DK. JOULE ON SOME THERMO-DYNAMIC PROPERTIES OE SOLIDS. 
127 
120. The above results, as in the case of the tension experiments, indicate a slight 
excess of experiment over theory. I at first thought that this might be owing to the 
diminution of elastic force by heat in metals, of which I had not taken account as in 
wood, for in applying or removing tension the thermal efiect would be increased in con- 
sequence of the increased expansion by heat in such a case. This cause would, however, 
diminish the thermal effect of the application or removal of pressure. The discrepancy 
must therefore be referred to experimental error, or to the incorrectness of the various 
coefllcients which make up the theoretical results. Having, however, been led to be- 
lieve that with a rise of temperature a certain change of elasticity takes place in metals, 
although too minute to be appreciated in the foregoing results, I made some experiments 
in which spirals weighted at one end were measured when exposed to cold air, and then 
again after they had been heated in the atmosphere of an oven. In the latter case there 
was considerable elongation, indicating, in the case of steel, a diminution of elasticity 
amounting to -00041 per degree Centigrade, and in the case of copper, to -00047. After 
I had made these experiments, I became acquainted with M. Kupffee’s valuable re- 
searches on this subject, by which, using the method of vibrations, he finds the decre- 
ment of elasticity per degree Centigrade in steel and copper to be -00047 and -00048 
respectively. 
121. Another source of error exists, which, although not of sufficient amount to make 
a sensible alteration in the thermal effects of tension and pressure on metals, yet ought 
not to be neglected in a complete view of the subject. Mr. Hodgkinson has long ago 
shown that any force, however small, is able to produce a certain permanent deflection 
in a bar, and that this deflection increases rapidly with the force which has produced it. 
Professor Thomson has added the observation, that even after a metal has been exposed 
to great tensile force, its elasticity is not thereby rendered perfect for smaller degrees of 
stress. Thus he flnds that when weights are successively hung to a wire so as gradually 
to increase its tension, and then successively removed, the wire never assumes immediately 
its just length, but is always shorter during the putting on of the weights than during 
their removal. Hence work is done on the wire which must necessarily evolve a certain 
quantity of heat ; and if, as is probable, a greater quantity of work is thus done whilst 
the tensile force is being removed than whilst it is being applied, the result will be 
that the cold of tension will not be diminished to the same extent as the heat, in con- 
sequence of the removal of tension, will be increased, and so the mean thermal effect 
will be increased. On the other hand, it is probable that in the act of compression less 
work is done on the wire than during the removal of the compressing force, the result 
being that the mean thermal effect of applying and removing the pressure is lessened. 
The foregoing experiments do not afford sufficiently delicate tests to detect the excess- 
ively minute quantities of heat developed frictionally in the above manner. 
122. Professor Thomson has pointed out that the dynamical theory of heat, with the 
modification of Caenot’s principle introduced by himself and Clausius, show that “ if 
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