By a third experiment, with a less degree of fire than the preceding, the same bullets with a fresh tin bullet, cooled in the following manner.

From these experiments, which I made with as much precision as possible, we may conclude, first, that the time of refrigeration of iron, so as to be held in the hand, is to that of copper : : 53¹/₂ : 45, and so to the point of temperature : : 142 : 125.

2dly, That the time of refrigeration of iron, so as to be held in the hand, is to that of the first refrigeration of common marble : : 53¹/₂ : 35¹/₂ and their entire refrigeration : : 142 : 110.

3dly, that the time of refrigeration of iron, to that of gres, so as to be held in the hand, is : : 53¹/₂ : 32 and : : 142 : 102¹/₂, for their entire refrigeration.

4thly, That the time of refrigeration of iron to that of lead, so as to be held in the hand, is : : 53¹/₂ : 27 and 142 : 94¹/₂ for their entire refrigeration.

In an oven hot enough to melt tin, although all the coals and cinders were drawn out, I placed, on a piece of iron wire, five bullets, distant from one another about nine lines, after which the oven was shut, and having drawn them out, in about 18 minutes they cooled,

In the same oven, but with a slower heat, the same bullets with an other bullet of tin, cooled,

In the same oven, but with a still less degree of heat, the same bullets cooled,

Having placed in the same oven five other bullets, placed the same and separated from each other, their refrigeration was in the following proportions.

In the same oven, and in the same manner, another bullet of Bismuth was placed, with six other bullets, which cooled,

There was put in the same oven a bullet of glass, another of tin, one of copper, and one of iron, and they cooled, of iron, and they cooled,

Bullets of gold, glass, porcelain, gypsum, and gres, were heated together, and cooled,

Bullets of silver, common marble, hard stone, white marble, and soft calcareous stone of Anieres, near Dijon, were heated like the former, and cooled,

The whole of these experiments were made with the utmost care and attention, not only by myself but in the presence of several persons, who also endeavoured to judge of the first degree of temperature by holding the bullets for half a second in their hands, and the relations of which are more exact than those of the actual temperature, because that being variable the result must sometimes vary also.

With a view to avoid that prolixity which would necessarily attend the continual repetition in a comparative statement of the refrigeration of these different bodies, we have connected them in a general table, and taking 10,000 for the standard of comparison, their differences may be seen at one view.

A TABLE
OF THE
Relations of different Mineral Substances.

IRON, with

EMERY, with

COPPER, with

GOLD, with

ZINC, with

SILVER, with

WHITE MARBLE, with

COMMON MARBLE, with

HARD CALCAREOUS STONE, with

GRES, with

GLASS, with

LEAD, with

TIN, with

STONE CALCAREOUS SOFT, with

CLAY, with

BISMUTH, with

PORCELAIN, with

ANTIMONY, with

OKER, with

CHALK, with

GYPSUM, with

WOOD, with

Notwithstanding the assiduity I used in my experiments, and the care I took to render the relations exact, I own there are still some imperfections in the foregoing table; but the defects are trivial, and do not much influence the general results; for example, it will easily be perceived, that the relation of zinc to lead being 10,000 to 6,051, that of zinc to tin should be less than 6,000, whereas it is found 6,777 in the table. It is the same with respect of silver to bismuth, which ought to be less than 6,308, and also with regard of lead to clay, which ought to be more than 8,000, but in the table is only 7,878. This difference proceeded from the leaden and bismuth bullets not being always the same; they melted, as well as those of tin and antimony, and, therefore, could not fail to produce variations, the greatest of which are the three I have just remarked. It was not possible for me to do better; the different bullets of lead, tin, bismuth, and antimony, which I successively made use of, were made in the same manner, but the matter of each might be somewhat different, according to the quantity of the alloy in the lead and tin, for I had pure tin only for the two first bullets; besides, there remains very often a small cavity in the melted bullet, and these little causes are sufficient to produce the little differences which may be remarked in the table.

On the whole, to draw from these experiments all the profit that can be expected, the matters which compose their object must be divided into four classes, viz. 1. Metals. 2. Semi-metals and Metallic Minerals. 3. Vitreous and Vitrescible Substances. And 4. Calcareous and Calcinable substances. Afterwards the matters of each class must be compared between themselves to discover the cause, or causes, or the order which follows the progress of heat in each, and then with each other, in order to deduce some general results.

First. The order of the six metals, according to their density, is tin, iron, copper, silver, lead, and gold; whereas the order in which they receive and lose their heat is tin, lead, silver, gold, copper, and iron; so that in tin alone it retains its place.

The progress and duration of heat in metals does not then follow the order of their density, except in tin, which being the least dense, is also that which soonest loses its heat; but the order of the five other metals demonstrates that it is in relation to their fusibility that they all receive and loose heat; for iron is more difficult to melt than copper, copper more than gold, gold more than silver, silver more than lead, lead more than tin; and therefore we may conclude that it is only by chance if the density and fusibility of tin be found so united as to place it in the last rank. Nevertheless, it would be advancing too much to pretend that we must attribute all to fusibility, and nothing to density. Nature never deprives herself of one of her properties in favour of another in an absolute manner; that is to say, in a mode that the first has not any influence on the second. Thus, density may be of some weight in the progress of heat; but we may safely affirm, that in the six metals it has very little comparatively with fusibility.

This fact was neither known to chemists nor naturalists; they did not even imagine that gold which is more than twice as dense as iron, nevertheless loses its heat near a third sooner. It is the same with lead, silver, and copper, which are all more dense than iron, and which, like gold, heat and cool more readily; for though the object of this, second memoir was only refrigeration, yet the experiments of the one that preceded it demonstrate, that there is ingress and egress of heat in bodies, and that those which receive it most quickly also lose it the soonest.

If we reflect on the real principles of density, and the cause of fusibility, we shall perceive, that density depends absolutely on the quantity of matter which Nature places in a given space; that the more she can make it enter therein, the more density there will be, and that gold, in this respect, is of all substances, that which contains the most matter relatively to its volume. It is for this reason that it has been hitherto thought, that more time is required to heat or cool gold than other metals; and it is natural enough to suppose, that containing double or treble the matter in the same volume, double or treble time would be required to penetrate it with heat; nay this would be true, if in every substance the constituent parts were of the same figure and ranged the same. But in the most dense the molecules of matter are, probably, of a figure sufficiently regular not to leave very void places between them; in others which are not so dense, and their figures more irregular, more vacuities are left, and in the lightest, the molecules being few, and most likely of a very irregular figure, a thousand times more void is found than plenitude; for it may be demonstrated by other experiments, that the volume of even the most dense substance contains more void space than full matter.

Now, the principal cause of fusibility is the facility which the particles of heat find in separating these molecules of full matter from each other; let the sum of the vacuities be greater or less, which causes density or lightness, it is indifferent to the separation of the molecules which constitute the plenitude; and the greater or less fusibility depends entirely on the power of coherence which retains the massive parts united, and opposes itself more or less to their separation. The dilatation of the total volume is the first degree of the action of heat; and in different metals it is made in the same order as the fusion of the mass, which is performed by a greater degree of heat or fire. Tin, which melts the most readily, is also that which dilates the quickest; and iron, which is the most difficult of all to melt, is likewise that whose dilatation is the slowest.

After these general positions, which appear clear, precise, and founded on experiments that nothing can contradict, it might be imagined that ductility would follow the order of fusibility, because the greater or less ductility seems to depend on the greater or less adhesion of the parts in each metal; nevertheless, ductility seems to have as much connection with the order of density, as with that of their fusibility. I would even affirm that it is in a ratio composed of the two others, but that would be only by estimation, and a presumption which is, perhaps not founded; for it is not so easy to exactly determine the different degrees of fusibility, as those of density; and as ductility participates of both, and varies according to circumstances, we have not as yet acquired the necessary knowledge to pronounce affirmatively on this subject, though it is most certainly of sufficient importance to merit particular researches. The same metal when cold gives very different results to what it does when hot, although treated in the same manner. Malleability is the first mark of ductility; but that gives only an imperfect idea of the point to which ductility may extend; nor can simple lead, the most malleable metal, be drawn into such fine threads as gold, or even as iron, which is the least malleable. Besides we must assist the ductility of metals with the addition of fire, without which they become brittle: even iron, although the most robust, is brittle like the rest. Thus the ductility of one metal, and the extent of continuity which it can support, depend not only on its density and fusibility, but also on the manner and space in which it is treated, and of the addition of heat or fire which is properly given to it.

II. By comparing those substances which we term semi-metals and metallic minerals, which want ductility, we shall perceive, that the order of their density is emery, zinc, antimony and bismuth, and that in which they receive and lose heat, is antimony, bismuth, zinc, and emery; and which does not in any measure follow the order of their density, but rather that of their fusibility. Emery, which is a ferruginous mineral, although as dense again as bismuth, retains heat longer. Zinc, which is lighter than antimony or bismuth, retains heat longer than either. Antimony and bismuth, receive and keep it nearly alike. There are, therefore, semi-metals, and metallic minerals, which, like metals, receive and lose heat nearly in the same relation as their fusibility, and partake very little of their density.

But by joining the six metals, and the four semi-metals, or metallic minerals, which I have tried, we shall find the order of the densities of these ten mineral substances to be emery, zinc, antimony, tin, iron, copper, bismuth, silver, lead and gold. And that the order in which these substances heat and cool, is antimony, bismuth, tin, lead, silver, zinc, gold, copper, emery and iron, in which there are two things that do not appear to perfectly agree with the order of fusibility.

First, Antimony, which, according to Newton, should heat and cool slower than lead, since by his experiments it requires ten degrees of the same heat to fuse, of which eight are sufficient for lead; whereas by my experiments antimony is found to heat and cool quicker than lead. But it should be observed that Newton made use of the regulus of antimony, and that I employed only melted antimony in experiments. Now this regulus of antimony, or native antimony, is much more difficult to fuse than antimony which has already undergone a first fusion, therefore that does not make an exception to the rule. On the whole, I do not know what relation native antimony, or regulus of antimony, may have with the other matters I have heated and cooled; but I presume, from the experiments of Newton, that it heats and cools slower than lead.

Secondly, it is pretended, that zinc fuses more easily than silver, consequently it should be found before silver in the order indicated by experiments, if this order were in all cases relative to that of fusibility; and I own that this semi-metal seems, at the first glance, to make an exception to the law which is followed by all the others; but it must be observed, that the difference given by my experiments between zinc and silver is very trifling. The small globe of silver which I made use of was of the purest silver, without the least mixture of copper; but I had my doubts whether that of zinc were entirely free from copper, or some other metal less fusible; and therefore, after all my experiments, I returned the globe of zinc to M. Rouelle, a celebrated professor of chemistry, requesting him carefully to examine it, which having done, after several trials, he found a pretty considerable quantity of iron, or saffron of steel in it.

I have, therefore, had the satisfaction of seeing that not only my own supposition was well founded, but also that my experiments have been made with sufficient precision to evince a mixture. Thus zinc exactly follows the order of fusibility, like the other metals and semi-metals, in the progress of heat, and does not make any exception to the rule. It cannot therefore, in general, be said that the progress of heat in metals, semi-metals, and metallic minerals, is in the same ratio, or even nearly to that of their fusibility.

III. The Vitrescible and Vitreous Matters, which I tried, being ranged according to their density, are, pumice-stone, porcelain, oker, clay, glass, rock-chrystal, and gres, for I must observe, that although chrystal is not set down in the table of the weight of each matter but for six drachms 22 grains, it must be supposed one drachm heavier, because it was sensibly too small; and it was for this reason that I excluded it from the general table of relations; nevertheless, as the general result agrees with the rest, I can present the following as the order in which these different substances are cooled:

Pumice-stone, oker, porcelain, clay, glass, crystal and gres, is according to that of their density, for the oker is here before the porcelain only because, being a fusible matter, it diminished by the friction it underwent in the experiments, and, besides, their density differs so little that they may be looked upon as equal.

Thus the law of the progress of heat in vitrescible and vitreous matters is relative to the order of their density, and has little or no relation with their fusibility but by the heat required to fuse those substances being in an almost equal degree, and the particular degree of their different fusibility being so near each other that an order of distinct terms cannot be made; thus their almost equal fusibility making only one term, which is the extreme of this order, we must not be astonished that the progress of heat here follows the order of density, and that these different substances, which are all equally difficult to fuse, heat and cool more or less quick in proportion to the matter they contain.

It may be objected to me that glass fuses more easily than clay, porcelain, oker, and pumice-stone, which, nevertheless, heat and cool in less time than glass; but the objection will fail when we reflect, that to fuse glass it is requisite to have a very fierce fire, the heat of which is so remote from the degrees which glass receives in our experiments on refrigeration, that it cannot have any influence on them. Besides, by powdering clay, porcelain, and pumice-stone, and by giving them their analogous fusers, as we give to sand to convert it into glass, it is more than probable that we should fuse all the matters in the same degree of fire, and that, consequently we must look upon it as equal, or almost equal, with their resistance to fusion; and it is for this reason that the law of the progress of heat in these matters is found proportionable to the order of their density.

IV. Calcareous matters, ranged according to the order of their density, are, chalk, soft stone, hard stone, common marble, and white marble, which is the same as that of their density. The fusibility is not here of any weight, because it requires at first a very great degree of fire to calcine them; and although the calcination divides the parts, we must look upon the effect only as a first degree and not as a complete fusion. The whole power of the best burning mirrors is scarcely sufficient to perform it. I have melted and reduced into a kind of glass some of these calcareous matters; and I am convinced that these matters may, like all the rest, be reduced ulteriorly into glass, without employing for this purpose any fusing matter, and only by the force of a fire superior to that of our furnaces; consequently the common term of their fusibility is still more remote, and more extreme, than that of vitreous matters, and it is for this reason that they also follow more exactly the order of density in the progress of heat.

White gypsum, improperly called alabaster, is a matter which calcines like all other plasters by a more moderate heat than that which is necessary for the calcination of calcareous matters, and it follows the order of density in the progress of heat which it receives or loses, for although much more dense than chalk, and a little more so than white calcareous stone, it heats and cools more readily than either of those matters. This demonstrates that the more or less easy calcination and fusion produces the same effects relatively to the progress of heat. Gypsous matters do not require so much fire to calcine as calcareous, and it is for this reason that, although more dense, they heat and cool much quicker.

Thus it may be concluded, that, in general, the progress of heat in all Mineral Substances is always nearly in a ratio of their greater or less facility to calcine, or melt: but that when their calcination, or their fusion, are equally difficult, and that they require a degree of extreme heat, then the progress of heat is made according to the order of their density.

I have deposited in the Royal Cabinet the globes of gold, silver, and of all the other metallic and mineral substances which served for the preceding experiments, that if the truth of their results, and the general consequences which I have deduced, be doubted, there may be an opportunity of rendering them more authentic.