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HISTORIA DENSI ET RARI.
BY ROBERT LESLIE ELLIS.
THE following treatise, which is one of the five histories mentioned in the Historia Naturalis, was published in 1658 by Dr. Rawley. A good deal of its contents occur in an imperfect and fragmentary state in the Phenomena Universi.?
It has somewhat the appearance of having been left unfinished, and excepting a table of specific gravities and an account of the way in which this table was constructed, contains little that is now of interest. The table occurs also in the Phenomena Universi: in the Historia Densi et Rari one substance is omitted and six added, so that the whole number of substances mentioned, which is seventy-three in the former, is seventy-eight in the latter work.
This table of specific gravities is the only collection of quantitative experimental results that we find in Bacon's works. Few experiments of the same kind had previously been made. The method which Bacon employed enables us to form some opinion as to the amount of his acquaintance with mathematical physics.
The first table of specific gravities was constructed by Marinus Ghetaldus“, whose Archimedes Promotus was published
One of the fragments published by Gruter in 1651, which will be printed in Part III. of this edition. My own impression is that much of the first portion of the present treatise — from the first tabula down to the monitum, p. 259.- is of earlier date than Gruter's copy, and less perfect ; and that the remainder only-extending from the first connexio to the end-is to be regarded as the Historia Densi et Rari which Rawley mentions as having been composed by Bacon during his last quinquennium; the previous part being made up of notes and loose papers written at various times, many of them long before, and never digested into order. See my note at the end of this preface. – J. S.
? It appears from Harriot's papers, now in the British Museum, that before the
in 1603. It contains only twelve substances, and is therefore, 80 far as the number of experiments is concerned, much inferior to Bacon's. But on the other hand Ghetaldus is the author of the method of finding specific gravities which, with certain modifications and corrections, has remained in use to the present day, whereas no one, probably, has attempted to find specific gravities by Bacon's process. The principle of Ghetaldus's method consists in weighing the substance which is to be examined in air and in water, and thus ascertaining the weight of the water which it displaces. By this method the comparison of the densities of different substances is made to depend on the first principles of hydrostatics. The often-told story of Archimedes and Hiero's crown contains the germ of the same method; and it is probably from this that Ghetaldus took the title of his book. It contains however, beside the tables of specific gravities, certain corollaries from propositions in Archimedes's treatise on the equilibrium of floating bodies, enough to show that Ghetaldus was entitled to profess himself a follower of Archimedes. Towards the end of his treatise he tells the story of Archimedes and Hiero, and remarks on the practical defects of the method which Archimedes employed. The chief inaccuracy arises from the effect of capillary attraction on the surface of the water, which makes it difficult to know when the vessel, into which the crown or other substance to be examined is introduced, is only just full. Ghetaldus's remark, that the water which overflows cannot be collected and measured without loss, is no doubt correct; but it does not seem that this way of trying the experiment was employed by Archimedes. After putting the crown into a vessel full of water and thus making a part of the water overflow, he filled the vessel again, measuring the quantity of water poured in. Repeating this experiment with a mass of gold equal in weight to the crown, and then again with a mass of silver also of equal weight, he found that the crown displaced more water than the gold and less than the silver, and thereby showed that the crown was not of pure gold. It does not seem, from what Vitruvius says, that Archimedes calculated the amount
publication of the Archimedes Promotus, he knew how to determine specific gravities by weighing in air and water. We are not however entitled to assert, as Baron Zach has done, that his experiments preceded those of Ghetaldi. See the supplement to Dr. Bradley's Miscellaneous Works, by Prof Rigaud, pp. 43 and 51.
“ Isti vero opusculo nomen ab Archimede, quem ducem sequor, imposui.”
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:"! — 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 ütrepeúpnka Énepɛúpnka.” ? 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“ I had rather know than be known," is one of the sentences in Bacon's Promus. - J. S.
? There is, of course, no sucb word as 'repeuploaw, 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: Pụt 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 : 80 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,
" If, in the case of the first, p and o are respectively the densities of gold and silver, and v, w, 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,
po + ou - - (v + x) = (- 1) V: and if the excess of weight in air is w, then
=po to u PV = 0 + u V
W = 9
u, instead of = go
And similarly in the second case,