The same year, 1807, is still more memorable for the first instalment of Fourier’s investigations on the Conduction of Heat, whose importance extends far beyond the special subject. Mathematicians so eminent as Hamilton, Maxwell, and Kelvin have found it difficult to speak of Fourier in measured terms of appreciation, whether of the ingenuity of his mathematical processes, the elegance of his results, or of his broad and philosophical outlook, as revealed especially in the preface to his formal treatise. Fourier had indeed the advantage of a rather varied career. He was trained at first for the priesthood, then rejected for the (royalist) artillery school, with the remark in so many words that the lowliness of his origin would have disqualified him “even if he had been a second Newton.” He became a pupil at the École Normale, and later professor at the École Polytechnique. He was included in Napoleon’s expedition to Egypt, as a Member of the ambitious Egyptian Institute which it was proposed to found, and of which Monge was President. Returning to France in 1802 he was made prefect of the Department of the Isère, possibly on account of the administrative talent which he is said to have displayed in Egypt, and it was at Grenoble that he began the composition of his classical work. His subsequent history, though interesting and honourable, hardly concerns us, but the facts I have mentioned suggest that his varied and responsible experience, as well as the literary studies which were an obligatory part of his early education, and in which he is said to have excelled, was not without influence on his work, or on the luminous style in which it is explained. [Pg 11] At the very outset of his book we meet for the first time with a process which now seems so obvious and familiar that the mention of it may appear trivial. I mean the device by which the rate of change of a physical property at any point of a medium is calculated in terms of its flux into an element of volume. But it could hardly have been quite obvious, for many years elapsed before so simple a matter as the equation of continuity in Hydrodynamics was proved in this way by William Thomson, who also pointed out its utility in the expression of Laplace’s equation in curvilinear co-ordinates. At a later period the process received a brilliant extension at the hands of Maxwell, in his theory of gases, where it was applied to the flux of momentum and also of energy.