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ideas which must be combined, in order to produce the latter, are chiefly such as are associated by those Nighter connexions which take place when the mind is careless and disengaged. “ If you have real wit,': fays Lord Chesterfield, “ it will flow spontaneously, " and you need not aim at it; for in that case, the “ rule of the gospel is reversed; and it will prove, “ seek and you shall not find.” Agreeably to this observation, wit is promoted by a certain degree of intoxication, which prevents the exercise of that at. tention, which is necessary for invention in matters of Science. Hence too it is, that those who have the reputation of Wits, are commonly men confident in their own powers, who allow the train of their ideas to follow, in a great measure, its natural course; and hazard, in company, every thing, good or bad, that occurs to them. Men of modesty and taste seldom attempt wit in a promiscuous fociety; or if they are forced to make such an exertion, they are seldom suc. cessful. Such men, however, in the circle of their friends, to whom they can unbolom themselves with. out reserve, are frequently the most amusing and the most interesting of companions; as the vivacity of their wit is tempered by a correct judgment, and refined manners; and as its effect is heightened by that sensibility and delicacy, with which we so rarely find it accompanied in the common intercourse of life.

When a man of wit makes an exertion to distin. guish himself, his fallies are commonly too far fetched to please. He brings his mind into a state approach. ing to that of the inventor, and becomes rather inge, nious than witty. This is often the case with the wriY



ters whom Johnson distinguishes by the name of the Metaphysical Poets.

Those powers of Invention, which necessity occafionally calls forth in uncultivated minds, some individuals possess habitually. The related ideas which, in the case of the former, are brought together by the flow efforts of attention and recollection, present themselves to the latter, in consequence of a more systematical arrangement of their knowledge. The instantaneousness with which such remote combinations are effected, sometimes appear so wonderful, that we are apt to ascribe it to something like inspiration; but it must be remembered, that when any subject strongly and habitually occupies the thoughts, it gives us an interest in the observation of the most trivial circumstance which we suspect to have any relation to it, however distant; and by thus rendering the com. mon objects and occurrences which the accidents of life present to us, subservient to one particular employment of the intellectual powers, establishes in the memory a connection between our favourite pursuit, and all the materials with which experience and reflection have supplied us for the farther prosecution of it.

II. I observed, in the second place, that invention may be facilitated by general rules, which enable the inventor to direct the train of his thoughts into particular channels. These rules (to ascertain which, ought to be one principal object of the logician) will afterwards fall under my consideration, when I come to examine those intellectual processes which are subservient to the discovery of truth. At present, I shall confine myself to a few general remarks ; in ftating which I have no other aim than to fhew, to how great a degree invention depends on cultivation and habit, even in those sciences in which it is generally fuppofed that every thing depends on natural genius.


When we consider the geometrical discoveries of the antients, in the form in which they are exhibited in the greater part of the works which have survived to our times, it is feldom possible for us to trace the steps by which they were led to their conclusions : and, indeed, the objects of this science are so unlike those of all others, that it is not unnatural for a pera fon when he enters on the study, to be dazzled by its novelty, and to form an exaggerated conception of the genius of those men who first brought to light such a variety of truths, fo profound and so remote from the ordinary course of our speculations. We find, however, that even at the time when the antient analysis was unknown to the moderns; such mathematicians as had attended to the progress of the mind in the discovery of truth, concluded a priori, that the discoveries of the Greek geometers did not, at first, occur to them in the order in which they are stated in their writings. The prevailing opinion was, that they had been possessed of some secret method of investigation, which they carefully concealed from the world ; and that they published the result of their labours in such a form, as they thought would be most likely to excite the admiration of their readers. “ O quam bene foret,” says Petrus Nonius, “ fi qui « in fcientiis mathematicis scripserint authores, scripra “ reliquissent inventa sua eadem methodo, et per

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“ eosdem discursus, quibus ipsi in ea primum incide“ runt; et non, ut in mechanica loquitur Aristoteles “ de artificibus, qui nobis foris ostendunt suas quas “ fecerint machinas, sed artificium abscondunt, ut “ nagis appareant admirabiles. Est utique inventio “ in arte qualibet diversa multum a traditione : neque “ putandum est plurimas Euclidis et Archimedis pro

pofitiones fuiffe ab illis ea via inventas qua nobis « illi ipfas tradiderunt*.” The revival of the antient analysis, by some late mathematicians in this country, has, in part, justified these remarks, by shewing to how great a degree the inventive powers of the Greek geometers were aided by that method of investigation; and by exhibiting some striking specimens of address in the practical application of it.

The solution of problems, indeed, it may be said, is but one mode in which mathematical invention may be displayed. The discovery of new truths is what we chiefly admire in an original genius; and the me thod of analysis gives us no satisfaction with respect to the process by which they are obtained.

To remove this difficulty completely, by explaining all the various ways in which new theorems may be brought to light, would lead to inquiries foreign to this work. In order, however, to render the process of the mind, on such occasions, a little less mys. terious than it is commonly supposed to be; it may be proper to remark, that the most copious source of discoveries is the investigation of problems; which

* See some other passages to the same purpose, quoted from dif. ferent writers, by Dr. Simfon, in the preface to his Restoration of the Loci Plani of Appollonius Pergæus, Glasg. 1749.


seldom fails (even although we should not succeed in the attainment of the object which we have in view) to exhibit to us some relations formerly unobserved among the quantities which are under consideration. Of so great importance is it to concentrate the atten. tion to a particular subject, and to check that wandering and dissipated habit of thought, which, in the case of most persons, renders their speculations barren of any profit either to themselves or to others. Many theorems, too, have been suggested by analogy; many have been investigated from truths formerly known by altering or by generalising the hypothesis ; and many have been obtained by a fpecies of induction. An illustration of these various processes of the mind would not only lead to new and curious remarks, but would contribute to diminish that blind admiration of original genius, which is one of the chief obstacles to the improvement of science.

The history of natural philosophy, before and after the time of Lord Bacon, affords another very striking proof, how much the powers of invention and discovery may be assisted by the study of method : and in all the sciences, without exception, whoever employs his genius with a regular and habitual success, plainly shews, that it is by means of general rules that his inquiries are conducted. Of these rules,


which the inventor never stated to himself in words; and, perhaps, he may even be unconscious of the assistance which he derives from them; but their influence on his genius appears un. questionably from the uniformity with which it pro

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