230 PROFESSOR E. G. COKER ON 
which he attributed to an internal cause. He deduced a theoretical formula in which 
the change of temperature ¢ was shown to bear a linear relation to the stress p and to 
the coefficient of expansion 4, which may be expressed in the form t=c k p, where c is 
a constant. He proved from his experiments that a wire when stretched within its 
elastic limit is lowered in temperature, and when compressed has its temperature raised. 
DuHAMEL* investigated the modifications which became necessary in Porsson’s elasticity 
equations, when allowance is made for change of temperature. The subject was placed 
on a sound basis by Lord Ketvrin,t who deduced from the laws of thermo-dynamics the 
general equations of thermo-elasticity. He showed that the thermal effect H produced 
by stresses p,, can be expressed in the form 
where ¢ is the temperature, J is JouLn’s equivalent, and @,, is the strain corresponding 
to the stress Pyy. 
The general conclusions deduced were that “‘cold is produced whenever a solid is 
strained by opposing, and heat when it is strained by yielding to any elastic force of its 
own, the strength of which would diminish if the temperature were raised, but that, on 
the contrary, heat is produced when a solid is strained against, and cold when it is 
strained by yielding to, any elastic force of its own, the strength of which would increase 
if the temperature were raised.” 
These conclusions were experimentally verified by JouLE,{ who showed that the 
thermal changes produced by stretching and compressing metals, timber, etc., and by 
the deflection of helical springs, was proportional to the stress applied, and obeyed the 
Thomson law. The change of temperature was measured by thermo-electric couples 
composed of iron and copper wires, either pressed against the specimen or inserted in 
holes drilled into them ; a galvanometer was placed in circuit with the thermo-junction 
to indicate the change of temperature ; to calibrate the galvanometer the test specimen 
was plunged into water, at a known temperature, to within a short distance of the 
junction. 
Epiunp § applied the methods of JouLE to the determination of the effects of stress 
on wires, and instead of an iron-copper junction he used crystals of bismuth and 
antimony cut to a cylindrical form, and the cut ends were pressed against the wire, so 
that no variation in the thermo-electric power was possible, as might be the case if the 
natural cleavage plans were used. His results amply verify Jouur’s earlier work, and 
he, moreover, obtained an approximately correct value of the mechanical equivalent of 
* “Mémoire sur le calcul des actions moleculaires développées par les changements de température dans le corps 
solides,’—Mémoires . . . par divers savans, vol. v., 1838. 
+ “On the Dynamical Theory of Heat,” Trans. R.S.E., 1851. 
+ “On some Thermo-Dynamical Properties of Solids,” Trans. R.S., 1853. 
§ “Untersuchung iiber die bei voluniverinderung fester kérper entstehenden wiirmephaénomene, sowie derein 
verhaltniss zu dabei geleisteten mechanischen arbeit,” Pogg. Annal., vol. cxiv., 1861, and “Quantitative bestimmung 
der bei volumverianderung der metalle enstehenden wirmephinomene und die mechanischen wirmeaequivalents, 
unabhingig von der inneren arbeit des metalls,” Pogg. Annal., vol. cxxvi., 1865. 
