdt + Ld;p = 



dt i _ -ia I 



d^~ ~K ~ 1K 



and therefore for small changes of pressure A'p and temperature ^t 

 we can write the equation in the form 



p = At 



For a tensional stress of aanount JT, the sign will be negative, 

 and hence if a compression stress applied to a bar raises the tempera- 

 ture, a tensional stress will lower it. 



The direction of the change of temperature depends essentially on 

 the sign of the coejfficient of expansion since all the other values are 

 positive. It therefore follows that the thermal change for a small in- 

 crease of stress is linearly proportional to the stress, provided the other 

 quantities entering into the equation remain constant. Of these it is 

 possible that under some conditions of stress the value of the specific 

 heat K of the bar may change under stress, but from the molecular 

 theory of the constitution of matter, we may infer that if any change 

 occurs it will probably be very small ; again, the coefficient of expansion 

 of metals may vary with the stress applied; we have found by experi- 

 ment upon thin tubes of brass and steel that there is practically no 

 alteration in the value of the coefficient of expansion for any stress 

 within the yield point, and the coefficient is the same in the case of 

 steel, even when the metal is stressed beyond the yield point, while for 

 brass there appears to be a small increase. 



The measurement of the small changes of temperature due to a 

 change in the stress is easily accomplished by the use of a thermal 

 junction or pile, and in this way Joule ^ verified the Thomson law 

 stated above for various solids, including such materials as wrought 

 iron, steel, cast iron, copper and various timbers, and this method has 

 been applied by Edlund ^ to determine the behaviour of wires under 

 stress. In a recent paper by Turner,^ ' the methods of Joule and 

 Edlund are substantially followed in some interesting experiments on 



^ On some thermo-dynamical properties of solids. Transactions of the Royal 

 Society, 1853. 



=^ Poggendorff Annalen. Vols. 114 and 126, 1865. 



' Transactions of the American Society of Civil Engineers, 1902. 



