I made the like experiments upon the same bullets twice or thrice, but found I could only rely on the first, because each time the bullets were heated they lost a considerable part of their weight, which was occasioned not only by the falling off of the parts of the surface reduced into scoria, but also by a kind of drying, or internal calcination, which diminishes the weight of the constituent parts, insomuch that it appears a strong fire renders the iron specifically lighter each time it is heated; and I have found, by subsequent experiments, that this diminution of weight varies much, according to the different quality of the iron. Experience has also confirmed me in the opinion, that the duration of heat, or the time taken up in cooling of iron, is not in a smaller, as stated in a passage of Newton, but in a larger ratio than that of the diameter.
Now if we would enquire how long it would require for a globe as large as the earth to cool, we should find, after the preceding experiments, that instead of 50,000 years, which Newton assigns for the earth to cool to the present temperature, it would take 42,964 years, 221 days, to cool only to the point where it would cease to burn, and 86,667 years and 132 days, to cool to the present temperature.
It might only be supposed, that the refrigeration of the earth should be considerably increased, because we imagine that refrigeration is performed by the contact of the air, and that there is a great difference between the time of refrigeration in the air and in vacuo; and supposing that the earth and air cool in the same time in vacuo, this surplus of time should be reckoned. But, in fact, this difference of time is very inconsiderable, for though the density of the medium, in which a body cools, makes something on the duration of the refrigeration, yet this effect is much less than might be imagined, since in mercury, which is eleven thousand times denser than air, it is only requisite to plunge bodies into it about nine times as often as is required to produce the same refrigeration in air. The principal cause of refrigeration is not, therefore, the contact of the ambient medium, but the expansive force which animates the parts of heat and fire, which drives them out of the bodies wherein they reside, and impels them directly from the centre to the circumference.
By comparing the time employed in the preceding experiments to heat the iron globes, with that requisite to cool them, we find that they may be heated till they become white in one sixth part and a half of the time they take to cool, so as to be held in the hand, and about one fifteenth and a half of that to cool to actual temperature, so that there is a great error in the estimate which Newton made on the heat communicated by the sun to the comet of 1680, for that comet having been exposed to the violent heat of the sun but a short time, could receive it only in proportion thereto, and not only in so great a degree as that author supposes. Indeed, in the passage alluded to, he considers the heat of red-hot iron much less than in fact it is, and he himself states it to be, in a Memoir, entitled, The Scale of Heat, published in the Philosophical Transactions of 1701, which was many years after the publication of his principles. We see in that excellent Memoir, which includes the germ of all the ideas on which thermometers have since been constructed; that Newton, after very exact experiments, makes the heat of boiling water to be three times greater than that of the sun in the height of summer; that of melted tin, six times greater; that of melted lead, eight times; that of melted regulus, twelve times; and that of a common culinary fire, sixteen or seventeen times; hence we may conclude, that the heat of iron, when heated so as to become white, is still greater, since it requires a fire continually animated by the bellows to heat it to that degree. Newton seems to be sensible of this, for he says, that the heat of iron in that state seems to be seven or eight times greater than that of boiling water. This diminishes half the heat of this comet, compared to that of hot iron.
But this diminution, which is only relative, is nothing in itself, nor nothing in comparison with that real and very great diminution which results from our first consideration. For the comet to have received this heat a thousand times greater than that of red-hot iron, it must have remained a very long time in the vicinity of the sun, whereas it only passed very rapidly at a small distance. It was on the 8th of December, 1680, at 6/1000 distance from the earth to the centre of the sun; but 24 hours before, and as many after, it was at a distance six times greater, and where the heat was consequently 36 times less.
To know then the quantity of this heat communicated to the comet by the sun, we here find how we should make this estimation tolerably just, and, at the same time, make the comparison with hot iron by the means of my experiments.
We shall suppose, as a fact, that this comet took up 666 hours to descend from the point where it then was, and which point was at an equal distance as the earth is from the sun, consequently it received an equal heat to what the earth receives from that luminary, and which I here take for unity; we shall likewise suppose that the comet took 666 hours more to ascend from the lowest point of its perihelium to this same distance; and supposing also its motion uniform, we shall perceive, that the comet being at the lowest point of its perihelium, that is, to 6/1000 of the distance from the earth to the sun, the heat it received in that motion was 27,766 times greater than that the earth receives. By giving to this motion a duration of 80 minutes, viz. 40 for its descent, and 40 for its ascent, we shall have, at 6 distance, 27,776 heat during 80 minutes at 7 distance 20,408 heat also during 80 minutes, and at 8 distance 15,625 heat during 80 minutes, and thus, successively, to the distance of 1000, where the heat is one. By summing up the quantity of heat at each distance we shall find 363,410 to be the total of the heat the comet has received from the sun, as much in descending as in ascending, which must be multiplied by the time, that is, by four thirds of an hour; we shall then have 484,547, which divided by 2,000 represents the solid heat the earth received in this time of 1332 hours, since the distance is always 1,300, and the heat always equals one. Thus we shall have 242,547/2000 for the heat the comet received more than the earth during the whole time of its perihelium instead of 28,000, as Newton supposed it, because he took only the extreme point, and paid no attention to the very small duration of time. And this heat must still be diminished 242,547/2000, because the comet ran, by its acceleration, as much more way in the same as it was nearer the sun. But by neglecting this diminution, and admitting that the comet received a heat nearly 242 times greater than that of our summer’s sun, and, consequently 172/7 times greater than that of hot iron, according to Newton’s estimation, or only ten minutes greater according to this estimation; it must be supposed, that give a heat ten times greater than that of red hot iron, it required ten times more time; that is to say, 1332; consequently, we may compare the comet to a globe of iron heated by a forge fire for 13320 hours, to heat it to a whiteness.
Now we find by calculation from my experiments, that with a forge fire, we can heat to a whiteness a globe whose diameter is 2283421/2 inches in 799200 minutes, and, consequently, the whole mass of the comet to be heated to the point of iron to a whiteness, during the short time it was exposed to the heat of the sun, could only be 2233421/2 inches in diameter; and even then it must have been struck on all sides, and at the same time, by the light of the sun. Thus comets, when they approach the sun, do not receive an immense nor a very durable heat, as Newton says, and as we at the first view might be inclined to believe. Their stay is so short in the vicinity of the sun, that their masses have not time to be heated, and besides only part of their surface is exposed to it; this part is burnt by the extreme heat, which by calcining and volatilizing the matter of this surface, drives it outwardly in vapours and dust from the opposite side to the sun; and what is called the tail of the comet, is nothing else than the light of the sun rendered visible, as in a dark room, by those atoms which the heat lengthens as it is more violent.
But another consideration very different and infinitely more important, is, that to apply the result of our experiments and calculation to the comet and earth, we must suppose them composed of matters which would demand as much time as iron to cool: whereas, in reality, the principal matters of which the terrestrial globe is composed, such as clay, stones, &c. cannot possibly take so long.
To satisfy myself on this point, I caused globes of clay and marl to be made, and having heated them at the same forge until white, I found that the clay balls of two inches, cooled in 38 minutes so as to be held in the hand; those of two inches and an half, in 48 minutes; and those of three inches, in 60 minutes; which being compared with the time of the refrigeration of iron bullets of the same diameters, give 38 to 80 for two inches, 48 to 102 for two inches and a half, and 60 to 127 for three inches; so that only half the time is required for the refrigeration of clay, to what is necessary for iron.