“As early as the time of Leibnitz, it was suggested that a general form might be discovered for differential coefficients, somewhat in the same way as that which applies to expansions. Notwithstanding this suggestion, the difficulty of the subject appears to have deterred mathematicians from engaging in it, until a few years since M. Liouville published a series of memoirs, in which its principles are developed, and theorems deduced applicable to the solution of a variety of difficult and important problems. Amongst a mass of particular results, the generalization of each of which would probably give a distinct aspect to the science, M. Liouville appears to have selected that one which is the most readily applicable to practice, and which, at the same time, affords conclusions remarkably convincing of its completeness.