infinity? or is there a limit to such divisibility, beyond which the process cannot possibly proceed? and if so, are the ultimate bodies into which it is capable of dissolving still susceptible of developement, or, from their attenuation, removed beyond all power of detection ?

These are questions which have agitated the world in almost all ages, and have laid a foundation for a variety of theories of too much consequence to be passed over in a course of physical investigation.

The tenet of an infinite divisibility of matter, whether in ancient or modern times, appears to have been a mere invention for the purpose of avoiding one or two self-contradictions supposed to be chargeable upon the doctrine of its ultimate and elementary solidity; but which, I much fear, will be found to have given birth to far more self-contradiction than it has removed. The mode of reasoning, however, by which this tenet was arrived at in ancient Greece, was essentially different from that by which it has been arrived at in our own day.

It being, as we observed in our last lecture, an uncontroverted maxim among all the Greek philosophers, of every sect and school whatever, that nothing could proceed from nothing, matter was of course conceived to have existed eternally, or it could not have existed at all. But it appeared obvious to most of them, that matter is as certainly unintelligent as they conjectured it is certainly eternal. The existence of intelligence, however, is still more demonstrable throughout nature than the existence of matter itself; and hence such philosophers were driven to the acknowledgment of an intelligent principle distinct from a material substance; and from the union of these two powers they accounted for the origin of the world: matter being merely passive and plastic, and put into form and endowed with the qualities and properties of body by the energy of the intelligent agent. But if form and corporeal properties have been communicated to it, it must, before such communication, and in its first or primal state, have been destitute of form; and that it was thus destitute is incontrovertible, continued the same schools of philosophy, because form presupposes the existence of intelligence, and must be, under every shape and modification, the product of an intelligent energy; for it is impossible that matter could have had a power of assuming one mode of form rather than another mode: since, if capable of assuming any kind, it must have been equally capable of assuming every kind, and, of course, of exhibiting intelligent effects without an intelligent cause, which would be utter nonsense.

Such is the general train of reasoning that seems to have operated upon the minds of Pythagoras, Plato, and Aristotle, in impelling them to the belief that matter, in its primary state, to adopt the words of Cicero, in which he explains the Platonic doctrine, "is a substance without form or quality, but capable of receiving all forms, and undergoing every kind of change; in doing which, however, it never suffers annihilation, but merely a solution of its parts, which are in their nature infinitely divisible, and move in portions of space which are also infinitely divisible."*

But if we abstract from matter form and quality, and at the same time deny it intelligence, what is there left to constitute it an eternal substance of any kind? and by what means could pure incorporeal intelligence endow it with form?

These difficulties are insuperable; and, though attempted to be explained in different ways by each of these philosophers, they press like millstones

* Acad. Quæst. lib. i. eap. 8.

upon their different systems, and are perpetually in danger of drowning them. Pythagoras compared the existence of matter, in its primary and amorphous state, to pure arithmetical numbers, before they are rendered visible by arithmetical figures." Unity," says he," and one (the former of which he denominated monad) are to be distinguished from each other: unity is an abstract conception, resembling primary or incorporeal matter in its general aggregate; one appertains to things capable of being numbered, and may be compared to matter rendered visible under a particular form." So again, "Number is not infinite any more than matter; but it is nevertheless the source of that infinite divisibility into equal parts which is the property of all bodies."*

Numbers, however, were not more generally had recourse to by Pythagoras, to typify elementary matter under different modifications, than they are in the present day by the most elaborate chemists, to express its particular combinations: "As in all well-known compounds," observes Sir Humphrey Davy," the proportions of the elements are in certain definite ratios to each other, it is evident that these ratios may be expressed by numbers." In consequence of which they are so expressed in various places by himself, and by many French, Swedish, and English chemists, the hint having been first suggested, I believe, by Higgins or Dalton. And hence the doctrine of numbers is well known to have been very largely and very repeatedly had recourse to under the Pythagorean system, and to have been used in explanation, not only of the endowment of different portions of matter with different forms, but of the harmony with which the different natures of matter and mind unite in identic substances. Numbers and forms are, in consequence, not unfrequently contemplated as the same thing-as the models or archetypes after which the world in all its parts is framed as the cause of entity to visible beings: Tous agituous AITIOUS είναι της ουσίας. Η

And hence, again, under the term monad, or unity, Pythagoras is ge nerally conceived to have symbolized God, or the active principle in nature; under duad, the passive principle, or matter; and under triad, the visible world, produced by the union of the two former.

Pythagoras, however, was as much attached to music as to numbers, regarding it as a mere branch of the science of numbers applied to a definite object. He has, indeed, the credit of having invented the monochord, and of having applied the principles of music, as well as those of numbers, to the study of physics. He conceived that the celestial spheres, in which 'the planets move, striking upon the elastic ether through which they pass, must produce a sound, and a sound that must vary according to the diversity of their magnitude, velocity, and relative distance; and as the adjustment of the heavenly bodies to each other is perfect in every respect, he farther conjectured, that the harmony produced by their revolutions must also be the most perfect imaginable; and hence the origin of a notion, which is now, however, only entertained in a figurative sense, a sense frequently laid hold of by our own poets, and thus exquisitely enlarged on by Dryden :

* Anon. Photii, lib. c. Nicomac. apud Phot. Themist. in Phys. lib. iii. sect. 25. p. 67. See also Enfield's Brucker, i. b. ii. ch. 12. p. 383.

† Davy, Elem. i. p. 112.

Arist. Met. lib. i. c. 6. Plut. Plac. Phil. lib. i. cap. 3. Athenag. Apol. 49.

What Pythagoras thus called numbers Plato denominated ideas, a term which has, hence, descended to our own day, and is on every one's lips, although in a different sense from what it originally imported. The reason or wisdom of the great First Cause, and which he denominates the logos of God, ὃ λογος, or ὅ λογισμος του Θεον, and not unfrequently Δημιουργος (Demiurgus), Plato describes as a distinct principle from the original Cause or Deity himself, from whom this efficient or operative cause, this divine wisdom or logos, emanates, and has eternally emanated, as light and heat from the sun. Thus emanating, he conceived it to be the immediate region or reservoir of ideas or intellectual forms, of the archetypes or patterns of things, subsisting by themselves as real beings-ra vTag OVT-in this their eternal and original well-spring; and the union of which with the whole, or any portion of primary or incorporeal matter, immediately produces palpable forms, and renders them objects of contemplation and science to the external senses.*

It is, hence, obvious that Plato contended for a triad or trinity of substances in the creation of the visible universe-God, divine wisdom, or the eternal source of intellectual forms or ideas, and incorporeal matter. And it is on this account that several of the earliest Christian fathers, who, as I have already observed, had been educated in the Platonic school, and had imbibed his notions, regarded this doctrine as of divine origin; and endeavoured, though preposterously, to blend the trinity of Plato, and that of the Christian scripture, into one common dogma: an attempt which has been occasionally revived in modern times, especially by Cudworth and Ogilvie, with great profundity of learning and great shrewdness of argument, but, at the same time, with as litth success as in the first ages of Christianity.

It is to this theory, which, indeed, is highly fitted for poetry, and much better so than for dry, dialectic discussion, Akenside beautifully alludes in the first book of his " Pleasures of Imagination :”

Ere the radiant sun

Sprang from the east, or, mid the vault of night

The moon suspended her serener lamp;

Ere mountains, woods, or streams adorn'd the globe,

Or Wisdom taught the sons of men her lore;

Then liv'd th' Eternal ONE; then, deep retir'd

In his unfathom'd essence, view'd the forms,

The forms eternal of created things;

The radiant sun, the moon's nocturnal lamp,

The mountains, woods, and streams, the rolling globe,

And Wisdom's mien celestial. From the first

Of days, on them his love divine he fix'd,

His admiration ; till, in time complete,
What he admir'd and lov'd his vital smile

Plac. Phil. lib. i. cap. x. Tim. lib. c.

Unfolded into being. Hence the breath
Of life in forming each organic frame;

Hence the green earth, and wild resounding waves;
Hence light and shade alternate; warmth and cold;
And clear autumnal skies, and vernal showers;
And all the fair variety of things.

While, however, we thus point out the fancifulness and imperfections of these hypotheses, let us, with the candour of genuine philosophy, do justice to the merits of their great inventors, and join in the admiration which has been so duly bestowed upon them by the wise and learned of every country. It was Plato who first suggested to Gallileo, even upon his own confession, that antagonist power by which a rectilinear motion can be converted into an orbicular, and thus laid a basis for our accounting for the regular movements of the heavenly bodies,* a subject upon which we shall enter to a certain extent in our next lecture; who, in some degree, anticipated that correct system of colours which nothing but the genius of a Newton could fully develope and explain ;† who in mathematics unfolded to us the analytic method of solving a problem, and in theosophy so far surpassed all the philosophers of his country, in his correct views and sublime descriptions of the Deity, that he seems almost to have drunk of the inspiration of Horeb or of Sinai; and who, in his Timæus, applies to the wisdom of God, the yious Tev ova term which in Hebrew could scarcely be translated by any other word than that of Jeveh or Jehovah —was OUTWG LEI, § "WHATEVER IS ESSENTIALLY ETERNAL.”

Of Pythagoras, it is only necessary to direct the attention to the two following very extraordinary facts, to place him beyond the reach of panegyric; the first of which has occasionally furnished reflection for other writers, though the latter remains unnoticed to the present moment. At an antedate of two thousand two hundred years from the age of Copernicus, this wonderful genius laid the first foundation of the Copernican system, and taught to his disciples that the earth revolves both around her own axis and around the sun; that the latter motion is conducted in an oblique path or zodiac ;|| and that the moon is an earth of the same kind as our own, and replete with animals, whose nature, however, he does not venture to describe. T

The second extraordinary fact to which I allude, is one we have already slightly glanced at, but which must not so cursorily be relinquished; I mean that, in ascribing to the primary or elementary forms of bodies, in their unions with each other, relative proportions so exact, yet so diversified, that forms and numbers may be employed as synonyms or convertible terms, he has exhibited so close a coincidence with one of the latest and most surprising discoveries of the present day, that though I dare not call it an anticipation, I am at a loss how else to characterize it: for it has been minutely ascertained within the last ten or twelve years, by an almost infinite variety of accurate and well-defined experiments by Higgens, Dalton, Gay Lussac, and Davy, that the combinations and separations of all simple

* Galilei Discorsi e Dimostrazioni Matematiche, p. 254. 4to. Leyd. 1638. Dutens, Origine des Decouvertes, &c. p. 90. 4to. Lond. 1796.

† Plut. de Placitis Philos. lib. i. cap. 15. p. 32. Dutens, ut supr. p. 101. Dutens, ut supr. p. 251.

Plutarch. in Tim. lib. iii. 34. 37.

Plutarch. de Placitis, lib. iii. cap. 11. 13. Diog. Laert. lib. viii. sect. 85. Copernicus himself admits that he derived his first hint of the earth's motion from Nicetas, a follower of Pythagoras. Vide his address to Paul III.

Plutarch. de Placit. Cicer. Acad. Quæst. lib. iv. p. 984. col. 1. Something of this doctrine is to be found in the Orphic Hymn. Procl. de Orpheo, lib. iv. in Timæum, p. 154.

bodies are conducted in a definite and invariable ratio of relative weight or measure ;* as that of one part, to one part, one part to two parts, one to three, or one to four; and, consequently, that every change in the compound thus produced, whether of addition or diminution, is a precise multiple or divisor of such ratio; or, in other words, that the different elementary bodies which enter into such compounds can never unite or separate, never lay hold of or let go each other, in Let us exemplify this remark by a familiar instance or two. any other proportions. well known to every one, that the calxes, oxydes, or, as they are often İt is now called, rusts, of metals, consist of a certain portion of oxygene with a certain portion of the metal, which is thus converted into a calx or oxyde. It is also known in the present day to most persons, that the greater number of metals are possest of two or more kinds of oxydes, produced by an union of different proportions of the oxygene and the metal, and often distinguishable even by their colour; as minium or red lead, and cerusse or white lead, which are equally oxydes of the metal whose name they bear. Now, in whatever proportion the oxygene unites with the metal to produce an oxyde of one kind, it invariably unites by a multiple or divisor of the same proportion to produce every kind of oxyde belonging to the same metal. Thus we have discovered not less than four different oxydes of antimony in different parts of the world: the lowest or simplest of them contains 4 parts of oxygene to 100 parts of metal; the next simplest contains 18 parts of oxygene to 100 parts of metal, which is four times 4; the third oxyde consists of 27 parts of oxygene to 100 parts of metal, which is six times 4; and the fourth oxyde, 36 parts of oxygene to 100 parts of metal, which is eight times 41. So tin, which possesses three discovered oxydes, has for its lowest the proportion of 7 parts of oxygene to 100 parts of metal; for its second oxyde, 14 parts of oxygene to 100 parts of metal, which is twice 7; and for its highest, 21 parts of oxygene to 100 parts of metal, which is three times 7. I have given the proportions in round numbers; but if I were to use the fractions that belong to them, the comparative results would be precisely the same. can we possibly combine these substances in any other proportions so as Nor to produce oxydes, for the corpuscles of which they consist will not lay hold of or let go each other in any other ratios. may hereafter detect an oxyde of antimony consisting of a less proportion It is possible that we of oxygene than 41; but if we ever should, we are confident beforehand that such proportion will be 21. It is also possible that we may meet with an oxyde containing more than 4 and less than 18 parts of oxygene in 103; but if we should do so, we can nearly anticipate that such proportion will be 9. And hence, as these proportions, though constantly true to their respective series, are constantly diversified in different substances, their radical figures or numbers may be employed, and now actually are employed, and that very generally, and in perfect coincidence with the system of the Pythagorists, as synonyms of the simple forms or substances whose progressive character they describe. This curious coincidence of ancient and modern philosophy, for at present I will call it nothing more, I cannot but regard as a very marvellous fact; and am not a little surprised that it should not hitherto have occurred, as it does not appear to have done, to

The only apparent exception I am aware of to this general principle is in the combination of the elements of M. Dulong's detonating substance, or azotane, as described by Sir Humphrey Davy, Phil. Trans. for 1813, p. 250: and it is, hence, probable that we are not yet put into possession of the proper results.