610 
Proceedings of the Boyal Society 
The following Communications were read 
1. On the Dynamical Theory of Heat. Part YII. By 
This paper commences with a condensed re-statement of the 
fundamental principles and formulae of the Dynamical Theory of 
Heat, from the first six parts of the author’s treatment of the sub- 
ject previously communicated to the Royal Society of Edinburgh, 
and his articles “ On the Thermo-elastic Properties of Matter,” 
in the “Quarterly Mathematical Journal” (April 1855), and 
on “ Thermo-magnetism,” and “ Thermo-electricity,” in Nichol’s 
Cyclopedia (Edinburgh 1860). 
The chief object of the paper is the deduction of numerical 
values in absolute measure for the thermo-electric effects which 
form the subject of Part VI. of this series (“ Transactions of the 
Royal Society of Edinburgh,” 1854; and “ Phil. Mag.” 1854, second 
half year, and 1855, first half year), especially for differences of 
temperature produced by electric convection of heat, and for the 
changes of temperature due to strain in elastic solids, investigated in 
the article on thermo-elastic properties of matter above referred to. 
The very valuable results, recently published, of the experiments of 
o 
Forbes and An^trbm for determining in absolute measure the 
thermal conductivities of iron and copper, supply a very important 
element, previously wanting, for definite estimates of those changes 
of temperature, and are taken advantage of in the present paper. 
Thus, the author has been enabled to give that practical character 
to some of his former conclusions, of which, when they were first 
published, he pointed out the want. In particular, with reference 
to elastic solids, the apjparent value of Young’s modulus * when 
the stress is applied and removed, or reversed so rapidly that the 
loss of thermal effect by conduction and radiation is insensible, is 
proved to be given by the following formula : — 
The amount of the force divided by the elongation produced by it, when 
any force within practical limits of elasticity is applied to elongate a bar rod 
or wire, of the substance, one square centimetre in section. 
Professor W. Thomson. 
