207 
of Edinburgh, Session 1863 - 64 . 
countryman, Mr Grreen, and was led to the principle of Electrical 
Images , by which he was enabled to solve many problems respect- 
ing the distribution of electricity on conductors, which had been 
regarded as almost hopeless by the most eminent mathematicians 
in Europe. 
In his researches on Thermo-dynamics, Professor Thomson has 
been equally successful. In his paper “ On the Dynamical Theory 
of Heat,” published in our Transactions for 1851, he has applied 
the fundamental propositions of the theory to bodies of all kinds, 
and has deduced many curious and important results regarding the 
specific heats of bodies, which have been completely verified by the 
accurate experiments of Mr Joule. 
No less important are Professor Thomson’s researches on Solar 
Heat, contained in his remarkable paper “ On the Mechanical Energy 
of the Solar Sj^^stem his researches on the Conservation of Energy 
as applied to organic as w^ell as inorganic processes ; and his fine 
theory of the Dissipation of Energy, as given in his paper “ On a Uni- 
versal Tendency in Nature to the Dissipation of Mechanical Energy.” 
To these we may add his complete Theory of Diamagnetic Action, and 
his investigations relative to the Secular Cooling of our Olobe, and 
the influence of Internal Heat upon the temperature of its surface. 
The value of labours like these could not escape the notice of 
the Council of this Society, and they would have entitled their 
author to the Keith Prize, had they not been presented to the 
Society when the Prize was devoted to other branches of Science. 
It is not, therefore, for these researches and discoveries that the 
Keith Medal has been awarded to Professor Thomson, but for the 
very interesting and important discovery, in Abstract Dynamics, 
which he has communicated to the Society during the biennial period 
appropriated to Physical Science. 
By the previous researches of Euler, Lagrange, Delaunay, and 
Bertrand, it had been established that when any system of bodies, 
connected by any invariable kinematic relations, is struck with 
impulses of any kind, the kinetic energy thus developed is a 
maximum. This remarkable principle is of very great use in the 
investigation of certain complex dynamical problems, but in many 
important cases it is inapplicable. In the motion, for example, of 
an incompressible liquid, contained in a vessel whose form is suddenly 
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