Soon after taking his degree Whewell began to lay the foundation of his reputation by great and varied activity as an author, as well as by the prominent part he took in all matters educational and constitutional concerning the college and university. His first work, An Elementary Treatise on Mechanics (1819), was influential—along with the works of Peacock and Herschel—in reforming the traditional method of mathematical teaching in Cambridge; and it was also largely due to him that, at a later period (1856), the circle of Cambridge studies was widened by the admission of the moral and natural sciences to an academic position. On the other hand, his attitude with respect to questions of university and college reform was (especially in later life) conservative. Claiming to be a reformer, he had yet no sympathy with the constitutional changes proposed at the time, and since commonly accepted as desirable and necessary. He upheld strenuously the tutorial system, while endeavouring to improve its efficiency; he opposed the admission of Dissenters to the university in a controversy with Thirl wall (1834); he defended the system of clerical fellowships, the custom which admitted a privileged class of students under the name of “fellow-commoners,” and the large powers which the “caput” or head of a college then possessed in university government. The appointment of the University Commission in 1850 encountered his opposition, and the proposed reform of the university in 1855 called forth from him two pamphlets of hostile Pemarks. The reform really wanted was, he contended, to encourage scientific and professorial work, and to utilize the college funds, not to put elections in the hands of the members of senate.

In the summer of 1826, and again in 1828, Whewell was engaged along with Airy in conducting experiments in Dolcoath mine, Cornwall, in order to determine the density of the earth. Their united labours were unsuccessful, and Whewell did little more in the way of experimental science. He was the author, however, of an Essay on Mineralogical Classification, published in 1828, and contributed various memoirs on the tides to the Philosophic,al Transactions of the Royal Society between 1833 and 1850. But it is on his History and Philosophy of the Sciences that his claim to an enduring reputation mainly rests. The History of the Inductive Sciences, from the Earliest to the Present Time appeared originally in 1837. Whewell’s wide acquaintance with various branches of science—though he cannot be said to have been a specialist in any department —enabled him to write a comprehensive account of their development, which has not yet been superseded, although it may want the thoroughness, and even in many respects the accuracy, of various subsequent histories of the special sciences. In his own opinion, moreover, the History was to be regarded as an introduction to the Philosophy of the Inductive Sciences (1840). The latter treatise analyses the method exemplified in the formation of ideas, in the new inductions of science, and in the applications and systematization of these inductions, all exhibited by the History in the process of development.

The Philosophy is described by the author as “an application of the plan of Bacon’s Novum Organum to the present condition of physical science,” and as an attempt “to extract from the actual past progress of science the elements of a more effectual and substantial method of discovery” than Bacon’s. The Philosophy is divided into two parts, treating respectively of ideas and of knowledge. The first part begins with an investigation of ideas in general, analysing the fundamental nature of scientific truths, the grounds of our knowledge of them, and the mental processes by which they are ascertained, and then applies these general principles to the philosophy of each of the subdivisions of science adopted in the History. The second part discusses knowledge or the construction of science, the processes by which our conceptions are brought to bear on facts, binding them together into ideal combinations. By the “explication of conceptions” the ideas appropriate to particular classes of facts are brought forward and explained; and by the “colligation of facts” the conceptions involving those ideas are united to the facts for the construction of science. But no art of discovery, such as Bacon anticipated, follows from the analysis of the method of scientific discovery; for the elements of “invention, sagacity, genius,” are needed at each forward step in scientific progress. At the same time Whewell claimed that the methods exhibited in his analysis were, not only the methods by which discoveries had actually been made, but also as definite and practical as any that had been put forward. The process of induction (or colligation of ascertained facts into general propositions) is analysed into three steps,—(1) the selection of the (fundamental) idea, such as space, number, cause, or likeness; (2) the formation of the conception, or more special modification of those ideas, as a circle, a uniform force, &c.; and (3) the determination of magnitudes. Upon these follow special methods of induction applicable to quantity, viz., the method of curves, the method of means, the method of least squares, and the method of residues, and special methods depending on resemblance (to which the transition is made through the law of continuity), viz., the method of gradation and the method of natural classification.

Whewell’s philosophy of science, as well as his ethical doctrine, was conditioned by opposition to the empirical tendency then prevalent amongst English thinkers. In this he was influenced by the results of the Kantian philosophy. He maintained the distinction between necessary and contingent truths,—the former involved in the innate constitution of the mind, the latter coming from experience. It is on this reference to the mind of what the current English philosophy attempted to derive from impressions of sense that the leading positions of his philosophy depend, and on it hinges the controversy between himself and J. S. Mill. He defended the a priori necessity of axioms attacked by the latter, and in his inductive theory attributed more importance to the function of the mental idea in the colligation of facts than Mill did, while he would have dispensed with the inductive methods of Mill by his rules for the constructioií of conceptions.

Between 1835 and 1861 Whewell was the author of various works on the philosophy of morals and politics, the chief of which, Elements of Morality, including Polity, was published in 1845. The peculiarity of this work—written, of course, from what is known as the intuitional point of view—is its fivefold division of the springs of action and of their objects, of the primary and universal rights of man (personal security, property, contrast, family rights, and government), and of the cardinal virtues (benevolence, justice, truth, purity, and order). Among Whewell’s other works—too numerous to mention—reference must be made to writings popular in their day, such as the Bridgewater Treatise on Astronomy (1833), and the essay, Of the Plurality of Worlds (1854), in which he argued against the probability of planetary life, and also to the Platonic Dialogues for English Readers (1859-61), to the Lectures on the History of Moral Philosophy in England (1852), to the essay, Of a Liberal Education in General, with particular reference to the Leading Studies of the University of Cambridge (1845), to the important edition and abridged translation of Grotius, De Jure Belli et Pacis (1853), and to the edition of the Mathematical Works of Isaac Barrow (1860).

Full bibliographical details are given by Isaac Todhunter, W. WΙιewell: αη Account of h is Writings, 2 vols. (1876). The Life of W. Wħewell has been written by Mrs Stair Douglas (1881).