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 characterise it: for it has been minutely ascertained within the last ten or twelve years, by an almost infinite variety of accurate and welldefined 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 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 any other proportions. col. 1. Something of this doctrine is to be found in the Orphic Hymn. Procl. de Orpheo, lib. iv. in Timæum, p. 154. * 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 Humphry Davy, Phil. Trans. for 1813, p. 250. and it is hence probable hat we are not yet put into possession of the proper results. : Let us exemplify this remark by a familiar instance or two. It is now well known to every one, that the calxes, oxydes, or, as they are often 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 possessed 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 ceruse 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 41; and the fourth oxyde, 36 parts of oxygene to 100 parts of metal, which is eight times 4. 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. Nor can we possibly combine these substances in any other proportions so as to produce oxydes; 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 oxyde of antimony consisting of a less proportion of oxygene than 4; but if we ever should, we are confident beforehand that such proportion will be 24. It is also possible that we may meet with an oxyde containing more than 4 and less than 18 parts of oxygene 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 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 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 well-known and more complicated compounds, so far as the experimental series has been carried, the elementary bodies which enter into them exhibit proportions equally definite and invariable; thus affording another proof of close connection between the phænomena 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 mountains in scales and the hills in a balance." LECTURE III. ON THE ELEMENTARY AND CONSTITUENT (The subject continued.) THE few steps we have hitherto taken in the wide and magnificent region 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 a few 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. 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 |