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 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, " si qui in scientiis mathematicis scrip"serint 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 Eucli"dis 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 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.

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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 dissi

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 Apollonius Pergaeus, Glasg 1749.

1

pated 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 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, there may be many 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 unquestionably from the uniformity with which it proceeds; and in proportion as they can be ascertained by his own speculations, or collected by the logician from an examination of his researches, similar powers of invention will be placed within the reach of other men, who apply themselves to the same study.

The following remarks, which a truly philosophical artist has applied to painting, may be extended with some trifling alterations, to all the different employments of our intellectual powers.

"What we now call genius begins, not where rules, abstractedly "taken, end; but where known, vulgar, and trite rules have no "longer any place.-It must of necessity be, that works of genius, "as well as every other effect, as it must have its cause, must like"wise have its rules; it cannot be by chance, that excellencies are "produced with any constancy, or any certainty, for this is not the "nature of chance; but the rules by which men of extraordinary "parts, and such as are called men of genius, work, are either such as they discover by their own peculiar observation, or of such a "nice texture as not easily to admit handling or expressing in words.

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"Unsubstantial, however, as these rules may seem, and difficult "as it may be to convey them in writing, they are still seen and felt "in the mind of the artist; and he works from them with as much certainty, as if they were embodied, as I may say, upon paper. It "is true, these refined principles cannot be always made palpable, "like the more gross rules of Art; yet it does not follow, but that "the mind may be put in such a train, that it shall perceive, by a "kind of scientific sense, that propriety, which words can but very "feebly suggest."*

*Discourses by Sir Joshua Reynolds.

part 1. § 5.]

OF THE HUMAN MIND,

SECTION V.

Application of the Principles stated in the foregoing Sections of this Chapter, to explain the Phenomena of Dreaming.

WITH respect to the Phenomena of Dreaming, three different questions may be proposed. First; What is the state of the mind in sleep? or, in other words, what faculties then continue to operate, and what faculties are then suspended? Secondly; how far do our dreams appear to be influenced by our bodily sensations; and in what respects do they vary, according to the different conditions of the body in health, and in sickness? Thirdly; what is the change which sleep produces on those parts of the body, with which our mental operations are more immediately connected; and how does this change operate, in diversifying, so remarkably, the phenomena which our minds then exhibit, from those of which we are conscious in our waking hours? Of these three questions, the first belongs to the philosophy of the Human Mind; and it is to this question that The second is the following inquiry is almost entirely confined. more particularly interesting to the Medical inquirer, and does not properly fall under the plan of this work. The third seems to me to relate to a subject, which is placed beyond the reach of the human faculties.

It will be granted, that, if we could ascertain the state of the mind in sleep, so as to be able to resolve the various phenomena of dreaming into a smaller number of general principles; and still more, if we could resolve them into one general fact, we should be advanced a very important step in our inquiries upon this subject; even although we should find it impossible to shew, in what manner this change in the state of the mind results from the change which sleep produces in the state of the body. Such a step would at least gratify, to a certain extent, that disposition of our nature which prompts us to ascend from particular facts to general laws, and which is the foundation of all our philosophical researches; and, in the present instance, I am inclined to think, that it carries us as far as our imperfect faculties enable us to proceed.

In conducting this inquiry with respect to the state of the mind in sleep, it seems reasonable to expect, that some light may be obtained from an examination of the circumstances which accelerate or retard its approach; for when we are disposed to rest, it is natural to imagine, that the state of the mind approaches to its state in sleep, more nearly, than when we feel ourselves alive and active, and capable of applying all our various faculties to their proper purposes. In general, it may be remarked, that the approach of sleep is accelerated by every circumstance which diminishes or suspends the exercise of the mental powers, and is retarded by every thing which When we wish for sleep, we naturally has a contrary tendency. endeavour to withhold, as much as possible, all the active exertions

VOL. I.

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of the mind, by disengaging our attention from every interesting subject of thought. When we are disposed to keep awake, we naturally fix our attention on some subject which is calculated to afford employment to our intellectual powers, or to rouse and exercise the active principles of our nature.

It is well known, that there is a particular class of sounds which compose us to sleep. The hum of bees; the murmur of a fountain; the reading of an uninteresting discourse, have this tendency in a remarkable degree. If we examine this class of sounds, we shall find that it consists wholly of such as are fitted to withdraw the attention of the mind from its own thoughts, and are, at the same time, not sufficiently interesting to engage its attention to themselves. It is also matter of common observation, that children and persons of little reflection, who are chiefly occupied about sensible objects, and whose mental activity is, in a great measure, suspended, as soon as their perceptive powers are unemployed, find it extremely difficult to continue awake, when they are deprived of their usual engagements. The same thing has been remarked of savages, whose time, like that of the lower animals, is almost completely divided between sleep and their bodily exertions.*

From a consideration of these facts, it seems reasonable to conclude, that in sleep those operations of the mind are suspended, which depend on our volition; for if it be certain, that before we fall asleep, we must withhold, as much as we are able, the exercise of all our different powers, it is scarcely to be imagined, that, as soon as sleep commences, these powers should again begin to be exerted. The more probable conclusion is, that when we are desirous to procure sleep, we bring both mind and body, as nearly as we can, into that state in which they are to continue after sleep commences. The difference, therefore, between the state of the mind when we are inviting sleep, and when we are actually asleep, is this; that in the former case, although its active exertions be suspended, we can renew them, if we please. In the other case, the will loses its influence over all our powers both of mind and body, in consequence of some physical alteration in the system, which we shall never, probably, be able to explain.

In order to illustrate this conclusion a little farther, it may be proper to remark, that if the suspension of our voluntary operations in sleep be admitted as a fact, there are only two suppositions which can be formed concerning its cause. The one is, that the power of volition is suspended; the other, that the will loses its influence over those faculties of the mind, and those members of the body, which, during our waking hours, are subjected to its authority. If it can be shewn, then, that the former supposition is not agreeable to fact, the truth of the latter seems to follow as a necessary consequence.

"The existence of the Negro slaves in America appears to participate more of sensation than of reflexion. To this must be ascribed, their disposition to sleep when abstracted from their diversions, and unemployed in their labour. An animal whose body is at rest, and who does not reflect, must be disposed to sleep of course."—Notes on Virginia, by Mr. JEFFERSON, p. 255.

1. That the power of volition is not suspended during sleep, appears from the efforts which we are conscious of making while in that situation. We dream, for example, that we are in danger, and we attempt to call out for assistance. The attempt, indeed, is, in general, unsuccessful, and the sounds which we emit are feeble and indistinct; but this only confirms, or, rather, is a necessary consequence of the supposition, that, in sleep, the connexion between the will and our voluntary operations, is disturbed or interrupted. The continuance of the power of volition is demonstrated by the effort, however ineffectual.

In like manner, in the course of an alarming dream, we are sometimes conscious of making an exertion to save ourselves by flight from an apprehended danger, but in spite of all our efforts, we continue in bed. In such cases, we commonly dream, that we are attempting to escape, and are prevented by some external obstacle; but the fact seems to be, that the body is, at that time, not subject to the will. During the disturbed rest which we sometimes have when the body is indisposed, the mind appears to retain some power over it; but as, even in these cases, the motions which are made, consist rather of a general agitation of the whole system, than of the regular exertion of a particular member of it, with a view to produce a certain effect, it is reasonable to conclude, that, in perfectly sound sleep, the mind, although it retains the power of volition, retains no influence whatever over the bodily organs.

In that particular condition of the system, which is known by the name of incubus, we are conscious of a total want of power over the body: and, I believe, the common opinion is, that it is this want of power which distinguishes the incubus from all the other modifications of sleep. But the more probable supposition seems to be, that every species of sleep is accompanied with a suspension of the faculty of voluntary motion; and that the incubus has nothing peculiar in it but this, that the uneasy sensations which are produced by the accidental posture of the body, and which we find it impossible to remove by our own efforts, render us distinctly conscious of our incapacity to move. One thing is certain, that the instant of our awaking, and of our recovering the command of our bodily organs, is one and the same.

2. The same conclusion is confirmed by a different view of the subject. It is probable, as was already observed, that when we are anxious to procure sleep, the state into which we naturally bring the mind, approaches to its state after sleep commences. Now it is manifest, that the means which nature directs us to employ on such occasions, is not to suspend the power of volition, but to suspend the exertion of those powers whose exercise depends on volition. If it were necessary that volition should be suspended before we fall asleep, it would be impossible for us, by our own efforts, to hasten the moment of rest. The very supposition of such efforts is absurd, for it implies a continued will to suspend the acts of the will.