The foregoing remarks, in so far as they relate to the possibility of assisting our reasoning and inventive powers by new instrumental aids, may perhaps appear to be founded too much upon theory; but this objection cannot be made to the reasonings I have offered on the importance of the study of method.-To the justness of these, the whole history of science bears testimony, but more especially, the histories of Physics and of pure Geometry; which afford so remarkable an illustration of the general doctrine, as can scarcely fail to be satisfactory, even to those who are the most disposed to doubt the efficacy of art in directing the exertions of genius.

With respect to the former, it is sufficient to mention the wonderful effects which the writings of Lord Bacon have produced, in accelerating its progress. The philosophers, who flourished before his time, were, undoubtedly, not inferiour to their successors, either in genius or industry but their plan of investigation was erroneous; and their labours have produced only a chaos of fictions and absurdities. The illustrations which his works contain, of the method of induction, general as the terms are in which they are expressed, have gradually turned the attention of the moderns to the rules of philosophizing; and have led the way to those important and sublime discoveries in physics, which reflect so much honour on the present age.

The rules of philosophizing, however, even in physics, have never yet been laid down with a sufficient degree of precision, minuteness, or method; nor have they ever been stated and illustrated in so clear and popular a manner, as to render them intelligible to the generality of readers. The truth, perhaps, is, that the greater part of physical inquirers have derived what knowledge of them they possess, rather from an attention to the excellent

models of investigation which the writings of Newton exhibit, than from any of the speculations of Lord Bacon, or his commentators: and, indeed, such is the incapacity of most people for abstract reasoning, that I am inclined to think, even if the rules of inquiry were delivered in a perfectly complete and unexceptionable form, it might still be expedient to teach them to the majority of students, rather by examples, than in the form of general principles. But it does not therefore follow, that an attempt to illustrate and to methodize these rules would be useless; for it must be remembered, that, although an original and inventive genius, like that of Newton, be sufficient to establish a standard for the imitation of his age, yet, that the genius of Newton himself was encouraged and led by the light of Bacon's philosophy.

The use which the ancient Greek geometers made of their analysis, affords an additional illustration of the utility of method in guiding scientific invention. To facilitate the study of this species of investigation, they wrote no less than thirty-three preparatory books; and they considered address, in the practice of it, (or, as Marinus calls it, a duvauis avaλutixn) as of much more value, than an extensive acquaintance with the principles of the science.* Indeed, it is well known to every one who is at all conversant with geometrical investigations, that although it may be possible for a person, without the assistance of the method of analysis, to stumble accidentally on a solution, or on a demonstration, yet it is impossible for him to possess a just confidence in his own powers, or to carry on a regular plan of invention and discovery. It is well known, too, that an acquaintance with this method brings

* Μείζον εςι το δυναμιν αναλυτικών κτίσασθαι, του πολλας αποδείξεις την επι

geometers much more nearly upon a level with each other, than they would be otherwise not that it is possible, by any rules, to supersede, entirely, ingenuity and address; but, because, in consequence of the uniformity of the plan on which the method proceeds, experience communicates a certain dexterity in the use of it, which must in time give to a very ordinary degree of sagacity, a superiority, on the whole, to the greatest natural ingenuity, unassisted by rule.*

To these observations, I believe I may add, that, after all that was done by the Greek philosophers to facilitate mathematical invention, many rules still remain to be suggested, which might be of important use, even in pure geometry. A variety of such occur to every experienced mathematician in the course of his inquiries, although, perhaps, he may not be at the trouble to state them to himself in words; and it would plainly have saved him much expense of time and thought, beside enabling him to conduct his researches on a more regular plan, if he had been taught them systematically at the commencement of his studies. The more varied, abstruse, and general investigations of the moderns stand in need, in a much greater degree, of the guidance of philosophical principles; not only for enabling us to conduct, with skill, our particular researches, but for directing us to the different

* "Mathematica multi sciunt, mathesin pauci. Aliud est enim nosse propositiones aliquot, et nonnullas ex iis obvias elicere, casu potius quam certa aliqua discurrendi norma, aliud scientiæ ipsius naturam ac indolem perspectam habere, in ejus se adyta penetrare, et ab universalibus instructum esse præceptis, quibus theoremata ac problemata innumera excogitandi, eademque demonstrandi facilitas comparetur. Ut enim pictorum vulgus prototypon sæpe sæpius exprimendo, quendam pingendi usum, nullam vero pictoriæ artis quam optica suggerit scientiam adquirit, ita multi, lectis Euclidis et aliorum geometrarum libris, eorum imitatione fingere propositiones aliquas ac demonstrare solent, ipsam tamen secretissimam difficiliorum theorematum ac problematum solvendi methodum prorsus ignorant."-Joannis de la Faille Theoremata de Centro Gravitatis, in præfat.-Antwerpiæ, 1632.

methods of reasoning, to which we ought to have recourse on different occasions. A collection of such rules would form, what might be called with propriety, the logic of mathematics; and would probably contribute greatly to the advancement of all of those branches of knowledge, to which mathematical learning is subservient.

The observations which have been now made, on the importance of method in conducting physical and mathematical researches, particularly those which relate to the last of these subjects, will not apply literally to our inquiries in metaphysics, morals, or politics; because, in these sciences, our reasonings always consist of a comparatively small number of intermediate steps, and the obstacles which retard our progress, do not, as in mathematics, arise from the difficulty of finding media of comparison among our ideas. Not that these obstacles are less real, or more easily surmounted; on the contrary, it seems to require a still rarer combination of talents to surmount them; for how small is the number of individuals, who are qualified to think justly on metaphysical, moral, or political subjects, in comparison of those, who may be trained by practice to follow the longest processes of mathematical reasoning. From what these obstacles arise, I shall not inquire particularly at present. Some of the more important of them may be referred to the imperfections of language; to the difficulty of annexing precise and steady ideas to our words; to the difficulty, in some cases, of conceiving the subjects of our reasoning; and, in others, of discovering, and keeping in view, all the various circumstances upon which our judgment ought to proceed; and above all, to the prejudices which early impressions and associations create, to warp our opinions.-To illustrate these sources of errour, in the different sciences which are liable to be affected by them, and to point out the most

effectual means for guarding against them, would form another very interesting article in a philosophical system of logic.

The method of communicating to others the principles of the different sciences, has been as much neglected by the writers on logic, as the rules of investigation and discovery, and yet, there is certainly no undertaking whatever, in which their assistance is more indispensably requisite. The first principles of all the sciences are intimately connected with the philosophy of the human mind; and it is the province of the logician to state these in such a manner, as to lay a solid foundation for the superstructures which others are to rear.-It is in stating such principles, accordingly, that elementary writers are chiefly apt to fail. How unsatisfactory, for example, are the introductory chapters in most systems of natural philosophy! not in consequence of any defect of physical or of mathematical knowledge in their authors, but in consequence of a want of attention to the laws of human thought, and to the general rules of just reasoning. The same remark may be extended to the form, in which the elementary principles of many of the other sciences are commonly exhibited; and, if I am not mistaken, this want of order among the first ideas which they present to the mind, is a more powerful obstacle to the progress of knowledge, than is generally imagined.

I shall only observe farther, with respect to the utility of the philosophy of mind, that as there are some arts, in which we not only employ the intellectual faculties as instruments, but operate on the mind as a subject, so, to those individuals who aim at excellence in such pursuits, the studies I have now been recommending are, in a more peculiar manner, interesting and important. In poetry, in painting, in eloquence, and in all the other fine arts, our