The paper by Maxwell “On Faraday’s Lines of Force,” written shortly after he had taken his degree, is now perhaps little read, but deserves attention if only for the introduction, written in his own incomparable style, where we find already laid down the lines on which his subsequent speculations were to proceed. From the mathematical standpoint the paper is a comprehensive statement, without a suggestion of theory, describing the known facts of Electro-magnetism in terms of a system of vectors supposed to exist at all points of the field. Precision is here given to Faraday’s idea of lines of [Pg 35] force, whether electric or magnetic, by means of the analogy of the motion of an incompressible fluid. The new vector here introduced into Electro-magnetism is that of momentum, and its rate of change is shewn by a dynamical, argument to be responsible for electro-magnetic induction. The proof of this depends on the expression for the energy of the field in terms of an integral extending over space, and is a deduction from the conservation of energy. The dynamical relation between pondero-motive and inductive forces had been indicated in a general way by Helmholtz in his celebrated tract, and this may possibly have been the first suggestion to Maxwell’s subsequent dynamical theory. The way was in fact now clear, so far as the mathematical scheme is concerned, for Maxwell’s definite theory. He ventured as we all know to go a step further and to look behind the mathematical relations for a deeper insight into the matter, and if possible for a physical or mechanical meaning of the analytical symbols. Regarding the question [Pg 36] as a dynamical one he sketched out a mechanical model of the ether which should reproduce the known electrical relations, rather with a view of convincing himself that such a model was possible than as a definite explanation in detail. This was followed by the classical paper in which the laws of electro-magnetism were shewn to be deducible from dynamical considerations, without the assumption of any particular mechanism. The final presentment in his treatise, in which use is made of Lagrange’s generalized equations, is too familiar to need further reference. Whether we prefer to regard it as an analogy or an explanation, it is a striking exemplification of the originality of Maxwell’s genius. At this point we may appropriately close our survey, for I do not undertake to be a guide in the subsequent history, which is still in the making. It is, however, to be remarked that Maxwell, who placed as it were the crown on one period of Mathematical Physics, was also in a sense the initiator of another, by his work on Gas Theory, which [Pg 37] involved the creation of a molecular calculus.