-"Hope and fear, alternate, sway'd his breast;

Like light and shade upon a waving field,
Coursing each other, when the flying clouds
Now hide, and now reveal, the sun.'

Here the analogy is remarkably perfect; not only between light and hope, and between darkness and fear; but between the rapid succession of light and shade, and the momentary influences of these 'opposite emotions: while at the same time, the new image which is presented to us, recalls one of the most pleasing and impressive incidents in rural scenery.

The foregoing observations suggest a reason why the principal stores of fancy are commonly supposed to be borrowed from the material world. Wit has a more extensive province, and delights to display its power of prompt and unexpected combination over all the various classes of our ideas: but the favorite excursions of fancy, are from intellectual and moral subjects to the appearances with which our senses are conversant. The truth is, that such allusions please more than any others in poetry. According to this limited idea of fancy, it presupposes, where it is possessed in an eminent degree, an extensive observation of natural objects, and a mind susceptible of strong impressions from them. It is thus only that a stock of images can be acquired; and that these images will be ready to present themselves, whenever any analogous subject occurs. And hence probably it is, that poetical genius is almost always united with an exquisite sensibility to the beauties of nature.

Before leaving the subject of fancy it may not be improper to remark that its two qualities are, liveliness and luxuriancy. The word lively, refers to the quickness of the association. The word rich, or luxuriant, to the variety of associated ideas.

IV. Of Invention in the Arts and Sciences.

To these powers of wit and fancy, that of invention in the arts and sciences has a striking resemblance. Like them it implies a command over certain classes of ideas, which, in ordinary men, are not equally subject to the will, and, like them, too, it is the result of acquired habits, and not the original gift of nature.

Of the process of the mind in scientific invention, I propose afterwards to treat fully under the article of reasoning, and I shall therefore confine myself at present to a few detached remarks upon some views of the subject which are suggested by the foregoing inquiries.

Before we proceed it may be proper to take notice of the distinction between invention and discovery. The object of the former, as has been frequently remarked, is to produce something which had no existence before; that of the latter to bring to light something which did exist, but which was concealed from common observation. Thus we say, Otto Guerricke invented the air-pump;

Sanctorious invented the thermometer; Newton and Gregory invented the reflecting telescope; Galileo discovered the solar spots; and Harvey discovered the circulation of the blood. It appears, therefore, that improvements in the arts are properly called inventions, and that facts brought to light by means of observation are properly called discoveries.

As

Agreeable to this analogy is the use which we make of these words when we apply them to subjects purely intellectual. truth is eternal and immutable, and has no dependence on our belief or disbelief of it, a person who brings to light a truth formerly unknown is said to make a discovery. A person, on the other hand, who contrives a new method of discovering truth is called an inventor. Pythagoras, we say, discovered the fortyseventh proposition of Euclid's first book; Newton discovered the binomial theorein; but he invented the method of prime and ultimate ratios, and he invented the method of fluxions.

In general, every advancement in knowledge is considered as a discovery; every contrivance by which we produce an effect, or accomplish an end, is considered as an invention. Discoveries in science, therefore, unless they are made by accident, imply the exercise of invention, and accordingly the word invention is commonly used to express originality of genius in the sciences as well as in the arts. It is in this general sense that I employ it in the following observations.

It was before remarked that in every instance of invention there is some new idea, or some new combination of ideas, which is brought to light by the inventor, and that although this may sometimes happen in a way which he is unable to explain, yet when a man possesses an habitual fertility of invention in any particular art or science, and can rely with confidence on his inventive powers whenever he is called upon to exert them, he must have acquired, by previous habits of study, a command over those classes of his ideas which are subservient to the particular effort that he wishes to make. In what manner this command is acquired, it is not possible, perhaps, to explain completely, but it appears to me to be chiefly in the two following ways. In the first place, by his habits of speculation he may have arranged his knowledge in such a manner as may render it easy for him to combine, at pleasure, all the various ideas in his mind which have any relation to the subject about which he is occupied or, secondly, he may have learned by experience certain general rules, by means of which he can direct the train of his thoughts into those channels in which the ideas he is in quest of may be most likely to occur to him.

1. The former of these observations I shall not stop to illustrate particularly at present, as the same subject will occur afterwards under the article of memory. It is sufficient for my purpose, in this chapter, to remark, that as habits of speculation have a tendency to classify our ideas, by leading us to refer particular facts

and particular truths to general principles, and as it is from an approximation and comparison of related ideas that new discoveries in most instances result, the knowledge of the philosopher, even supposing that it is not more extensive, is arranged in a manner much more favorable to invention than in a mind unaccustomed to system. How much invention depends on a proper combination of the materials of our knowledge, appears from the resources which occur to men of the lowest degree of ingenuity when they are pressed by any alarming difficulty and danger, and from the unexpected exertions made by very ordinary characters when called to situations which rouse their latent powers. In such cases, I take for granted, that necessity operates in producing invention, chiefly by concentrating the attention of the mind to one set of ideas, by leading us to view these in every light, and to combine them variously with each other. As the same idea may be connected with an infinite variety of others by different relations, it may, according to circumstances, at one time suggest one of these ideas, and at another time a different one. When we dwell long on the same idea, we obtain all the others to which it is any way related, and thus are furnished with materials on which our powers of judgment and reasoning may be employed. The effect of the division of labor in multiplying mechanical contrivances is to be explained partly on the same principle. It limits the attention to a particular subject, and familiarizes to the mind all the possible combinations of ideas which have any relation to it.

These observations suggest a remarkable difference between invention and wit. The former depends, in most instances, on a combination of those ideas, which are connected by the less obvious principles of association; and it may be called forth in almost any mind by the pressure of external circumstances. The ideas which must be combined, in order to produce the latter, are chiefly such as are associated by those slighter connexions which take place when the mind is careless and disengaged. "If you have real wit," says 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 attention 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 society; or if they are forced to make such an exertion, they are seldom successful. Such men, however, in the circle of their friends, to whom they can unbosom themselves without 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 distinguish himself, his sallies are commonly too far-fetched to please. He brings his mind into a state approaching to that of the inventor, and becomes rather ingenious than witty. This is often the case with the writers whom Johnson distinguishes by the name of the metaphysical poets.

Those powers of invention, which necessity occasionally calls forth in uncultivated minds, some individuals possess habitually. The related ideas which, in the case of the former, are brought together by the slow 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 circumstances which we suspect to have any relation to it, however distant: and by thus rendering the common 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 connexion between our favorite 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 stating which I have no other aim than to show, to how great a degree invention depends on cultivation and habit, even in those sciences in which it is generally supposed that everything depends on natural genius.

When we consider the geometrical discoveries of the ancients in the form in which they are exhibited in the greater part of the works which have survived to our times, it is seldom 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 person 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, so profound and so remote from the ordinary course of our speculations. We find, however, that even at the time when the ancient analysis was unknown to the moderns, such

mathematicians as had attended to the progress of the mind in the discovery of truth, concluded à 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 possessed some secret method of investigation, which they carefully concealed from the world; and that they published the result of their labors 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, "si qui in scientis mathematicis scripserint authores, scripta reliquissent inventa sua eadem methodo, et per eosdem discursus, quibus ipsi in ea primum inciderunt; et non, ut in mechanica loquitur Aristoteles de artificibus, qui nobis foris ostendunt suas quas fecerint machinas, sed artificium abscondunt, ut magis appareant admirabiles. Est utique inventio in arte qualibet diversa multum a traditione: neque putandum est plurimas Euclidis et Archimedis propositiones fuisse ab illis ea via inventas qua nobis illi ipsas tradiderunt."* The revival of the ancient analysis, by some late mathematicians in this country, has, in part, justified these remarks, by showing 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 method 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 mysterious 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 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 attention 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 generalizing the hypothesis; and many have been obtained by a species of induction. An illustration of these various processes of the mind would not only lead to

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