of alloy which it contained. In truth he had not sufficient data for the purpose, unless it was clear that the gold was alloyed only with silver.

After pointing out the defects of Archimedes's method, Ghetaldus remarks that they are effectually avoided by weighing the body in air and water, in the manner which he has already described. In this manner it is not necessary to take masses of equal weight in air, in order to compare the specific gravities; any particle of each is sufficient for the required experiments.

The simplicity and modesty of Ghetaldus's style - he says of himself, "is enim ego sum, qui malim scire quam nosci; discere quam docere :"1— make us unwilling to believe that he was aware that the method of weighing in air and water, in order to compare specific gravities, was not new. Yet it had been given in a slightly different form in one of the most popular books of the time, -the Natural Magic of Porta. The error however which Porta has made in applying it seems to be good evidence in favour of Ghetaldus, who would scarcely have omitted an opportunity of pointing it out.

Porta, like Ghetaldus, tells the story of Hiero's crown, and after saying something of the practical objections to the method which Archimedes employed, goes on to remark that the method he is about to describe is so much better than the old one, "ut dicere possimus vπepεúρηка νπερεúрηκa." Take, he says, the metal whose purity is to be examined, and an equal weight of the same metal known to be free from all alloy. Place them in the scales of an accurate balance, and when they are in equilibrium, immerse both scales in water. It will be seen that the impure metal will rise, and that the other will sink. Thus, in the case of gold alloyed with silver, if we would know how much silver it contains, we must put it in the one scale, and in the other as much pure gold as will produce equilibrium under water. Then lift both scales out of the water, and determine the excess of weight which was necessary to produce equilibrium in the water. This excess is the weight of the alloy. Again, if you would

"I had rather know than be known," is one of the sentences in Bacon's Promus. -J. S.

* 2 There is, of course, no such word as wepeuplow, nor would it mean what Porta wishes to express. But his meaning is obvious.

know how much gold there is in the gilding of a silver vessel: Put the vessel in one scale, and balance it in air with pure silver: : put both scales into water; and the weight of the gold which must be added to the pure silver in order to restore the balance is the weight of the gilding. Both these methods are entirely wrong. But Porta goes on, after remarking that they are applicable to other alloys beside that of gold and silver, to give certain statements of the weight of iron and other metals as weighed in air and in water, which constitute in effect a table of specific gravities. For some reason or other, they almost all err in the same direction, making the substances to which they relate appear lighter than they really are. Probably Porta forgot that the scale in which the body was placed, was itself buoyed up by the water. However that may be, he says that an iron ball weighing nineteen ounces in air weighs fifteen in water, which would make the specific gravity of iron only four and three quarters. Similarly a ball of lead of thirty-one ounces in air loses four ounces in water: so that the specific gravity of lead is less than eight. He states similar results for six kinds of gold; the highest specific gravity being seventeen. The error in this case may have been caused by the alloy; which is the more probable, as in the case of silver his result is almost absolutely accurate. Silver weighing a hundred and twenty-five grains in air weighs a hundred and thirteen in water. This gives a specific gravity of 10-41. For the precious metals he probably used greater care in making the experiment. Porta manifestly but half understood what he was doing: still he had got possession of the idea that specific weights were to be compared by weighing in air and water; and this idea once got, any person who had read Archimedes's treatise on floating bodies, might easily have done what Ghetaldus did.

I have thought this digression allowable, as the most recent account of the progress of science in Italy, namely M. Libri's,

1 If, in the case of the first, p and σ are respectively the densities of gold and silver, and v, u, and V the volumes of the gold in the debased metal, of the silver, and of the pure gold respectively; then, as they balance in water,

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 sйрηка 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 penny weights 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 κarà TOσÒν TOσÓν, 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 be

wildered 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.