the Idea of a Hundred; because the Chain that holds the Parts together is to him wholly unserviceable, nor can he represent to his Mind the several interjacent Combinations, without which it is impossible in this Case, to arrive at a diftinct Perception.

The great Advantages of Address in classing our complex Con

ceptions.

VII. I HAVE insisted the more largely upon this, not only because it is by Number that we measure all other Things, as Duration, Extenfion, Motion, &c. but also, because it lets us into the most natural View of the Conduct and Procedure of the Understanding, and makes us sensible of the great Art and Address that is neceffary in the classing of our very complex Conceptions. He that can so put together the component Parts of an Idea, as that they shall lie obvious to the Notice of the Mind, and prefent themselves, when Occasion requires, in a just and orderly Connection, will not find it very difficult to obtain clear and accurate Perceptions in most of those Subjects about which our Thoughts are conversant. For the great Art of Knowledge lies in managing with Skill the Capacity of the Intellect, and contriving fuch Helps, as, if they strengthen not its natural Powers, may yet expose them to no unnecessary Fatigue, by entangling and perplexing them with Confiderations remote from the Business in Hand. When Ideas become very complex, and by the Multiplicity of their Parts, grow too unwieldy to be dealt with in the Lump, we must ease the View of the Mind, by taking them to Pieces, and setting before it the several Portions separately, one after another. By this leisurely Survey, we are enabled to take in the Whole; and if we can draw it into such an orderly Combination, as will naturally lead the Attention Step by Step, in any succeeding Confideration of the fame Idea, we shall ever have it at Command, and with a fingle Glance of Thought be able to run over all its Parts. I have therefore explained here at some Length the Conduct of the Mind in Numbering; it feeming to me the best Modelin this Kind, whether we confider the many Advantages derived from fuch an orderly Difpofition of our Ideas, or the great Art and Skill displayed in binding these Ideas together.. This alfo is farther remarkable, in the Confideration of Number, that from it chiefly we derive the Notion we have of Infinity; it being apparent, that in adding Number to Number there is no End, the Poffibility of doubling or increasing our Stock in any Degree remaining as obvious to the Under

ftanding,

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standing, after a great and continued Run of Progreffions, as when we first began the Computation.

Duration.

VIII. IF we now turn our Thoughts towards Space and Duration, here too we shall find, that The Confidewe very feldom arrive at clear and distinct Ideas ration of of either, but when we introduce the Confidera- Number of tion of Number. great Uje in The more obvious and limited afcertainin Portions, it is true, easily flide into the Mind in our Ideas of the natural Way of Perception; but it was the Space and Neceffity of comparing these together that put us upon the Contrivance of certain ftated Measures, by which precisely to determine the Quantity in each. Thus Inches, Feet, Yards, Miles, &c. afcertain our Ideas of Extenfion; as Minutes, Hours, Days, Years, &c. meafure the Progress of Duration. The leffer Parts, as lying most open to the Notice of the Understanding, and being more on a Level with its Powers, are retained with tolerable Exactness; and the larger Portions, when the Number of Repetitions of which they are made up is known, are thereby also reduced into clear and determinate Conceptions. A Foot, and Yard, are Measures easily comprehended by the Mind; nor do we find any Difficulty in conceiving a Mile, when we consider it as equal to a certain Number of Yards. If we are still for increasing the Standard, we may take up the Semidiameter of the Earth, and, fuppofing it equal to 8000 Miles, make use of it as a Measure by which to afcertain the Distance of the Sun or fixed Stars. Just so it is in Duration; from Hours we rife to Days, Months, and Years; by these, repeated and added together, we measure Time past, or can run forward at Pleasure into Futurity, and that without any Confufion or Perplexity.

IX. IT is however to Number alone that we Without it, owe this Diftinctness of Perception, inafinuch they are apt as Space and Time, confidered apart from the to degenerate regular and orderly Repetition of Miles or Years, into a confuleave no determinate Impressions in the Mind, by fed and irre which to know and diftinguith their feveral Por- gular Heap. tions. Ideas of either, thus taken in at a Venture, are a confufed and irregular Heap, especially where we endeavour to enlarge and magnify our Views, and give full Play to the Powers of the Intellect. Something indeed the Mind conceives vast and mighty, but nothing that is precife, accurate, and just. But when it begins to confider these Ideas as made up of Parts, and, fixing upon fuch as are propor tioned

1

tioned to its Reach, fets itself to examine how often they are repeated to make up the Whole, the Perceptions of the Understanding put on a new Form, and discover their exact Bounds and Limits.

X. AND thus, as before in Number, so here in Infinity an Extenfion and Duration, the Mind begins with Object too mighty for the fimple and obvious Notices, advancing by DeSurvey of the grees to more enlarged and intricate Conceptions. buman Mind. A Day, or a Furlong, are of easy Apprehenfion

to the Understanding, and, by their Subdivisions into still lesser Spaces, exhibit themselves diftinctly in all their Parts. With these variously repeated, we travel thro' Space and Time, so that, being able to reduce all our Ideas of this Class, however mighty and enlarged, to the clear and determinate Perceptions of Number, we can conduct our Thoughts without Perplexity, and never find ourselves puzzled, but when, prefuming too much on our own Strength, we launch into Speculations that stretch beyond the Powers of the human Intellect. Number may be compared to a Line, that, fetting out from Unity, runs on in a continual Increase of Length, without a Poffibility of ever arriving at its ultimate Period. So far as we pursue it in our Thoughts, and trace its regular Advances, so far our Ideas are accurate and just. But when we let loose our Understandings after a boundless Remainder, and would fathom the Depth of Infinity, we find ourselves loft amidst the Greatness of our own Conceptions. Some Notions it is true we have, but such as, exceeding the Dimenfions of the Mind, lie involved in Darkness and Obscurity; and, being deftitute of Order, Method, and Connection, afford no Foundation whereon to build any just and accurate Conclufions,

Never repre-
XI. AND this perhaps may be the Reafon
fented in its
why many modern Philofophers, in their Dif-
full Dimensi courses concerning Infinity, have run into appa-
rent Contradictions; because, encountering with
an Object too large for the Survey of the Un-
derstanding, they found themselves furrounded
with inextricable Difficulties, which their scanty
and defective Ideas were by no Means able to diffipate or res
The Truth of it is, finite Ideas alone are proporti
oned to a finite Understanding; and altho' we are not wholly
without a Notion of the Infinity of Number, yet it is not
fuch a one as comprehends and exhausts its Object, or ex-

hibits it to the Mind, in its full Size and Dimensions. We only see the Idea, as capable of an endless Increase, but cannot by any Effort of Thought take in the whole Profpect; and indeed it is properly that Part of it which lies beyond the Reach of our Perception, and still remains to be taken into the Account, to which we give the Name of Infi nity.

XII. THIS Idea of the Infinity of Number, Duration imperfect as it may seem, is nevertheless that by whether conwhich the Mind afcends to the Conception of fidered as past Eternity and Immensity. For when we confider or to come Duration either boundless, as past or to come, we find whence our nothing to stop the Progress of our Thoughts, Idea of Eterin the Repetition of Years, or Millions of Years: nity. The farther we proceed, the more the Idea grows upon us; and when we have wearied ourselves with vain Efforts, we must own at last, that we can no more arrive at the End of Duration than at the End of Number. It is true, the several Generations of Men rise and disappear in very quick Succeffions; Earth itself may decay, and those bright Luminaries that adorn the Firmament of Heaven be extinguished. But the Course of Time will not be thereby disturbed; that flows uniform and invariable, nor is bounded by the Period of their Existence. This double View of Duration, as having already revolved thro' numberless Ages, and yet still advancing into Futurity in an endless Progreffion, properly constitutes our Idea of Eternity. We speak indeed of an Eternity past, and an Eternity to come, but both these are bounded at one Extreme; the former terminates in the present Moment, and therefore has an End; the latter fets out from the same Period, and therefore has a Beginning; but, taken together, they form a Line both Ways infinitely extended, and which represents Eternity in its full Dimensions.

tion of Space

XIII. As in the Confideration of Time we The Idea of fix upon the present Moment, regarding it as Immenfity dethe middle Point which divides the whole Line rived from of Duration into two equal Parts; so in the the Confidera Confideration of Space, that particular Place in ever growing which we exist is looked upon as a Kind of on all Sides Center to the whole Expanfion. From thence of us. we let loose our Thoughts on every Side, above, below, around; and find we can travel on, in the Repetition of Miles, and Millions of Miles, without ever arriving at the End of the Progression. It is not difficult indeed to carry our VOL. II.

D

Conceptions

1

Conceptions to the utmost Bounds of the Universe; at least so far as it falls within our Notice. But then the Imagination rests not here; it fees immeafurable Spaces beyond, capable of receiving new Worlds, which it can pursue, as rifing one above another in an endless Succeffion. This Confideration of Space, ever growing on all Sides of us, and yet never to be exhausted, is that which gives us the Idea of Immensity; which is in Fact nothing else but the Infinity of Number, applied to certain Portions of Extenfion, as Miles, or Leagues, &c. and these conceived as extended every Way around us in infinite and innumerable right Lines.

Compound Ideas refulting from the Union of Perceptions of different

XIV. HITHERTO we have confidered the Mind as employed about one and the fame Idea, enlarging and diverfifying it in various Forms. We have feen it rifing from the most simple and obvious Notices to the Conception of Infinity

itself; and taken a View of it in all the diffeKinds. rent Stages of its Improvement. Let us now proceed to the more complicated Act of Composition, when the Mind brings several Ideas of different Kinds together, and voluntarily combines them into one complex Conception. Such for Instance is our Idea of a Tune, as comprehending a Variety of Notes, with many different Modulations of Sound, And here it is to be observed, that tho' the complex Idea may be excited in us by hearing the Air itself struck off upon a proper Instrument; yet, considered originally, it still belongs to this Class of Perceptions, which are diftinguished as the arbitrary Collections of the Mind. It was the Mufician, or Composer, that combined the several Notes, and determined the Order in which they were to follow one another; nor had that particular Compofition of Sounds any real Union in Nature before they were thus brought together in his Mind. Of the same Nature are most of our Ideas of hu'man Actions; for tho' many of them come to our Notice, by seeing the Actions themselves, or hearing them described by others, as Diftilling, Carving, Treason, &c. yet it is plain, that they must have been projected and contrived in the Mind of Man before they had a real Existence.

How the Mind is determined in

XV. IT is here that the Understanding has the greatest Scope, and finds moft Employment for its active Powers; nor indeed is it possible making these to fer any Bounds to the Ideas of this Class; the Combinations. Combinations already made being almost innumerable, and those yet in the Power of the Mind affording an endless Diversity, It may not however be amiss to con