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PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
depending on circumstances which we cannot completely control. Take as an example 
the energy possessed by a stretched spring : part of the energy depends upon the 
extension of the spring; we have complete control over this, but another part of the 
energy (the heat energy) depends upon the motion of the molecules of the spring, and, 
although we have some control over the average motion of all the molecules, we have 
none over the motion of individual molecules. Let us for the moment call the energy 
of the first kind “ controllable energy,” that of the second “ intrinsic energy.” We may 
look on an engine as a means of converting intrinsic into controllable energy. Then, 
if we follow the connection between the axiom and the principle that the efficiency of 
a perfectly reversible engine is a maximum (which we may take as equivalent to the 
Second Law), we shall see that if the axiom is to cover all the cases to which the Second 
Law has been applied it must be equivalent to the statement that it is impossible to 
derive mechanical effect by abstracting intrinsic energy from the refrigerator. Now 
the intrinsic energy consists, in addition to sensible heat, of wdiat Clausius calls the 
internal energy of the body, that is, energy depending upon the arrangement of the 
molecules, and, it may be, also upon their motion. If we consider the various forms 
which this intrinsic energy can take, the statement that it is impossible to derive 
mechanical effect by abstracting intrinsic energy from the refrigerator would seem to 
be hardly more axiomatic than the Second Law itself. 
The Second Law of Thermodynamics, like the Law of Gravitation, seems then to be 
proved rather by the truth of its consequences than by any a 'priori considerations. 
For this, among other reasons, I have thought it might perhaps be interesting to 
deduce by the use of purely dynamical principles many results which are usually 
obtained by the aid of the Second Law 7 of Thermodynamics, as well as some others 
which, so far as I know, have not previously been obtained. This I have endeavoured 
to do in the following paper, as I did in one previously published under the same title 
in the ‘ Philosophical Transactions,’ 1885, Part 1. In the first paper I considered the 
relation between thermal, elastic, and magnetic phenomena, but did not consider any 
phenomena in which chemical or quasi-chemical processes w 7 ere concerned, such as 
dissociation, evaporation, solution, chemical combination : or any effects which are not 
reversible, such as those produced by the electric resistance of metals and electro¬ 
lytes. In this paper I shall endeavour to apply the same or analogous principles to 
the phenomena mentioned above, as well as to a few additional phenomena of the 
kind discussed in the first paper. 
Though the dynamical method is open to the objection that the quantities made 
use of are those which occur in abstract Dynamics, such as mass, velocity, energy, 
acceleration, and so require further knovdeclge before w 7 e can connect them with such 
things as temperature, electric current, resistance, and so on—a knowdedge which, in 
many cases, we do not possess—while, in the Second Law, the results are expressed 
in terms of quantities which can be readily measured; still it has advantages which 
make it worthy of consideration. 
