contains nothing on the subject. M. Libri remarks, that it is difficult to enumerate Porta's speculations, and still more so to ascertain how much of them he is entitled to claim as his In the present case however he is, I think, entitled to at least the credit due to an ingenious mistake.

own.

Porta's method, like that of Archimedes, requires us to have a mass of pure gold equal in weight to the crown or other portion of alloyed metal which is to be examined. Ghetaldus's, on the contrary, is free from this condition, which would in many cases make the other methods wholly useless. But Bacon's, so far from being an improvement on any of those which had preceded it, is the most unmanageable of all. His experiments must have been carefully made in order to give him the degree of accuracy which he has in most cases attained; for nothing can be more inartificial than the process employed. He formed a hollow prism, of which the height is a little greater than the side of the base-the base being a square, and just equal to a side of a cube of gold weighing one ounce. Any substance to be compared with gold is to be formed into a cube of dimensions equal to the ounce cube of gold, which is ascertained by its just fitting into the prism: the weight of the prism being known both when it is empty, and when it carries a cube of the given substance, that of the latter is also known, and its gravity compared to that of gold is thence determined. Consequently this method requires it to be possible to give a cubical form to the substance to be examined; a condition in many cases wholly impracticable, and which in all cases will give rise to many sources of error. In the original problem of Hiero's crown, for instance, Bacon could not have been permitted to cut a piece out in order to mould it into a cube. His method must have been changed, and he could only have advised the king to have another crown made on the same pattern, and of gold known to be unalloyed, and then to see whether the two crowns were of equal weight. It is tolerably certain that he had formed no distinct notion of the problem proposed to Archimedes,—namely, to compare the specific weights of bodies of given forms; because, after remarking that a table of specific gravities may be usefully employed in determining the composition of alloys, he goes on to say, "Arbitror hoc esse sйρnка illud Archimedis; sed utcunque ita res est." As in the Sylva Sylvarum he has copied largely from the Natural Magic, and

even from the neighbourhood of the passage of which I have been speaking, it may appear odd that he had not learnt from Porta what was the real difficulty which Archimedes had to overcome. The most obvious explanation is, that the Historia Densi et Rari was written before he had become acquainted with Porta's work.'

The use of making the height of the prism greater than the side of the base was this: when fluids were examined, the prism was filled up to a mark placed inside, at the height of the top of the cube, and the depth of the prism being somewhat greater than this height prevented the fluid from overflowing. In a small prism the surface of the fluid will be perceptibly convex; but this source of error was disregarded, or not observed. But, probably, the most remarkable error which Bacon has committed is chiefly owing to this circumstance. Both in the Phænomena Universi and the Historia Densi et Rari, the weight of the cube of mercury is stated at nineteen pennyweights and nine grains, that of the cube of gold being, as we know, one ounce. The specific gravity of gold is therefore to that of mercury as twenty to nineteen and three eighths; whereas the real ratio is less than twenty to fourteen and a half. Of this large error, a considerable part is accounted for by the convexity of the surface of the mercury. In the other specific gravities of fluids, which admit of an accurate comparison with modern results, there will be found. an error in the same direction, though, as we should expect, of a much smaller amount.

Beside solids and fluids, Bacon also made experiments on substances reduced to powder; not however distinguishing between merely mechanical pulverization, and that which is the result of some chemical process. Thus he compares lead "in corpore" and in ceruss, mercury and corrosive sublimate, &c. It was not however to be expected that he should make this distinction.

With respect to the philosophical inferences which he proposes to deduce from the quantitative theory of Density and Rarity, he seems, as usual, to bear somewhat too hardly on Aristotle. It was a received opinion among the disciples of

1 His attention seems to have been drawn to the point in question afterwards. See "Certain Experiments made by the Lord Bacon about Weight in Air and Water," Part III. of this edition near the end, and Mr. Ellis's note, J. S.

Aristotle that one measure of earth is transmutable into ten of water, and one of water into ten of air. This opinion was no doubt founded on a passage in which Aristotle arguing against the doctrine of Empedocles, who recognising four elements did not admit that they could be transmuted into one another, remarks that if this be denied, we cannot compare them κaτà TOσÒV TOσóv, according to quantity as such. If we say that one measure of water becomes ten of air, then we may also assert that one measure of water is in point of quantity equal to ten of air; and conversely, in order that the latter statement may have a definite meaning, we must admit that water may be changed into air, or vice versa. Therefore, Aristotle says, we may well be surprised that any of those who compare the elements according to quantity deny their mutual transmutability. In this argumentum per incommodum there are two points worthy of notice: in the first place, the complete absence of any notion that the quantity of matter was to be measured by the weight; and in the second, the recognition of the possibility of definite quantitative comparisons among the elements. So clearly is this fixed in Aristotle's mind, that he uses it to show that the elements must be transmutable. There is however no foundation for Bacon's censure1, that under the sanction of the doctrine that matter is wholly indifferent to differences of form, the schoolmen in effect maintained that any given portion of water might possibly become any quantity of air. He remarks, that if any one asserts that one measure of water can be transmuted into an equal measure of air, he in reality asserts that something which previously existed can be absolutely annihilated; since, taking for argument's sake the common opinion as to the relation between water and air, the single measure of water might have been made into ten of air; so that in order to arrive at the single measure of air nine must have been annihilated. No one, he says, can be so bewildered with abstract subtleties as to believe that there is as much matter in one measure of air as in ten. Certainly not; and the follower of Aristotle would simply remark, that the phrase "as much matter" is, in his sense of the word matter, a phrase without meaning. For to him matter apart from form has no actual existence; it is not ens actu, and therefore does

This censure is implied throughout the Aditus. I have expressed his argument rather more fully than he has done himself.

not admit of any determination either in the category of quantity or any other. Whatever may be thought of the value of the Aristotelian antithesis of form and matter, we are not at liberty to charge it with difficulties which only arise when we forget that, in this antithesis, matter does not mean any actually existing thing. We must not replace the merely negative notion of the Aristotelian λŋ by the positive idea of substance, and then interpret the dictum that matter is indifferently susceptible of all forms, so as to make it mean that the quantity of a given portion of substance can be conceived to vary. That this transition from matter to substance has been often made, may readily be admitted; it is only one instance of the tendency of the mind to replace highly abstract notions by others which are less so,-a tendency which, in the history of philosophy, is as the ódòs eis Tò Káτw of Heraclitus.

In commending those who deny that primitive matter is "quanto plane spoliata, licet ad alias formas æqua," Bacon refers to the Averroists, who ascribed to matter, considered apart from any form, extension in three dimensions-interminate extension, as it was usually expressed. Any attempt to give metes and bounds to this interminate extension would have been in the opinion of Averroes, as well as in that of the other followers of Aristotle, to introduce an sidos or form. This doctrine was however regarded by the orthodox schoolmen as little less of a heresy than that which Averroes had promulgated touching the soul of man. Another and a somewhat earlier doctrine ascribed to all matter a form of corporeity, prior to the introduction of any special or particular form. Both these doctrines are of Arab origin, the last-mentioned being that of Avicenna: they seem to spring from the same character of mind, though Avicenna's opinion is strongly condemned by Averroes. It does not seem to have ever been received with much assent, though the phrase "form of corporeity" became long afterwards famous, when Duns Scotus introduced it into his psychological theory.

Bacon is scarcely justified in asserting that Aristotle reduced the whole question of density and rarity to "the frigid distinction of act and power." He said, on the contrary, that density and rarity, instead of being, as at first they seem to be, purely qualitative conceptions, pass into another category than that of quality, when they are more narrowly examined. His

expressions are sufficiently remarkable to be quoted :— olke.. ἔοικε ἀλλότρια τὰ τοιαῦτα (namely the rare and the dense, the smooth and the rough) εἶναι τῆς περὶ τὸ ποιὸν διαιρέσεως· θέσιν γὰρ μᾶλλόν τινα φαίνεται τῶν μορίων ἑκάτερον δηλοῦν· πυκνὸν μὲν γὰρ τῷ τὰ μόρια σύνεγγυς εἶναι ἀλλήλοις, μανὸν δὲ τῷ διεστάναι ἀπ' ἀλλήλων, καὶ λεῖον μὲν τῷ ἐπ ̓ εὐθείας πὼς τὰ μόρια κεῖσθαι, τραχὺ δὲ τῷ τὸ μὲν ὑπερέχειν τὸ δὲ ἐλλείπειν. “ The dense and the rare, the smooth and the rough, seem to be foreign from the classification of qualities. For each of them seems rather to denote a mode of disposition of the particles: the dense consists in their being near one another, and the rare in their standing apart; the smooth in their lying somehow in a straight line, and the rough in this that one particle projects and another comes short."

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This explanation is precisely the same as Bacon's; and on the other hand Aristotle would have adopted Bacon's caveat Neque propterea res deducitur ad atomum, qui præsupponit vacuum et materiam non fluxam (quorum utrunque falsum est), sed ad particulas veras quales inveniuntur."1

In this as in some other instances, Bacon speaks of Aristotle with needless disrespect. Yet even now Aristotle has not lost his claim to be accounted " il maestro di coloro che sanno."

One of the applications which Bacon makes of his table of specific gravities is to the common doctrine of the elements, to which he esteems it a fatal objection, that many bodies, as gold for instance, are much heavier than the densest of the elements. The objection would be conclusive if it were more difficult to believe that any mixture of the elements could by condensation become of the same specific gravity as gold, than to believe that it could possess the qualities by which gold is distinguished from other substances.

From comparing the densities of tangible bodies "quæ pondere dotantur," Bacon proceeds to speak of aeriform or pneumatical bodies, whose density cannot be judged of by their weight. In classifying aeriform bodies, he distinguishes, as in the Historia Vita et Mortis, between the crude spirits which are present in every tangible substance, and the animal spirits which are peculiar to living creatures. The latter are much the rarer, and possess positive levity; which appears in

1 Nov. Org. ii. 6.