Thomson showed in the Elasticity article how, by the value of M'⧸M, derived as above from thermodynamic theory, the value of K⧸N could be obtained for different substances and for different types of stress, and gave very interesting tables of results for solids, liquids, and gases subjected to pressure-stress (bulk-modulus) and for solids subjected to longitudinal stress (Young's modulus). The discussion as to the relation of the adiabatic and isothermal moduli of elasticity is part of a very important paper on "Thermoelastic, Thermomagnetic, and Thermoelectric Properties of Matter," which he published in the _Philosophical Magazine_ for January 1878. This was in the main a reprint of an article entitled, "On the Thermoelastic and Thermomagnetic Properties of Matter, Part I," which appeared in April 1855 in the first number of the _Quarterly Journal of Mathematics_. Only thermoelasticity was considered in this article; the thermomagnetic results had, however, been indicated in an article on "Thermomagnetism" in the second edition of the _Cyclopædia of Physical Science_, edited and in great part written by Professor J. P. Nichol, and published in 1860. For the same Cyclopædia Thomson also wrote an article entitled, "Thermo-electric, Division I.--Pyro-Electricity, or Thermo-Electricity of Non-conducting Crystals," and the enlarged _Phil. Mag._ article also contained the application of thermodynamics to this kind of thermoelectric action. This great paper cannot be described without a good deal of mathematical analysis; but the student who has read the earlier thermodynamical papers of Thomson will have little difficulty in mastering it. It must suffice to say here that it may be regarded as giving the keynote of much of the general thermodynamic treatment of physical phenomena, which forms so large a part of the physical mathematics of the present day, and which we owe to Willard Gibbs Duhem, and other contemporary writers.