I. The bullet of half an inch was heated white in two minutes, cooled
so as to be held in the hand in 12, and to the actual temperature in 39
minutes.
II. That of an inch, heated white in five minutes and a half, cooled
so as to be held in the hand, in 35-1/2 minutes, and to the actual
temperature in one hour and 23 minutes.
III. That of an inch and an half, heated white in nine minutes,
cooled so as to be held in the hand in 58 minutes, and to the actual
temperature in two hours and 35 minutes.
IV. That of two inches heated white in 13 minutes, cooled so as to be
held in the hand in one hour 20 minutes, and to the actual temperature
in three hours 16 minutes.
V. That bullet of two inches and an half heated white in 16 minutes,
cooled so as to be held in the hand in one hour 42 minutes, and to the
actual temperature in four hours 30 minutes.
VI. That bullet of three inches heated white in 19-1/2 minutes, cooled
so as to be held in the hand in two hours seven minutes, and to the
actual temperature in five hours eight minutes.
VII. That of three inches and a half heated white in 23-1/2 minutes,
cooled so as to be held in the hand in two hours 36 minutes, and to the
actual temperature in five hours 56 minutes.
VIII. That of four inches heated white in 27 minutes and a half, cooled
so as to be held in the hand in three hours two minutes, and to the
actual temperature in six hours 55 minutes.
IX. That of four inches and a half heated white in 31 minutes, cooled
so as to be held in the hand in three hours and 25 minutes, and to the
actual temperature in seven hours 46 minutes.
X. That of five inches heated white in 34 minutes, cooled, so as to
be held in the hand, in three hours 52 minutes, and to the actual
temperature in eight hours 42 minutes.
The most constant difference that can be taken between each of the
terms which express the time of cooling, from the instant the bullets
were drawn from the fire, to that when we can touch them unhurt, is
found to be about 24 minutes, for, by supposing each term to increase
24, we shall have 12, 36, 60, 84, 108, 132, 156, 180, 204, 228 minutes.
And the continuation of the real time of these coolings are, 12,
35-1/2, 58, 80, 102, 127, 156, 182, 205, 232 minutes, which approach
the first as nearly as experiment can approach calculation.
So, likewise, the most constant difference to be found between each of
the terms of cooling to actual temperature is found to be 54 minutes,
for by supposing each term to increase 54, we shall have 39, 93, 147,
201, 255, 309, 363, 417, 471, 525 minutes, and the continuation of
the real time of this cooling is found, by the preceding experiments,
to be 39, 93, 145, 196, 248, 308, 356, 415, 466, 522 minutes, which
approaches also nearest to the first.
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 17-2/7 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 228342-1/2 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 223342-1/2 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.
I found also, that lumps of clay, or marl, of two inches, refrigerated
so as to be held in the hand in 45 minutes; those of two inches and a
half in 58; and those of three inches in 75, which being compared with
the time of refrigeration of iron bullets of the same diameters, gives
46 to 80 for two inches, 58 to 102 for two inches and a half, and 75 to
127 for three inches, which nearly form the ratio of 9 to 5; so that
for the refrigeration of clay, more than half the time is required than
for iron.
It is necessary to observe, that globes of clay heated white, lost
more of their weight than iron bullets, even to the ninth or tenth
part of their weight: whereas marl heated in the same fire, lost
scarcely any thing, although the whole surface was covered over with
scales, and reduced into glass. As this appeared singular, I repeated
the experiment several times, increasing the fire, and continuing it
longer than for iron; and although it scarcely required a third of the
time to redden marl, to what it did to redden iron, I kept them in the
fire thrice as long as was requisite, to see if they would lose more,
but I found very trifling diminutions; for the globe of two inches
heated for eight minutes, which weighed seven ounces, two drachms,
and thirty grains, before it was put in the fire, lost only forty-one
grains, which does not make a hundredth part of its weight; and that
of three inches, which weighed twenty-four ounces, five drachms, and
thirteen grains, having been heated by the fire for eighteen minutes,
that is nearly as much as iron, lost only seventy-eight grains, which
does not make the hundredth and eighty-first part of its weight. These
losses are so trifling, that it may be looked upon, in general, as
certain that pure clay loses nothing of its weight in the fire; for
those trifling diminutions were certainly occasioned by the ferruginous
parts which were found in the clay, and which were in part destroyed by
the fire. It is also worthy of observation, that the duration of heat
in different matters exposed to the same fire for an equal time, is
always in the same proportion, whether the degree of heat be greater or
smaller.
I have made similar experiments on globes of marble, stone, lead, and
tin, by a heat only strong enough to melt tin, and I found, that iron
refrigerated in eighteen minutes, so as to be able to hold it in the
hand, marble refrigerated to the same degree in twelve minutes, stone
in eleven, lead in nine, and tin in eight. It is not, therefore, in
proportion to their density, as is commonly supposed, that bodies
receive and lose more or less heat, but in an inverse ratio of their
solidity; that is, of their greater or lesser _non fluidity_; so that,
by the same heat, less time is requisite to heat or cool the most dense
fluid.
To prevent the suspicion of vainly dwelling upon assertion, I think it
necessary to remark upon what foundation I build this theory; I have
found that bodies which should heat in ratio of their diameters, could
be only those which were perfectly permeable to heat, and would heat
or cool in the same time; hence, I concluded that fluids, whose parts
are only held together by a slight connection, might approach nearer to
this perfect permeability than solids, whose parts have more cohesion.
In consequence of this, I made experiments, by which I found, that
with the same heat all fluids, however dense they might be, heat and
cool more readily than any solids, however light, so that mercury, for
example, heats much more readily than wood, although it be fifteen or
sixteen times more dense.
This made me perceive that the progress of heat in bodies cannot, in
any case, be made relatively to their density; and I have found by
experience, that this progress, as well in solids as fluids, is made
rather by reason of their fluidity, or in an inverse ratio of their
solidity. I mean by _solidity_ the quality opposite to fluidity; and I
say, that it is in an inverse ratio of this quality that the progress
of heat is made in both bodies; and that they heat or cool so much the
faster as they are the more fluid, and so much the slower as they are
more solid, every other circumstance being equal.
To prove that solidity, taken in this sense, is perfectly independent
of density, I have found, by experience, that the most or least dense
matters, heat or cool more readily than other more or less dense
matters, for example, gold or lead, which are much more dense than iron
and copper, heat and cool much quicker; while tin and marble, which are
not so dense, heat and cool much faster than iron and copper; and there
are likewise many other matters which come under the same description;
so that density is in no manner relative to the scale of the progress
of heat in solid bodies.
It is likewise the same in fluids, for I have observed, that
quicksilver, which is thirteen or fourteen times more dense than water,
nevertheless heats and cools in less time than water; and spirit of
wine, which is less dense than water, heats and cools much quicker;
so that generally the progress of heat in bodies, as well with regard
to the ingress as egress, has no affinity with their density, and is
principally made in the ratio of their fluidity, by extending the
fluidity to a solid; from hence I concluded, that we should know the
real degree of fluidity in bodies, by heating them to the same heat;
for their fluidity would be in a like ratio as that of the time during
which they would receive and lose this heat; and that it would be the
same with solid bodies. They will be so much the more solid, that
is to say, so much the more _non fluids_, as they require more time
to receive and lose this heat, and that almost generally to what I
presume; for I have already tried these experiments on a great number
of different matters, and from them I have made a table, which I have
endeavoured to render as complete and exact as possible.
I caused several globes to be made of an inch diameter with the
greatest possible precision, from the following matters, which nearly
represent the Mineral kingdom.
M. Tillet, of the Academy of Sciences, made the globe of refined gold
at my particular request, and the whole of them weighed as follows:
oz. d. gr.
Gold 6 2 17
Lead 3 6 28
Pure silver 3 3 22
Bismuth 3 0 3
Copper-red 2 7 56
Iron 2 5 10
Tin 2 3 48
Antimony melted, and which had
small cavities on its surface 2 1 34
Fine 2 1 2
Em 1 2 24-1/2
White marble 1 0 25
Pure clay 0 7 24
Marble common of Montbard 0 7 20
White gypsum, improperly called
Alabaster 0 6 36
Calcareous white stone of the quarry
of Anieres, near Dijon 6 6 6
Rock chrystal: it was a little too
small, and had many defects. I
presume that without them it
would have weighed 0 6 22
Common glass 0 6 21
Pure earth, very dry 0 6 16
Oker 0 5 9
Porcelain of the Court de Lauraguais 0 5 2-1/2
White chalk 0 4 49
Cherrywood, which although lighter
than most other woods, is that
which takes in the least fire 0 1 59
I must here observe, that a positive conclusion must not be made of
the exact specific weight of each matter from the preceding table,
for notwithstanding the precaution that was taken to render the
globes equal, yet, as I was obliged to employ different workmen, some
were too large, and others too small. Those which were more than an
inch diameter were diminished, but those of rock chrystal, glass and
porcelain, which were rather too small, we suffered to remain, and only
rejected those of agate, jasper, and porphyry, which were sensibly so.
This precision in size was however not absolutely necessary, for it
could very little alter the result of my experiments.
Previously to ordering these globes, I exposed to a like degree
of fire, a square mass of iron, and another of lead of two inches
diameter, and found, by reiterated essays, that lead heated and
cooled in much less time than iron. I made the same experiment on red
copper, and that required more time to heat and cool than lead, and
less than iron. So that of these three matters, iron appeared the least
accessible to heat, and, at the same time, that which retained it the
longest. From which I learn that the law of the progress of heat in
bodies was not proportionable to their density, since lead, which is
more dense than iron or copper, nevertheless heats and cools in less
time than either. As this object appeared important, I was induced
to have these globes made, and to be more perfectly satisfied of the
progress of heat in a great number of different matters, I always
placed the globes at an inch distance from each other, before the same
fire, or in the same oven, 2, 3, 4, or 5, together with a globe of
tin in the midst of them. In most of my experiments I suffered them
to be exposed to the same active fire till the globe of tin began to
melt, and at that instant they were all removed, and placed on a table
in small cases. I suffered them to cool without moving, often trying
whether I could touch them, and the moment they left off burning, and
I could hold them in my hands half a second, I marked the time which
had passed since I drew them from the fire. I afterwards suffered them
to cool to the actual temperature, of which I endeavoured to judge
by means of touching other small globes of the same matters that had
not been heated. Of all the matters which I put to the trial, there
was only sulphur which melted in a less degree of heat than tin, and
notwithstanding its disagreeable smell I should have taken it for a
term of comparison, but being a brittle matter which diminishes by
friction, I preferred tin, although it required nearly double the heat
to melt.
Having heated together bullets of iron, copper, lead, tin, gres, and
Montbard marble, they cooled in the following order:
_So as to be held in the hand _To actual temperature._
for half a second._
Min. Min.
Tin in 6-1/2 In 16
Lead in 8 In 17
Gres in 9 In 19
Common marble in 10 In 21
Copper in 11-1/2 In 30
Iron in 13 In 38
By a second experiment with a fiercer fire, sufficient to melt the tin
bullet, the five others cooled.
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Lead in 10-1/2 In 42
Gres in 12-1/2 In 46
Common marble 13-1/2 In 50
Copper 19-1/2 In 51
Iron 23-1/2 In 54
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.
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Tin in 7-1/2 In 25
Lead in 9-1/2 In 25
Gres in 10-1/2 In 37
Common marble 12 In 39
Copper 14 In 44
Iron 17 In 50
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 : : 53-1/2 :
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 : : 53-1/2
: 35-1/2 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 : : 53-1/2 : 32 and : : 142 : 102-1/2, 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 : : 53-1/2 : 27 and 142 : 94-1/2 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,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Melted tin in 8 In 24
Silver in 14 In 40
Gold in 15 In 46
Copper in 16-1/2 In 50
Iron in 18 In 56
In the same oven, but with a slower heat, the same bullets with an
other bullet of tin, cooled,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Tin in 7 In 20
Silver in 11 In 56
Gold in 12-1/2 In 40
Copper in 14 In 43
Iron in 16-1/2 In 47
In the same oven, but with a still less degree of heat, the same
bullets cooled,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Tin in 6 In 17
Silver in 9 In 26
Gold in 9-1/2 In 28
Copper in 10 In 31
Iron in 11 In 35
Having placed in the same oven five other bullets, placed the same and
separated from each other, their refrigeration was in the following
proportions.
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Antimony in 6-1/2 In 25
Bismuth in 7 In 26
Lead in 8 In 27
Zinc in 10-1/2 In 30
Emery in 11-1/2 In 38
In the same oven, and in the same manner, another bullet of Bismuth was
placed, with six other bullets, which cooled,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Antimony in 6 In 23
Bismuth in 6 In 25
Bismuth in 6 In 25
Lead in 7-1/2 In 28
Silver in 9-1/2 In 30
Zinc in 10-1/2 In 32
Gold in 11-1/2 In 34
Emery in 13-1/2 In 39
There was put in the same oven a bullet of glass, another of tin, one
of copper, and one of iron, and they cooled,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Tin in 8 In 27
Glass in 8-1/2 In 22
Copper in 14 In 42
Iron in 16 In 50
Bullets of gold, glass, porcelain, gypsum, and gres, were heated
together, and cooled,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Gypsum in 8 In 24
Porcelain in 8-1/2 In 25
Glass in 2 In 26
Gres in 10 In 32
Gold in 14-1/2 In 45
Bullets of silver, common marble, hard stone, white marble, and soft
calcareous stone of Anieres, near Dijon, were heated like the former,
and cooled,
_So as to be held in the hand._ _To actual temperature._
Min. Min.
Soft calcareous
stone in 8 In 25
Hard stone in 10 In 34
Common marble in 11 In 35
White marble in 12 In 36
Silver in 13-1/2 In 40
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.