Looking back on this long history we can trace through all the details an increasing tendency. The period we have been reviewing began under the influence of the great achievements of Laplace and Lagrange in the development of the Newtonian Astronomy. The notion of action at a distance, though not regarded by Newton himself as the last word on the matter, had had a great success, and when the field of Physical Astronomy was beginning to be fully occupied, the mathematicians who turned their attention to physical questions very naturally assumed that the same conception would be fruitful in other directions. Fortunately there was one physical process where these ideas obviously did not apply. Heat was indeed imagined to be a material, and moreover a fluid substance, but hardly molecular, and its transmission in conductors was naturally regarded as a continuous process. To this we owe the work of Fourier, which stands by itself, outside the historical order of development, except in so far as the solution of particular [Pg 38] problems involved analytical processes, and led to analytical theorems which had a much wider scope. When the molecular structure of bodies was taken into account, as in the early days of Elasticity, the steps were somewhat vague and uncertain, and I think that the writers themselves must have experienced some relief when they had finally arrived at their differential equations, and felt really at home. It was a great improvement when the consideration of molecular forces could be dispensed with and replaced by Cauchy’s theory of stress. The same tendency to discard unnecessary and unverifiable hypothesis has been exemplified in Electricity, in the transition from Poisson and Ampère to Thomson and Maxwell.