Passages from the Life of a Philosopher

a finger, those passages which gave her most delight. These quiet indications, unobserved by my friends, formed the electric wire by which I directed the expressions of my own {428} countenance and the very modest applause I thought it prudent to develop. After receiving the con­grat­u­la­tions of my friends upon my great musical taste, I informed them how easily that reputation had been acquired. Such are the feeble bases on which many a public character rests. During my residence with my Oxford tutor, whilst I was working by myself on mathematics, I oc­ca­sion­al­ly arrived at conclusions which appeared to me to be new, but which from time to time I afterwards found were already well known. At first I was much discouraged by these disappointments, and drew from such occurrences the inference that it was hopeless for me to attempt to invent anything new. After a time I saw the fallacy of my reasoning, and then inferred that when my knowledge became much more extended I might reasonably hope to make some small additions to my favourite science. 〈PHILOSOPHY OF INVENTION.〉 This idea considerably influenced my course during my residence at Cambridge by directing my reading to the original papers of the great discoverers in math­e­mat­i­cal science. I then endeavoured to trace the course of their minds in passing from the known to the unknown, and to observe whether various artifices could not be connected together by some general law. The writings of Euler were eminently instructive for this purpose. At the period of my leaving Cambridge I began to see more distinctly the object of my future pursuit. It appeared to me that the highest exercise of human faculties consisted in the endeavour to discover those laws of thought by which man passes from the known to that which {429} was unknown. It might with propriety be called the philosophy of invention. During the early part of my residence in London, I commenced several essays on Induction, Generalization, Analogy, with various illustrations from different sources. The philosophy of signs always occupied my attention, and to whatever subject I applied myself I was ever on the watch to perceive and record the links by which the new was connected with the known. 〈EARLY ESSAYS.〉 Most of the early essays I refer to were not sufficiently matured for publication, and several have appeared without any direct reference to the great object of my life. I may, however, point out one of my earlier papers in the “Philosophical Transactions for 1817,” which, whilst it made considerable additions to a new branch of science, is itself a very striking instance of the use of analogy for the purpose of invention. I refer to the “Essay on the Analogy between the Calculus of Functions and other Branches of Analysis.”—Phil. Trans. 1817.