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And could not heave her head,
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: τους αριθμούς αιτίους είναι της ουσίας.*
And hence, again, under the term monad, or unity, Pythagoras is generally 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 :
From harmony, from heav'nly harmony,
This universal frame began.
Or jarring atoms lay,
Arise, ye more than dead!
And Music's power obey,
From harmony to harmony
The diapason closing full in man. 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, 6 dbyos, or 8 doyiouds toữ Ocoù, and not unfrequently AnuLovpyds (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-- Övrws ovra—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.f
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 little success as in the first ages of Christianity.
* Arist. Met. lib. i. c. 6. Plut. Plac. Phil lib. i. cap 3. Athenag Apol 49
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
While, however, we thus point out the fancifulness and imperfections of these hypotheses, let us, with the candour of genuine philosophıy, 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 Galileo, 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 ;t 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 doycouds roữ Ocolma term which in Hebrew could scarcely be translated by any other word than that of Jevah or Jehovah-Tās 8vows åer, “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 won. derful 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 ;ll 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.P
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 synonymes 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 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 ad. dition 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 any other proportions.
* Galilei Discorsi è Dimostrazioni Matematiche, p. 254, 4to. Leyd, 1638. Dutens, Origine des Decou vertes, &c. p. 90, 4to. Lond. 1796. 1 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.
1 Plutarch. de Placít. 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.
Let us exemplify this remark by a familiar instance or two. It is now well known to every one that the calxes, oxides, or, as they are often called, rusts, of metals, consist of a certain portion of oxygen with a certain portion of the metal, which is thus converted into a calx or oxide. It is also known in the present day to most persons, that the greater number of metals are possessed of two or more kinds of oxides, produced by a union of different proportions of the oxygen and the metal, and often distinguishable even by their colour; as minium or red lead, and ceruse or white lead, which are equally oxides of the metal whose name they bear. Now, in whatever proportion the oxygen unites with the metal to produce an oxide of one kind, it invariably unites by a multiple or divisor of the same proportion to produce every kind of oxide belonging to the same metal. Thus we have discovered not less than four different oxides of antimony in different parts of the world: the lowest or simplest of them contains 44 parts of oxygen to 100 parts of metal; the next simplest contains 18 parts of oxygen to 100 parts of metal, which is four times 44 ; the third oxide consists of 27 parts of oxygen to 100 parts of metal, which is six times 44; and the fourth oxide, 36 parts of oxygen to 100 parts of metal, which is eight times 41. So tin, which possesses three discovered oxides, has for its lowest the proportion of 7 parts of oxygen to 100 parts of metal ; for its second oxide, 14 parts of oxygen to 100 parts of metal, which is twice 7; and for its highest, 21 parts of oxygen 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. Nor can we possibly combine these substances in any other proportions, so as to produce oxides; for the corpuscles of which they consist will not lay hold of or let go each other in any other ratios. It is possible that we may hereafter detect an oxide of antimony consisting of a less proportion of oxygen 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 oxide containing more than 44 and less than 18 parts of the oxygen in 100 ; 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 synonymes 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 minds of any of those learned and ingenious chemists who have chiefly been employed in applying and building up the discovery. And it is not the least important part of this discovery, that not only in the union or separation of simple substances, but in all wellknown and more complicated compounds, so far as the experimental series has been carried, the elementary bodies which enter into them exhibit pro
The only apparent exception I am aware of to this general principle is in the combination of the elaments of M. Dulong's detonating substance, or azotane, as described by sir Humphry Davy, Phil. Trans. for 1813, p. 250: and it is hence probable that we are not yet put into posscasion of the proper results.
portions equally definite and invariable; thus affording another proof of close connexion between the phenomena of nature and the occasional developements of revelation; the philosopher beholding now, as the prophet beheld formerly, that the Almighty architect has literally adjusted every thing by weight and measure; that he has measured the waters and meted out the heavens, accurately comprehended the dust of the earth, weighed the moun. tains in scales and the hills in a balance.
ON THE ELEMENTARY AND CONSTITUENT PRINCIPLES OF THINGS.
(The subject continued.) The few steps we have hitherto taken in the wide and magnificent scope before us have only led to an establishment of two or three fundamental axioms, of no small importance in the science of physics, and to a developement of two or three of the most ingenious and most popular hypotheses of former times, invented to account for the origin of the world around us, and the elementary and constituent principles of things: especially the hypothesis of numbers, as proposed by Pythagoras, and that of ideas, as proposed by Plato; and their application to primary and incorporeal matter, in order to endow it with form and quality. There are yet two or three other hypotheses upon the same subject that amply demand our attention, and are replete with an equal degree of ingenuity and fine imagination; especially the Peripatetic and the Atomic, or that of Aristotle and that of Epicurus; and we have also to trace out the relative degree of influence which each of these has exerted on the philosophical theories of later times.
Aristotle had too much penetration not to see that the hypothesis of Plato was just as inadequate as that of Pythagoras to a solution of the great question concerning the production of the visible world: and he proposed a third scheme, which has also had its share of popularity. According to this remodelled plan, the sensible universe is the result of four distinct principles, -intelligence, matter, form, and privation; which last term is little more than a mere synonyme for space or vacuum; and thus far the theory of Aristotle chiefly differs from that of Plato, by interweaving into it his fourth prin. ciple, derived from Democritus, and the other Atomic philosophers, and which he seems to have added to it with a view of providing a proper theatre for the two principles of form and matter to move in. He supposes all these to have equally existed from eternity; and the three last to have been eternally acted upon or thrown into a definite series of motions, upon which alone the existence and harmony of things are dependent, by the immutable and immaterial principle of intelligence, whose residence he places in the purest and lostiest sphere or circle of the heavens; a sphere that in its vast embrace comprehends ten lower or subordinate spheres, that lie between itself and the earth, which forms the centre of the whole, and, in conjunction with the earth, constitutes the universal world.
This Supreme Intelligence Aristotle conceived to be in himself for ever at rest; and the tranquil and peaceable sphere in which he resides he denominated the empyreum or heaven of bliss. But though enjoying eternal rest himself, he communicates motion, necessarily and essentially, upon this theory, to the sphere immediately below him; as this, in its turn, communicates it in different directions, and with different velocities, to the other spheres that revolve within its range ;* whence the sphere thus earliest receiving motion, and nearest to the empyreum, Aristotle denominated the perMUM MOBILE, or first moving power: it constituted the tenth in the regular series; the ninth, or that which lies next to it, being denominated the crys.
* Diog. Laert. lib. v. soct. 23. Arist. Phyo. lib. 1. cap. 3, 4. De Cal. lib. 2. cap. 3. 11.
talline heavens; the eighth, the starry sphere, or heavens; and the remaining seven deriving their names from, and being appropriated to, the different revolutions of the different planets, as Saturn, Jupiter, Mars, Apollo or the sun, Venus, Mercury, and Diana or the moon: the earth, forming the centre of the whole, being an imperfect sphere, with a larger proportion of matter at the equator; on which account the earth was conceived to turn on her axis in a rocking motion, revolving round the axis of the ecliptic, and making the stars appear to shift their places at the rate of about one degree in seventy-two years. According to which calculation, all of them will appear to perform a complete revolution in the space of 25,920 years, and, consequently, to return to the precise situation they occupied at the commencement of such period. This period was hence denominated the ANNUS MAGNUs, or GREAT YEAR, and not unfrequently the PLATONIC YEAR, as the same kind of revolution was in some measure taught also by Plato.
The motory power, thus impressed by the intelligent moving principle, not voluntarily but by necessity, upon the different heavenly spheres, and finally upon the earth, and productive of that catenation of effects which is equally without beginning and without end, Aristotle denominated NATURE, and thus furnished us with a word, which has for ages been so extensively made use of, that, though there is nothing in all language more imprecise, there is nothing we could spare with more inconvenience. The same term, indeed, is occasionally employed by Plato, but in a sense still less definite if possible, and at the same time still less comprehensive.
On the revival of literature, this theory, together with the other branches of Peripatetic science, was chiefly restored and studied; and continued, indeed, to be generally adhered to for upwards of a century after the publication of the Copernican system ; which is well known to have at first ex. perienced but a very cold and inhospitable reception from the literary world. And it is hence this theory that is principally adverted to and described in the productions of all the early poets as well as philosophers of every part of modern Europe. And so complete was the triumph of the Peripatetic school in all its doctrines throughout Christendom, at this period, that Melancthon makes it a matter of complaint that, even in the sacred assemblies, parts of the writings of Aristotle were read to the people instead of the Gospel. Even Milton himself, though born considerably more than a century after Copernicus, wavers as to the propriety of adopting his hypothesis of the heavens, and hence, in his Paradise Lost,* leaves it doubtful which of the two, the new or the old, ought to be preferred. The best and most splendid description of the Aristotelian theory that I have ever met with is contained in the Lusiad of Camoens: the whole is too long for quotation, but I may venture to affirm, that you will be pleased with the following lines from Mr. Mickel's very spirited version of the Portuguese bard, as delineating the different heavenly spheres that were supposed, as I have already observed, to lie one within another, like the different tunics of an onion :
These spheres behold: the first in wide embrace
These hypotheses are abstruse, and perhaps ill calculated to afford amusement; but in a course of physical study they ought by no means to be over