321 ideas which must be combined, in order to produce the latter, are chiefly fuch as are affociated by those flighter connexions which take place when the mind is careless and difengaged. "If you have real wit,' fays Lord Chesterfield, "it will flow spontaneously, " and you need not aim at it; for in that cafe, the "rule of the gospel is reverfed; and it will prove, "seek and you fhall not find." Agreeably to this observation, wit is promoted by a certain degree of intoxication, which prevents the exercise of that attention, which is neceffary 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 modefty and taste seldom attempt wit in a promifcuous fociety; or if they are forced to make fuch an exertion, they are seldom fuccessful. Such men, however, in the circle of their friends, to whom they can unbofom themselves without reserve, are frequently the most amufing 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 fenfibility and delicacy, with which we fo rarely find it accompanied in the common intercourse of life.

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

ters

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

Those powers of Invention, which neceffity occafionally calls forth in uncultivated minds, fome individuals poffefs habitually. The related ideas which, in the cafe of the former, are brought together by the flow efforts of attention and recollection, prefent themselves to the latter, in confequence of a more fyftematical arrangement of their knowledge. The inftantaneoufnefs with which fuch remote combinations are effected, fometimes appear fo wonderful, that we are apt to ascribe it to fomething like inspiration; but it must be remembered, that when any fubject ftrongly and habitually occupies the thoughts, it gives us an intereft in the obfervation of the most trivial circumstance which we suspect to have any relation to it, however diftant; and by thus rendering the common objects and occurrences which the accidents of life present to us, fubfervient to one particular employment of the intellectual powers, establishes in the memory a connection between our favourite purfuit, and all the materials with which experience and reflection have supplied us for the farther prosecution of it.

II. I obferved, in the fecond place, that invention may be facilitated by general rules, which enable the inventor to direct the train of his thoughts into parti cular channels. These rules (to ascertain which, ought to be one principal object of the logician) will afterwards fall under my confideration, when I come to examine those intellectual proceffes which are fubfervient to the discovery of truth. At prefent, I shall

confine

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 confider the geometrical discoveries of the antients, in the form in which they are exhibited in the greater part of the works which have furvived to our times, it is feldom poffible for us to trace the steps by which they were led to their conclufions: and, indeed, the objects of this fcience are fo unlike thofe of all others, that it is not unnatural for a perfon 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 fuch a variety of truths, fo profound and fo remote from the ordinary courfe of our fpeculations. We find, however, that even at the time when the antient analyfis was unknown to the moderns; fuch mathematicians as had attended to the progrefs 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 poffeffed of fome fecret method of investigation, which they carefully concealed from the world; and that they published the refult of their labours in fuch a form, as they thought would be moft likely to excite the admiration of their readers. "O quam bene foret," fays Petrus Nonius, " fi qui "in fcientiis mathematicis fcripferint authores, fcripta

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reliquiffent inventa fua eadem methodo, et per

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"eofdem

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"eofdem difcurfus, quibus ipfi in ea primum inciderunt; et non, ut in mechanica loquitur Ariftoteles ❝de artificibus, qui nobis foris oftendunt fuas quas "fecerint machinas, fed artificium abfcondunt, ut "magis appareant admirabiles. Eft utique inventio "in arte qualibet diverfa multum a traditione: neque "putandum eft plurimas Euclidis et Archimedis pro"pofitiones fuiffe ab illis ea via inventas qua nobis "illi ipfas tradiderunt*." The revival of the antient analysis, by fome late mathematicians in this country, has, in part, juftified these remarks, by fhewing to how great a degree the inventive powers of the Greek geometers were aided by that method of investigation; and by exhibiting fome ftriking fpecimens of address in the practical application of it.

The folution of problems, indeed, it may be faid, 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 method of analysis gives us no fatisfaction with refpect 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 procefs of the mind, on fuch occafions, a little less myf. terious than it is commonly fuppofed to be; it may be proper to remark, that the moft copious fource of discoveries is the investigation of problems; which

*See fome other paffages to the fame purpofe, quoted from different writers, by Dr. Simfon, in the preface to his Restoration of the Loci Plani of Appollonius Pergæus, Glafg. 1749.

feldom

feldom fails (even although we should not succeed in the attainment of the object which we have in view) to exhibit to us fome relations formerly unobferved among the quantities which are under confideration. Of fo great importance is it to concentrate the attention to a particular fubject, and to check that wandering and diffipated habit of thought, which, in the case of most perfons, renders their fpeculations barren of any profit either to themselves or to others. Many theorems, too, have been fuggefted by analogy; many have been investigated from truths formerly known by altering or by generalifing the hypothefis; and many have been obtained by a fpecies of induction. An illustration of these various proceffes 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 obftacles to the improvement of science.

The history of natural philofophy, before and after the time of Lord Bacon, affords another very strik ing proof, how much the powers of invention and discovery may be affifted by the study of method: and in all the sciences, without exception, whoever employs his genius with a regular and habitual fuccefs, plainly fhews, that it is by means of general rules that his inquiries are conducted. Of these rules, there may be many which the inventor never stated to himself in words; and, perhaps, he may even be unconscious of the affiftance which he derives from them; but their influence on his genius appears unquestionably from the uniformity with which it proceeds;

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