or/ou
Read my introductory burble below, or jump straight to the text.
Before trying to understand this paper, it is necessary to understand that Fourier is *not* a climatologist attempting to provide useful information on terrestrial temperatures. Oh no indeed. I started off assuming that, and got very confused. And I thought he was silly. But he's not (well, mostly not. The stuff about heat from interplanetary space is silly): he's just interested in something different, namely an interesting application of his theory of heat transfer. This means, inter alia, that he tends to concentrate on (what would seem today rather uninteresting) matters that *can* be dealt with by his theory. Also, by "temperature of the earth" he includes (indeed gives priority to) the interior of the globe and wurbles on at vast length on results that are nowadays of very little interest concerning said interior temperature.
It may help to know that I got rather impatient with his wurbling and repetition a few times - forgive the odd intemperate footnote. It is possible - suggested by this phrase - that this memoir is actually the transcription of a talk. In which case one could forgive some of the repetitions. On the other hand, this is supposed to be a reporint of an 1824 article, which suggests otherwise. Unless the 1824 article was a talk. Arghhhhh...
Thanks: RMG for causing me to read this.
In the following, references [1] are to footnotes containing "helpful" additions by me. Smaller comments are added within the text [like this]. Sometimes I have added the original word [lit: mot], either because I am unsure of the correct translation or because I have been deliberately rather free in translation or because the word is for some reason interesting.
I have made no great effort to produce a free-flowing translation; in general I have been quite literal even when this makes for stilted english.
I have broken the lines roughly where the line breaks were in the original (of course you can't see this in html but you can if you look at the source). Page numbers are indicated (thus) and are links to jpegs of the photocopies, taken with a nikon 950 at "normal" 600x800 res. Most of the fuzziness is due to the UL's photocopying, not the camera.
Links to particular phrases:
The question of the terrestrial temperature, one of the most
important and most difficult of all natural philosophy,
is composed of diverse elements which can be
considered under a general point of view. I thought that it
would be useful to reunite in a single text the principal consequences
of this theory; the analytical details which one
omits here can be found for the most part in works which
I have already published. I wish above all to present to physicists,
in a short tableau, the ensemblage of phenomena and
the mathematical relations between them.
The heat of the earth derives from three sources which it is
necessary first to distinguish.
1. The earth is heated by solar radiation, whose
unequal distribution produces the diversity of climates [3]
2. It participates in the communal temperature of the planetary
spaces, being exposed to the irradiation of innumerable stars which
surround all parts of the solar system [4]
3. The earth conserves in the interior of its mass a
part of the original heat, which it contained when the
planets were formed [5].
In considering each of these three causes and the phenomena
which they produce, we will understand as clearly
as is possible, insofar as the state of science
permits today, the principal characters of
these phenomena.
Our solar system is placed in a region of the
universe of which all the points have a communal and
constant temperature, determined by the rays of light and heat
which come from the surrounding stars.
This cold temperature of the planetary sky is a little less than
that of the polar regions of the globe [6]
The earth would have the same temperature as the sky, if two causes
did not act to warm it. One is the interior heat which
the earth has possessed since the planets were formed,
and of which only a part has been dissipated across the surface.
The second cause is the continual action of the solar
radiation which has penetrated all the mass [7], and which entrain
in the surface the different climates.
The original heat of the globe doesn't cause any sensible
effect at the surface; but it can be immense in the interior
of the earth. The surface temperature does not exceed by one
thirtieth of a degree centigrade the value to which it
will come: it at first diminished very rapidly;
but, in its actual state, this change continues with
extreme slowness [8].
The observations received to this day indicate
that the diverse points of a single vertical prolonged into
the solid earth are hotter when the
depth is greater, and one has evaluated an increase
of a degree per 30 or 40 meters. Such a result supposes
a very elevated interior temperature; this cannot come from
the action of solar radiation; it is naturally explained
by the heat which the earth holds from its origin.
This increase, about one degree per 32 meters,
will not always be the same, it diminishes progressively;
but a great number of centuries (much
more than 30,000 years) before it is reduced to a
half of its current value.
If other causes ignored today can explain the
same facts, and it there exist other sources (either general
or accidental) of terrestrial heat, one will discover
this by comparison of the results of this theory with
observations [9].
The rays of heat which the suns sends incessantly
to the globe there produces two effects which are very distinct:
one is periodic and is accomplished in the exterior
envelope, the other is constant; one observes it in
deep places, for example, 30 meters below the surface
[10].
The temperature of these places does not change
sensibly during the year, they are fixed; but
they are very different in different climates: they result
from the perpetual action of solar radiation and the unequal
exposition of the surface, from the equator to the
poles. One can determine the time which must pass for
this solar radiation to produce the diversity
of climates that we observe today.
All these results accord with the dynamical theories
which have told us of the stability of the rotation
axis of the earth [11].
The periodic effect of the solar heat consists of
diurnal and annual variations. This order of facts is
represented exactly and in all its details by the theory.
The comparison of the results with observations serves to
measure the conductivity of the material of which the
earths envelope is formed [12].
The presence of the atmosphere and the waters has the general
effect of rendering the distribution of heat more uniform.
In the ocean and the lakes, the coldest molecules, or
those of the highest density, travel
continually towards the lower regions, and the movements
of heat due to this cause are much more
rapid than those in solid masses which
occur due to conduction [13]. Mathematical examination
of this effect would require exact and numerous observations:
they would serve to know how these interior movements
prevent the effects of the original heat of the
globe being sensible in the depths of the waters [14].
Liquids conduct heat very badly; but
they have,like the airy regions, the property of
transporting heat rapidly in certain directions. It is this
same property which, combined with the centrifugal force,
displaces and mixes all parts of the atmosphere and the
ocean; it causes regular and immense currents.
The interposition of the air greatly modifies the effects of the
heat at the surface of the globe. The solar rays,
traversing the atmospheric layers compressed by their own
weight, heat them quite unequally: those which are most
rarified are also coldest, because they extinguish and absorb
a smaller part of these rays [15]. The heat of the
sun, arriving in the state of light, has the property of
penetrating diaphanous solids or liquids, and
loses this property nearly entirely when they are converted, by their
interaction with terrestrial bodies, into IR [16].
This distinction of SW [17] and IR
explains the elevation of temperature caused by
transparent bodies [**gh?**]. The mass of water which covers a
great part of the earth, and the polar ice, present less
obstacles to the SW than to the IR,
which returns to exterior space.
The presence of the atmosphere produces an effect of the same type,
but which, in the current state of theory and because
of the lack of observations, cannot be
exactly defined [18]. Whatever, one cannot doubt
that the effect due to the impression of SW onto a
solid body of enormous size greatly surpasses
that which one would observe in exposing a
thermometer to the light of this star [19].
The radiation from the highest levels of the atmosphere,
whose cold is very intense and nearly constant,
influences all the meteorological things which we observe:
it can be rendered more sensible by reflection in the surface
of concave mirrors. The presence of clouds which intercepts
the rays tempers the cold of nights [20].
One sees that the near-surface of the earth is placed
between a solid mass who central temperature can
surpass that of incandescent matter, and an immense encircling region
whose temperature is less that the freezing point
of mercury.
All the preceding arguments apply to
other planetary bodies. One can consider them as placed
in a enclosure, whose temperature is communal and
constant, and a little less than that of the terrestrial poles.
This same temperature of the sky is that of the surface of the most
distant planets; because the impression of the rays from the sun,
even augmented by the disposition of the surface regions, would
be too feeble to cause sensible effects; and we
know, from the state of the earth, that, on the
planets (whose formation cannot be less ancient), there
remains no elevation of the surface temperature
due to the original heat [21].
It is equally likely that, for most of the
planets, the temperature of the poles is a little
above that of the inter-planetary space. As to the average
temperature which each of these bodies has due to the action of the sun,
it is not exactly known, because it depends on the
presence of an atmosphere and the state of the surface. On can
only assign in an approximate manner the average
temperature that the earth would acquire, if it was transported
into the same place as the other planet.
After this exposition, we will successively examine the
different parts of the question, and we must first
insert a remark which appertains to all these parts,
because it is founded on the nature of the differential
equations of heat transport. It is that
the effects which come from the three causes
which we have indicated can be calculated separately,
as if each of the causes existed alone. It then
suffices to reunite the partial effects: they superpose
freely like the natural oscillations of bodies [22].
We describe, firstly, the principal results
due to the long-term effects of solar radiation on the earth.
If one places a thermometer at a considerable
depth below the surface of the solid earth, for
example, at 40 meters, this instrument shows a fixed temperature
[23].
One observes this fact at all the points of the globe. This
temperature of deep places is constant for a given
place; but it is not the same in the diverse climates.
It decreases in general as one moves polewards.
If one observes the temperature of points much
closer to the surface, for example at one meter or 5 or 10
meters depth, one sees very different effects.
The temperature varies during a day or a
year: but we shall make first of all the abstraction of this
envelope where these variations occur, and supposing
that this envelope is removed, we will consider fixed the
temperatures on the new surface of the globe
[24].
One can conceive that the state of the mass has
varied continually according to the heat received from the
"oven" [lit: foyer]. This variable state of the interior temperatures is
altered by degrees, and approaches a final
state which is not subject to change. Thus each interior
point of the solid sphere acquires and keeps a determined temperature
which only depends on the location of the point
[25].
The final state of the mass, when the heat has penetrated all the
parts, is exactly comparable to that of a vase which
receives liquid from upper openings which
furnishes it with a constant source, and escapes an
equal quantity by one or more outflows.
Thus the solar heat accumulates in the interior
of the globe, and renews itself constantly. It penetrates the
parts of the surface near the equator, and dissipates
from the polar regions. The first question of this
genre which was subjected to calculus, is found in a
memoir which I read at the Institut de France at the end on 1807,
article 115, page 167: this piece is deposited in the archives of
the Academy of Sciences. I treated this first question
then to offer a remarkable example of the application of the
new theory explained in the memoir, and to show
how analysis can allow us to know the routes which the
solar heat follows through the earth.
If we now reestablish the suppressed envelope around
the earth, in which points are not deep enough
for temperatures to be
fixed, one notices a set of more complex facts to which
our analysis gives complete expression. At a medium
depth, like 3 or 4 meters, the temperature
observed does not vary during one day; but it
changes very sensibly in the course of the year; it
rises and lowers successively. The range of these
variations, that is to say the difference between the maximum and the
minimum, is not the same at all depths;
it is less as the distance to the
surface is bigger. The different points on a single
vertical do not show the extremes at the same
times [phase lag]. The range of the variations, the times of
year which correspond to the greatest, to the average
or minimum, changes with the position of the
point in the vertical. It is the same with the quantities
of heat which descend and rise alternatively: all
these values have certain relation between them, which
experience indicates and analysis explains very
distinctly. The observed results conform to the theoretical
predictions; there is no natural effect more completely
explained. The average temperature of a point
anywhere on the vertical, that is to say the mean value of
all those observed in the course of a
year, is independent of the depth, and by consequence that
which one observes immediately below the surface:
this is the same as the fixed temperature of the depths
[26].
It is evident that, in the enunciation of this proposition, we
have abstracted the interior heat of the earth, and for
strong reasons accessory causes which could modify this
result in certain places. Our principal object is to
understand the general phenomena [14].
We said above that the diverse effects could be
considered separately. We must also observe, with
respect to all the numerical evaluations cited in this
memoir, that they are only presented as examples of
calculus. The meteorological observations necessary to furnish
the necessary data, those which would tell us the
heat capacity and the permeability of the matter of which
the globe is composed, are too uncertain and too circumscribed to
allow us, now, to deduce from calculus precise results; but
we indicate the numbers to show how the formulas
could be applied. As approximate [lit: approchee] as
these evaluations are, they are better used to
give a good [lit: juste] idea of the phenomena than general
expressions stripped of numerical applications.
In the parts of the envelope nearest the surface
the thermometer rises and falls during
each day. These diurnal variations cease to be sensible
at a depth of 2 or 3 meters. Below this one can
only observe annual variations, which themselves disappear
deeper down.
If the rotation of the earth about its axis
became incomparably faster, and the same occurred
for the movement of the earth about the sun, the
diurnal and annual variations would cease
to be observed; the points of the surface would acquire
and keep the same fixed temperature as the deeps. In
general, the depth which must be attained for the
variations to cease to be sensible has a very simple relation with
the period which drives the same effects at the surface.
This depth is exactly proportional to the
square root of the period. It is for this reason that the
diurnal variations do not penetrate further than a depth 19
times less than that observed for the annual
variations
[27].
The question of the periodic movement of solar heat
was treated for the first time and resolved in a separate
text which I submitted [lit: remis] to the Institut of France in October 1809.
I reproduced this solution in a piece sent at the
end of 1811, which was published in the Collection of our [the Institut's?]
Memoirs.
The same theory gives the means of measuring the total quantity
of heat which, in the course of a year, determines the
alterations of the seasons. One has the aim, in choosing
this example of the application of the formulae, to show that
there exists a necessary relation between the law of periodic variations
and the total quantity of heat which accomplishes this
oscillation; so that, this law being known, by the observations
made in a given climate, one can conclude the
quantity of heat which is introduced into the earth and
returned to the air.
Considering thus a law similar to that established
for the interior of the globe, one find the following
results. One eighth of the year, after the temperature of the
surface is elevated to its mean value, the earth begins to
warm; the solar radiation penetrate for 6 months.
Following this the heat of the earth takes an opposing course;
it comes out and into the air and the exterior space; but the
quantity of heat which causes [lit: subit] these oscillations in the course
of a year is explained by calculus. If the terrestrial envelope
was formed of a metallic substance, forged iron (I chose this
example having measured the specific
coefficients), the heat which produced the alternation of the
seasons would be, for the climate of Paris and for a square meter
of surface, equivalent to that which would melt a cylindrical
column of ice having for base a square meter, and whose
height would be about 3.1 m [lit: 3m, 1]. Although no one has yet
measured the value of the correct coefficients for the materials of which
the globe is formed, on easily sees that they would give a
result much less than that which was just indicated.
It is proportional to the square root of the product of the
heat capacity divided by [rapportee au] volume and
permeability [exact formula here?].
Let us now consider the second cause of the terrestrial heat
which resides, according to us, in the planetary spaces.
The temperature of this space, exactly defined, is that
which a thermometer would mark, if one could conceive that
the sun and all the planetary bodies which accompany it
ceased to exist, and if the instrument were placed in a point
of the region of the sky currently occupied by the
solar system.
We will indicate the principal facts which have
indicated to us the existence of this proper heat of the
planetary spaces, independent of the presence of the sun and
independent of the original heat conserved in the earth.
To understand this singular phenomenon, one
must examine what would be the thermometric state of the
terrestrial mass if it only received solar heating; and to
render this examination easier, one first supposes that the
atmosphere is suppressed. But if there did not exist any cause
to give to the interplanetary spaces a communal and constant
temperature, that is to say if the globe and
all the bodies of the solar system were placed
in a heatless surrounding, one would observe
effects entirely contrary to those which we know.
The polar regions would suffer an immense cold, and the
decrease of temperatures between the equator to the
poles would be incomparably more rapid and more extended [etendu] than
observed [28].
In this hypothesis of the absolute cold of space, if it
is possible to conceive it, all the effects of heat, such
that we observe on the surface of the globe, would be due to
the presence of the sun. The least variation in the distance
from this star to the earth would occasion very considerable
changes in temperatures, the eccentricity of the orbit
would give birth to diverse seasons.
The intermittence of days and nights would produce effects
sudden and totally different to those which exist. The
surface of bodies would be suddenly, on the commencement of night,
exposed to an immense cold. Animated bodies and plants could not
resist at all an action so strong and prompt, which would reproduce in
an opposite sense at the rising of the sun.
The original heat conserved in the earth
could not supplement the heat from space,
and would not impede any of the effects which one
has just described; because we know with certainty, by
theory and observations, that this central heat
has for a long time been insensible at the surface,
although it could be important at a medium depth.
We conclude from these diverse remarks, and
principally from the mathematical examination of the question, that there exists
an ever-present physical cause which moderates
temperatures at the surface of the globe, and gives to the
planet a fundamental heat independent of the action of
the sun, and the original heat conserved in the
interior. This fixed temperature which the earth receives from
space differs little from that which one would measure at the
terrestrial poles. It is necessarily less than the temperature
of the coldest countries; but, in this
comparison, one cannot admit any but certain observations,
and not consider the accidental effects of a very-intense
cold occasioned by evaporation, by
violent winds and an extraordinary dilation of the air.
Having realised the existence of the fundamental temperature
of space without which the effects of heat observed
at the surface of the globe would be inexplicable, we
interject that the origin of this phenomenon is
evident. It is due to the rays from all the bodies of the
universe, whose light and heat can arrive at
us. The stars which we see with the eye, the
innumerable multitude visible by telescope or the obscure
bodies which fill the universe, the atmospheres which
surround the immense bodies, the rarified material spread
in the diverse parts of space, combines to form rays
which penetrate all parts of the planetary space.
One cannot conceive that there exist such a system of
luminous or heated bodies, without admitting that a point
anywhere in space containing them would acquire a determined
temperature.
The immense number of bodies compensates for the inequalities
in their temperatures, and renders the radiation
uniform.
This temperature of space is not the same in
different regions of the universe; but it does not vary in
those parts where the planetary system is, because the
dimensions of this space [the solar system] are incomparably smaller
than the distances separating the radiating bodies. And so,
on all points of the earths orbit, the planet finds the
same sky [space] temperature.
It is the same for the other planets of our system;
they all participate equally in the communal
temperature, which is more or less augmented, for each
of them, by solar radiation, according to the
distance of the planet from the sun. As to the question
of finding the temperature of each planet,
here are the principals which furnish an exact theory.
The intensity and the distribution of heat at the surface of these
bodies results from the distance from the sun, the inclination of the axis
of rotation and the state of the surface. It is
very different, even in its average value, than that which
an isolated thermometer would show if placed in place
of the planet; because the of the solid state, the very big size,
and without doubt the presence of the atmosphere and the nature of the
surface combine to determine the average value.
The original heat which is conserved in the interior of
the mass has long ago ceased to have a sensible effect
at the surface [this is only about the 10th time he's said this]; the present state of the terrestrial envelope
allows us to know with certainty that the original heat
of the surface is nearly entirely dissipated. We regard
as very probable, according to the constitution of
our solar system, that the temperature of the poles of each
planet, or at least most of them, is little different
to that of space [wrong]. This polar temperature is
sensibly the same for all the bodies, even though their
distance to the sun is very unequal.
One can determine in an approximate [lit: approchee] manner the
degree of heat that the earth would acquire if it was
substituted for [in the orbit of] each of these planets; but the temperature of the
planet itself cannot be assigned; because it would
be necessary to know the state of the surface and the atmosphere. Anyway
this uncertainty does not exist for bodies at the extremities
of the solar system like the planet discovered by Herschell [didn't it have a name yet?].
The solar radiation on this planet is nearly
insensible. The temperature of the surface is thus very little
different to that of the planetary spaces. We have
indicated this last result in a public discourse given
recently in the presence of the Academy. One sees that this
consequence only needs to apply to the most distant planets.
We do not know a means of assigning with
similar precision the average temperature of the other planetary
bodies.
The movements of the air and the waters, the extent of the seas,
the elevation and the form of the surface, the effects of human industry [29]
and all the accidental changes to the terrestrial surface
modify the temperatures in each climate. The characters
of phenomena due to general causes remain; but
the thermometric effects observed at the surface are different
to those which would take place without the accessory
causes.
The mobility of the waters and that of the air tends to modify the
effects of heat and cold; it renders the distribution more
uniform; but it would be impossible that the action of the
atmosphere could make up for the universal cause which upholds the
communal temperature of planetary space; and if this cause
did not exist, one would observe, non withstanding the action of
the atmosphere and the oceans, enormous differences between the
temperatures of the equatorial and polar regions.
[30].
It is difficult to know up to what point the atmosphere
influences the average temperature of the globe, and one ceases
to be guided in this examination by a regular mathematical
theory. We owe to the celebrated voyager M. de Saussure an
experiment which appears very important in illuminating this question.
It consists of exposing to the rays of the sun a vase covered
by one or more layers of well transparent glass,
spaced at a certain distance. The interior
of the vase is lined with a thick envelope of blackened cork [or burnt cork?],
to receive and conserve heat. The heated air
is sealed [contenu] in all parts, either in the box or
in each interval between plates. Thermometers
placed in the vase and the intervals
mark the degree of heat acquired in each place.
This instrument has been exposed to the sun near
midday, and one saw, in diverse experiments, the
thermometer of the vase reach 70, 80, 100, 110 degrees and beyond
(octogesimal division[30.5]). Thermometers placed in the
intervals acquired a lesser degree of heat,
and which decreased from the depth of the box towards the outside.
The effect of solar heat on the air trapped by the
transparent envelopes has been observed long since.
The apparatus which we have just described has the objective of
taking the heat acquired to its maximum, and above all to compare
the solar effect on a high mountain to that
taking place on the plain beneath. This observation is
principally remarkable for the sound [juste] and
extensive consequences [results?] that the inventor has been able to make: it has been repeated
several times at Paris and Edinburgh, and has given analogous
results [31].
The theory of this instrument is easy to understand. It suffices
to remark, firstly that the heat acquired is concentrated, because
it is not immediately dissipated by the renewing of
the air; secondly that the heat emanating from the sun has different
properties to that of IR. The SW
is nearly completely transmitted by
the panes of glass [in all capacities] to the bottom of the
box. It heats the air and the walls which contain it:
then their heat thus communicated ceases to be luminous;
it only conserves the properties of IR.
In this state it cannot freely traverse
the panes of glass which cover the vase; it
accumulates more and more in a space enveloped in
poorly conducting material, and the temperature rises until
the incoming heat is exactly compensated for
by that which dissipates. One could verify this explanation, and
render the consequences more sensible, if one
varied the conditions, in employing glasses coloured or blackened, and if
the spaces which hold the thermometers are emptied
of air. When one examines this effect via calculus, one finds
results entirely conforming with those given by
observations. It is necessary to consider attentively
this order of facts and the results of calculus when
one wishes to know the influence of the atmosphere and the waters on
the temperature of the earth.
In effect, if all the levels of the air of which the atmosphere is
formed were to retain their density and transparency, and
lose only their mobility, this
mass of air thus becoming solid, being exposed to the rays
of the sun, would produce an effect of the same type as that which
one has just described. The heat, arriving as SW
at the surface of the earth, would suddenly lose
entirely the faculty which it had of traversing
diaphanous solids; it would accumulate in the lower levels of
the atmosphere, which would thus acquire elevated temperatures.
One would observe at the same time a diminution of
the degree of heat acquired, above [a partir de] the surface of the earth [31.5].
The mobility of the air which moves rapidly in all
directions and which rises when heated, the radiation of IR
in the air, would diminish the intensity of the effects
which would take place under an transparent and solid atmosphere,
but would not entirely remove these effects. The decrease
of heat in the higher regions of the air does not
cease to take place; it is thus that the temperature is
augmented by the interposition of the atmosphere, because the
heat finds fewer obstacles in penetrating the air, when it is
SW, than in repassing when converted into IR.
We will now consider the original heat which the
earth had former epochs after the planet had
formed, and which continues to dissipate through the surface under the
influence of the cold temperature of the interplanetary sky.
The idea of an interior fire, the perpetual cause of many
grand phenomena, is re-introduced in all the ages of
philosophy. The thing that I propose is to
understand exactly following what laws a solid sphere,
heated by a long immersion in a medium, would lose
this original heat if it was transported into a space
with a constant, lower, temperature.
This difficult question, which does not belong
[encore] to the mathematical sciences, was resolved by
a new method of calculus which applies to divers
other phenomena [32].
The form of the terrestrial spheroid, the regular disposition
of interior layers made manifest by experiments
with pendula, their density increasing with depth and
diverse other considerations together prove that a
very intense heat previously penetrated all parts of
the globe. This heat dissipates by radiation into surrounding
space whose temperature is very much less than that
of the freezing point of water [on p574, its the freezing
point of mercury...]. But the mathematical expression of
the law of cooling shows that the original heat
contained in a spherical mass as big as the
earth diminishes much more rapidly at
the surface than in the depths.
These conserve nearly all their heat for
an immense time [oh go on; how long?]; and there is no doubt of the truth
of the results, because I have calculated these times for
metallic substances more conductive than the materials of the
earth [33].
But it is evident that the theory alone can only teach
us the laws to which phenomena are subject.
It remains to examine if, in the levels of the globe where we
can penetrate, one finds any indication of this
central heat. One must verify, for example, if below the
surface, at the distances where diurnal and annual variations
have entirely ceased, the temperatures of a vertical
increase with
depth: but all facts received and discussed
by the most skilled observers show that
this increase exists: it has been estimated at about a degree
per 30 or 40 meters.
The mathematical question has the object of discovering the
certain consequences which one can discover from this single fact,
in admitting it as given by direct observation, and
to prove that it determines, firstly the situation of the source of
heat, and secondly the excess of temperature which still subsists at the
surface.
It is easy to conclude, and it results anyway from an exact
analysis, that the augmentation of heat in the sense of
depth cannot be produced by the prolonged action of
sunlight. The heat emanating from this star is
accumulated in the interior of the globe; but the progress has
nearly entirely ceased; and if the accumulation were still continuing,
one would observe an increase in a precisely opposite
sense to that we have just indicated.
The cause which gives to the deepest levels a higher
temperature is thus an interior source of heat
constant or variable [!!! if only he had gone on to consider this !!!] placed below the points of the globe
where one has been able to penetrate. This cause elevates the temperature of the
surface above that due to the
sun alone [has he forgotten his favourite "planetary sky" radiation?]. But this excess temperature of the
surface has become nearly insensible, and we are assured,
because their exists a mathematical rapport between the
value of increase per meter, and the quantity by which the
surface temperature still exceeds that which would have
place if the interior cause did not exist. It is for
us the same thing to measure the increase per unit
of depth or to measure the excess of temperature at the
surface [except the latter, of course, cannot be measured].
In a globe of iron, the increase of a thirtieth of
a degree per meter gives only a quarter of a degree
centigrade for the actual elevation of the surface
temperature. This elevation comes directly from the
conductivity of the substance of which the envelope is formed,
all other conditions being the same. And so
the excess temperature which the surface has presently
because of this interior source is very small; it is
probably below a thirtieth of a degree centigrade.
One must remark that this last consequence
applies to all suppositions which one could make
about the nature of the cause, whether one regards it as local
or universal, constant or variable.
When one examines attentively and according to the principals
of dynamic theories, all the observations relative to the
figure of the earth, one cannot doubt that this planet
received at its origin an elevated temperature, and, from
another side, thermometer observations show that
the actual distribution of the heat in the terrestrial
envelope is that which occur if the globe had been formed
in a milieu with a very high temperature, and which subsequently
has continually cooled.
The question of the terrestrial temperatures has always appeared to me
to be one of the great objectives of cosmological studies, and I
had it principally in view whilst establishing the
mathematical theory of heat. I firstly determined the variable
state of a solid globe which, having been plunged for a long time
in a heated medium, is transported into a
cold space. I also considered the variable state of a solid
sphere which, having been plunged successively and for a certain
time in two or more milieu of diverse temperatures, then is subject to a final cooling in
a space of constant temperature. Having remarked the
general consequences of the solution to this question,
I examined more specially the case where the original
temperature acquired in the heated milieu becomes common
to all the mass; and attributing to the sphere a very large
size, I found what would be the
progressive dimunitions of temperatures in the layers
closest to the surface. If one applies the
results of this analysis to the earth to understand
what would be the successive effects of an initial formation
like that which we have just considered, one sees that
the increase of a thirtieth of a degree per meter, considered
as a result of the central heat, has been previously
much bigger, and that it varies now extremely
slowly. As to the excess of the surface temperature, it
varies according to the same law; the secular diminution or
the quantity by which it decreases during a century is equal to the
actual value divided by twice the number of centuries which
have past since the beginning of the cooling, and as
a limit to this number is given by historical
monuments, one concludes that, between the greek school of
Alexandria and now, the temperature of the surface
has not diminished, by this cause, by as much as three hundredths
of a degree. One finds here the character of stability which
all the great phenomena of the universe present. This
stability is anyway a necessary result, and independent
of all considerations of the initial state, since the actual excess
of the temperature is very small, and this cannot but
diminish during an indefinitely prolonged time.
The effect of the original heat which the earth has conserved
has thus become insensible at the surface;
but it manifests in the accessible depths,
since the temperature of the levels increase
with their distance from the surface. This increase,
reported per meter, would not have the same value at
much greater depths; it diminishes with
depth; but the same theory shows that the
temperature excess, which is nearly nothing at the
near-surface, can be enormous at the distance of several
ten-thousands [lit: myria] of
meters, so much so that the heat of the intermediate levels
could greatly surpass that of incandescent
materials.
The course of centuries would cause great changes in
these interior temperatures; but at the surface these
changes are [already] accomplished, and the continual loss of
original heat cannot cause any further cooling
of climate.
It is important to observe that the average temperature
of a place can be subject, for other accessory causes, to
variations incomparably more sensible than those which
are provided by the secular cooling of the globe.
The establishment and progress of human societies, the
action of natural forces, can notably change, and
in vast regions, the state of the surface, the distribution
of water and the great movements of the air. Such
effects are able to make to vary, in the course of many
centuries, the average degree of heat; because the analytic
expressions contain coefficients relating to the
state of the surface and which greatly influence the
temperature [34].
Although the effect of the interior heat is no longer
sensible at the surface, the total quantity of this
heat which dissipates in a given time, such as a
year or a century, is measurable, and we have determined it:
that which in a century traverses a square meter of
surface into the celestial spaces, would
melt a column of ice with a base of a square meter
and a height of about 3 meters.
This result derives from a fundamental proposition
which relates to all questions of the movement of
heat, and which applies above all to terrestrial
temperatures: I wish to speak of the differential equation which
expresses for each instant the state of the surface. This equation,
whose veracity is sensible and easy to demonstrate, establishes
a simple relation between the temperature of an element of the
surface and the normal flux of heat. What makes
this result important and more useful than
any other in casting light upon the questions which are the object of this Memoir,
is that it is true regardless of the form and dimensions
of the body, and whatever the nature of the
homogeneous or diverse of which the interior mass is
composed. And so the consequences which one deduces from this
equation are absolute; they are valid, whatever may be the
material constitution and the original state of the globe [35].
We [we?] have published, in 1820, an extract
from a Memoir on the secular cooling of the
earth (Bulletin des sciences, Societe philomatique, year
1820, pag. 58 and following). One reported there the principal
formulae, and notably those which deal with the variable state
of a solid uniformly heated up to a certain great depth.
If the initial temperature,
in place of being the same up to a great distance from the
surface, results from a successive immersion in several
milieu, the consequences are no less simple or
remarkable. Anyway, this case and many others [spare us] which we
have considered are contained in the general expressions
which have been indicated.
The reading of this extract gives me the opportunity to remark that
the formulae (1) and (2) which are reported there have not
been exactly transcribed. I will make up at a later date for the mistake [lit: omissions],
which, anyway, doesn't change any other formulae, nor
any consequences announced in the extract.
To describe the principal thermometric effects which
come from the presence of seas, let us first of all consider what would happen if
the waters of the oceans were to retire from their basins,
leaving immense cavities
in the earth. If this state of the surface,
deprived of atmosphere [?] and oceans, had lasted
a great number of centuries, the
solar heat would produce alterations of temperature similar
to those observed on the continents, and subject
to the same laws. The diurnal and annual variations
would cease at a certain depth [below the surface], and in the
lower layers there would be a constant state which would consist
of continual transport of equatorial heat towards the
polar regions [36].
At the same time, the original heat of the globe dissipating
across the exterior surface of the basins, one would observe there,
like all the other parts of the surface,
an increase of temperature in penetrating to greater
depths, following a line normal to the surface [continues: du fond].
It is necessary to remark here that the increase in
temperature due to the original heat depends principally
on the normal depth. If the surface was
horizontal, one would find equal temperatures in a lower
horizontal level: but if the surface
is concave, these levels of equal temperature are not
horizontal, and differ entirely from level
levels. They follow the sinuous forms of the surface:
it is for this reason that, in the interior of mountains,
the original heat can penetrate to a great height.
Its a compound effect which one determined by mathematical
analysis, having regard to the form and the absolute elevation
of the masses.
If the surface is concave, one would observe an analogous effect in the
inverse sense, and this would have place in the hypothesis which
we are considering. The levels of equal temperature
would be concave, and the state would continue as long as the
earth was not recovered by waters.
Consider now that this state having continued a
great number of centuries, one re-established water in
the bottom seas and lakes, and that they were non withstanding exposed
to alternating seasons. When the temperature of the
upper levels of the liquid became less than that of the
lower parts, although several degrees higher
than the melting point of ice, the density
of the upper levels would increase; they would descend
further and further, and would come to occupy the depths of the basins which they
would cool by contact: in the same time, the warmer
and lighter water would rise to replace the
upper waters, and in the liquid masses there would establish
infinitely varied movements whose general effect
would be to transport heat towards elevated regions.
These phenomena are more compound in the interior of
big seas,because there the inequalities of temperature
occasion currents directed in contrary senses, and
thus displace the water of the furthest regions [?].
The continual action of these causes is modified by another
property of water, which limits the increase of
density, and makes it vary in a sense opposite when the
temperature continues to decrease and approaches the freezing
point [i.e., waters density does not increase monotonically towards freezing]. The bottom of the seas
is thus subject to a special action which always renews itself,
and which perpetually cools it since an immense time by
contact with a liquid of a temperature only a few degrees about
the freezing point. One finds that the temperature of the water
diminishes according to the increase in depth of sondes;
this temperature is in our climates about 4 degrees
at the bottom of most lakes. In general, if one observes
the temperature of the sea at increasing depths,
one approaches the limit corresponding to the
greatest density; but one must, in questions of this
type, have regard to the nature of the water, and above all to the
communications established by currents: this last cause
can totally change the results.
This increase in temperature, which we observe in
Europe in carrying a thermometer into the interior of the globe
to great depths, thus doesn't occur in
the interior of the seas, and usually the order of
temperatures is reversed.
As to the parts immediately below the
bottoms of the seas, the law of increasing heat is not
that which holds on the continents [37]. These
temperatures are determined by a special cause of
cooling, the vase [perhas, "vessel", or "box"?] being exposed, as one said, to
perpetual contact with a liquid which keeps the same
temperature. It is to illuminate this part of the question
that I determined, in the analytical theory of heat
(chapter IX, page 495 and following),
the expression for a solid, originally
heated in some manner, whose surface is
kept for an indefinite time at a constant temperature.
The analysis of this problem shows distinctly
according to what law the exterior cause can vary the temperatures
of then solid. In general, after establishing the fundamental
equations for the movement of heat and the method of
calculus which serves to integrate them, I devoted myself to resolving
interesting questions of the study of terrestrial temperatures
and to know the relations between this study and the system
of the world.
After having separately explained the principals of the question
of the terrestrial temperature, one must reunite under a
general point of view all the effects which one has just described, and
thus one will form an accurate idea of the ensemble of the phenomena.
The earth receives solar radiation, which is absorbed by [lit: penetrent] its mass
and is there converted into heat [lit: chaleur obscure]; it also
possesses an original heat retained from its origin, and which
continually dissipates at the surface; finally the planet
receives rays of light and heat from innumerable stars
amongst which the solar system is placed. These are the
three general causes which determine the terrestrial
temperatures. The third, the influence of the stars,
is equivalent to the presence of an immense encircling region closed in all parts,
whose constant temperature would be a little less than
that which we would observe in the polar countries of the earth.
One could without doubt attribute to the radiant heat properties
currently unknown, which would stand in place of
this fundamental temperature which we
attribute to space; but in the current state of physical
sciences and without recourse to other properties than those which
derive from positive observations, all known facts
are naturally explained. It suffices to represent the situation as the
planetary bodies being in a space whose temperature
is constant. We have thus sought to know what would be
this temperature so that the thermometric effects would be
similar to those observed: but they would be entirely
different if one admitted an absolute cold to
space; but if one progressively elevates the communal
temperature of the surrounding, one sees
born effects similar to those we know [bollocks].
One may affirm that the actual phenomena are those
that would be produced if the rays from the stars gave
to space a temperature of
about 40 degrees below zero. (division octogesimale).
The original heat of the interior, which is not yet
dissipated, does not produce more than a very small effect at the surface
of the earth; it manifests itself by an augmentation
of temperature in the deep levels. Further
from the surface, it can surpass the
highest temperatures which we have measured so far.
The effect of solar radiation is periodic in the
superficial levels of the terrestrial envelope; it is fixed in all
deep places. This fixed temperature of the lower parts
is not the same for all; it depends principally
on the latitude.
The solar heat accumulates in the interior of the
earth [38], whose state becomes invariable. That which penetrates
in the equatorial regions is exactly compensated by the
heat which flows across the polar regions. Thus the
earth returns to space all the heat which it receives
from the sun, and adds a part from its original
heat.
All the terrestrial effects of the solar heat are modified
by the interposition of the atmosphere and the presence of the
waters [39]. The great movements of these fluids renders the
distribution more uniform.
The transparency of the waters and the air augments
the degree of heat acquired, because the SW
penetrates easily into the interior
of the mass, and the IR leaves with more difficulty.
The alterations of the seasons are maintained by an
immense quantity of solar heat which oscillates in the terrestrial
envelope, passing below the surface for six months,
and returning from the earth into the air during the other half of
the year. Nothing can have more effect in clarifying this
part of the question than the experiments which aim
to measure with precision the effect produced by the rays of
the sun on the terrestrial surface [39.5].
I have reunited, in this memoir, all the principal elements of
the analysis of terrestrial temperatures. It is formed of many
results from my researches, which have been published some time ago.
Before I set out to treat this genre of question, there did not
exist a mathematical theory of heat, and one
might even have doubted if such a theory was possible. The
memoirs and works in which I established it contain
the exact solution of the fundamental questions; they have been
placed and communicated publicly, or printed, and
analysed in scientific journals for several
years.
In the present paper I proposed another
aim, that of calling attention to one of the greatest
objects of natural philosophy, and to present the general
views and consequences. I hoped that the geometers
would not only go in their researches into
questions of calculus, but that they would consider also the
importance of this subject. One cannot today resolve
all doubts in a matter so extensive which comprises,
as well as the results of a difficult and new analysis,
very varied physical notions. One should follow-up by
making more exact observations; by studying the laws of the movement of
heat in liquids and in air. One would perhaps discover
other properties of radiant heat [aha! so he does know that he doesn't know the law of radiative emission?], or
causes which modify the temperatures of the globe. But all
the principal laws of the movement of heat are
known; this theory, which rests on invariable foundations,
forms a new branch of mathematical science:
it is composed today of the differential equations of
the movement of heat in solids and in liquids,
the integrals of these first equations, and theorems
relating to the equilibrium of the radiant heat.
One of the principal characteristics of the analysis which explains the
distribution of heat in solid bodies, consists
of the composition of simple movements [linear superposition, I think]. This property
derives from the nature of the differential equations of the movement
of heat, and it applies also to the normal modes of oscillation
of bodies [22]; but it belongs more specially
to the theory of heat, because the most complex effects
really resolve into simple movements.
This proposition is not a law of nature, and
I do not attribute it as such; it explains a
remaining [lit: subsistant] fact, and not a cause. One would find the same result
in the questions of dynamics where one considers
the resistant forces which rapidly cause-to-cease the effect
produced.
The applications of the theory of heat have required
long analytical research, and it is first of all necessary
to form the method of calculus, regarding as constants
the specific coefficients which enter into the
equations; because this condition establishes itself and lasts for
an infinite time, when the differences in temperatures have become
small enough, as one observes in the question of terrestrial
temperatures. Besides which, in this question which is the
most important application, the demonstration of the
principal results is independent of the homogeneity and the
nature of the interior layers [what *does* this all means?]
One could give to the analytical theory of heat all
the extensions which explain the most varied applications.
Here is the enumeration of the principles which serve to generalize
this theory.
1. The coefficients being subject to very small variations
which observations show us, one determines, by the
process of successive substitutions, the corrections
which one must make to the results of the first calculation.
2. We have shown numerous general theorems which
do not depend on the form of the body, or on its homogeneity.
The general equation relative to the surface is a
proposition of this genre. One finds another very remarkable
example if one compares the movements of heat
in similar bodies, whatever may be the nature of
the bodies.
3. Since the complete resolution of the differential
equations depends on expressions that are difficult to discover or on tables [of observations?]
which are not yet formed, one determines the limits
between which the unknown quantities are necessarily
bounded; one also arrives at certain consequences on
the object in question.
4. In researches on the temperatures of the earth,
the grandeur of the dimensions gives a special form
to the results of calculus, and renders the interpretation
easier. Although one ignores the nature of the interior masses
and their properties relative to heat, one can deduce from the
only observations made in accessible depths,
strongly important consequences on the stability of climates,
on the excess of heat due to the original heat,
on the secular variation in the increase of temperature
with depth. It is thus that we have been able to
demonstrate that this increase which is, in diverse places of
Europe, about one degree in 32 meters, has previously had
a much bigger value, which has diminished
insensibly, and which would take thirty thousand years
before it would be reduced to half its present value. This
consequence is not uncertain, although we ignore
the interior state of the globe; because the interior masses, no
matter what their temperature or state, do not communicate
more than an insensible amount of heat to the surface during an
immense lapse of time. For example, I wished to know
what would be the effect of an extremely heated mass, of the
same extent of the earth, placed below
the surface at some depth. Here are the results
of this research.
If, below a depth of twelve leagues, one replaced
the earth by
some matter whose temperature would be equal to five
hundred times that of boiling water [50000 oC?], the heat communicated
by this mass to the parts close to the surface would remain
for a very-long-time insensible; it would certainly cool
more than two hundred thousand years before one could observe
at the surface an increase of a single degree.
Heat penetrates solid masses so slowly, and
above all those of which the earth of formed, that an
interval of a very-small number of leagues suffices to
render inappreciable for twenty centuries [no, I didn't get it wrong above, he's dropped a factor of 10] the impression of
the most intense heat [40].
The attentive examination of the conditions to which the system of the
planets is subject allows us to conclude that these bodies
were part of the sun [?!?], and one can say that
there is no phenomenon which does not allow us to found
this opinion. We do not know how much the interior
of the earth has lost of this original heat; one can only
affirm [all together now...] that at the surface, the excess of heat due to this
sole cause has become insensible;
the thermometric state of the globe does not vary anymore except with
extreme slowness; and if one could conceive that below
a depth of a few leagues one replaced
the interior masses with
a frozen body, of by portions of the substance
even of the sun at the temperature of this star, it
would take a great number of centuries before one
could observe any appreciable change in the temperature
of the surface. The mathematical theory of heat furnishes
many other consequences of this type whose certitude
is independent of all hypotheses of the interior
state of the earth.
These theories will acquire in the future many more extents,
and nothing will contribute more to their perfectioning than
numerous series of precise experiments; because the mathematical analysis
(from which permit us to introduce here this
reflection) (1) can deduce from general and simple phenomena
the expression of the laws of nature; but the application of
these laws to complex effects requires a long series
of exact observations.
OK folks, thats it for the text. Thank-you for staying
with old Joseph this far. Its footnotes by me from here on down...
[2] Suppressed as too unhelpful.
[3] So: if its the solar radiation that produces diverse climates, why
bother with points 2 and 3? Because, he is not interested principally
in the diverse climates. Coming from a climatological background,
it is hard to realise this.
[4] This is essentially wrong: stellar radiation (excluding the sun)
is totally negligible, and
interplanetary space has a temperature nearly
indistinguishable from zero and contributes just about no radiation
to the earth (I think). Anyone who knows better is invited to comment.
For the wise: of the tiny radiation that is non-solar (and non-lunar:
solar radiation reflected from the moon does have a very small but
measurable effect), which (stellar; cosmic microwave background; whatever)
has the largest effect?
[5] OK, so he doesn't know about radioactive decay heating the earth:
this is fair enough.
[6] Clearly, this is wrong. Also, you might think: he doesn't know
the temperature of the north pole (in summer much less in winter)
and doesn't even know if the south pole is land or sea. Nor does he
know the interplanetary temperature. But, be patient: later on
he explains why he thinks these (unknown) temperatures need to be the same.
[7] The assertion that "the solar radiation which has
penetrated all the mass" reads oddly, since insofar as heat flow
is concerned the flow is from the interior of the earth, as F was
well aware and goes into in great detail later. But this claim is
repeated later. See-also [38].
[8] I think what he means is: looked on as a mathematical problem; assuming
a constant heat input to the surface
from solar radiation and a given initial heat distribution,
with the interior being very hot, one can calculate the change in
surface temperature with time. Of course, this assumes no
change in solar constant, orbital parameters, etc. If you do this, you
conclude that the earth has already cooled far enough to be within 1/30 oC
of its final surface temperature. This is probably a disappointment
to those hoping to use the change of this temperature as some kind of measure
of the age of the earth.
[9] This rescues him (if such were needed) from the comment [5].
Although radioactivity was not discovered by people trying
to find what kept the earths interior warm. Or was it?
[10] This is a bit odd, because after all the two regions are not really
distinct: there is just a depth beyond which diurnal/annual
variations become too small to measure. And, perhaps, another region
beyond which geothermal heat becomes important. But, this comment
prefigures some later analysis where he considers the two regions
separately.
[11]
Was this in question? I guess what he is saying is that the stability of the
interior temperatures proves that the surface temperatures has not
varied too wildly in the past (but this then becomes a bit odd,
because whatever analysis he has done has failed to pick up the
last ice age, only 10,000 years ago). Maybe a change of only
5-10 K is too small to see?
[12]
Yes, I think you can deduce the conductivity by measuring the
annual cycle within the earth. A useful application of his theory,
I guess.
[13] If only the coldest molecules descend, no heat will be transferred
down...
[14] Yet again, we see what he is really interested in.
[15] This is quite wrong. To first order, the higher layers of the
troposphere are colder because most of the solar radiation is absorbed
at the surface, not differentially in the atmosphere as he suggests.
Furthermore, mass-for-mass, higher layers absorb just about as much
radiation as the lower (assuming the lesser water vapour in the higher
layers does not affect this too much).
[16] No, of course he doesn't say infra-red (IR) radiation. He says
"chaleur rayonnante obscure". But here and in future, I shall translate
this as IR.
[17] And he doesn't say short-wave (SW) either, he says "chaleur lumineuse",
but thats going to be SW in what follows.
[18] I would argue that the transmission of IR through the atmosphere
is rather distinct from its transmission through the ocean (or ice!?!).
Water (liquid) is essentially 100% opaque to IR. Nobody
puts a radiation scheme into an ocean model.
By contrast the atmosphere is somewhat, but not totally, opaque,
and is thus a much harder problem.
[19] "star" is presumably the sun. There may possibly be a negative
in this sentence. But either way round, I have no idea what
he is trying to say.
[20] Bit of an odd paragraph. He is talking about IR radiation, and
the observation here that makes sense is that it trapped by
clouds, resulting in warmer nights. Quite true.
Other observations make less sense: "the higher levels
of the atmosphere are most cold" is wrong: temperatures in
general decrease from the surface to the tropopause (at about
200 hPa / 8 km) then increase into the stratosphere then...
The assertion that the temperature of these layers is nearly
constant (day-to-night) is true, because their radiative timescale
is long, but does he know this?
As for reflecting IR from concave mirrors: is this right?
See-also the extrasolar heat stuff on
p 580.
[21] In fact, the arguments don't apply to the gas giants at all...
(insert ref to planetary temperatures here if I can find one) the
temperature of Neptune and Uranus is about 60K, that of Saturn
about 90K, that of Jupiter about 120K (figures from memory
from a talk recently), the difference, I think, principally
arising precisely from internally generated heat of compression
which is sort-of equivalent to "original heat" (***check all this
sometime***). The pole-to-equator temperature difference
of the gas giants is tiny: a few degrees, as compared to tens
of degrees for earth.
[22] Firstly, "natural oscillations of bodies" is my
awkward translations of "dernieres oscillations des corps",
by which I think he is referring to normal modes of oscillation.
But anyway: what he is saying in this paragraph is that he is
assuming that the different forcings can be considered to be
linearly superposable. This would not nowadays be an obvious
thing to think about the climate system, which is often
non-linear, but it is done when no choice exists or existed:
for example, flux-corrected AOGCMs run for CO2-changed scenarios.
Note: this is an important paragraph for understanding what
follows. When it looks like he has forgotten about, say, internal
heat, this is because he is doing this considering-effects-separately
stuff.
[23] This is, in fact, a
very useful fact for measuring the annual average temperature of
the surface of the ice sheets: drill a core down to 10 m depth
and measure the temperature there: it is very close to the annual
average at the surface.
[24] This can appear rather obscure. What he is doing is
transforming the question into a boundary-value problem on the
sphere, where the temperatures on the surface are fixed and
one thereby deduces the heat-flow through the globe. Once
again, we see that he is *not* interested in the surface
temperature - the climatology of the earth - except as
a means to doing some interesting mathematics.
[25] Some slight doubts about the translation of this paragraph.
But I think what he is saying is, that if we start from an earth
with an arbitrary temperature, then impose constant solar forcing,
then we end up with the interior temperatures trending towards fixed values.
You might say, aha, but what about the seasonal variations, but
no, remember that he has already suppressed the region in which
seasonal changes occur and is considering a boundary value problem
with fixed surface temperatures on the new "surface".
[26] Since he has gone to such great lengths to say how exact his
theory is, it seems only fair to point out that this is only correct
if the annual cycle repeats exactly: if temperatures shift year-to-year
then there are slight variations in the average. In fact, deep borehole
temperatures can be used to track (approximately) temperature histories
back into the last ice age.
[27] Spiffy. So in fact several pages of repetitive and
near-incomprehensible prose could be more comprehensibly
summarised by one simple formula. So where is it?
[28] As far as I can see, this paragraph is a rather simple
(and incorrect) assertion unsupported by any evidence whatsoever.
Next para: Why does he believe this? As for the eccentricity, he must be
perfectly well aware that it is tiny. Why does he think that tiny
variations in the solar distance should be so important? He is quite
well aware of things like heat capacity, and of the oceans, and so
ought to know about them "buffering" temperature changes. Its
all in his theory, after all.
Next para: this is all getting a bit odd. he knows
- see p 573 - that IR radiation from the sky
and clouds exists and tempers the cold nights, so why has
he suddenly forgotten it? All this has the hallmarks of an
argument got up to demonstrate a point - the temperature of space -
regardless of inconvenient facts. In fact p 573 directly
contradicts this stuff, in that it points out (correctly)
that clouds temper cold nights, whereas what he is
saying here should suggest that clouds make the nights colder,
by intercepting this mysterious radiation.
If you feel tempted to believe any of his arguments, remember
that the temperatures of the outer planets -
see [21] - are much less than those at the
terrestrial poles.
[later:] I have just noticed that he considers what the situation
would be with no extrasolar radiation, assuming that the
atmosphere has been removed "to make things easier". But this
removes a vital part of what does keep the planet warm at night...
[29] Aha! this appears to be the source of the assertion - which I've seen
somewhere - that Fourier was the first to notice the possibility of
human modification of climate. This would appear to be supported by this,
but from the context I think he is probably talking about land-use
and albedo changes, not about release of "greenhouse" gases.
See-also a later, less ambiguous, reference.
[30] Yet another repetition of this assertion unsupported by
facts or arguments.
Incidentally, yet another disproof of his idea is the fact that the
diurnally-averaged insolation on the polar regions during
summer is actually greater than in the tropics, due to the constant
daylight. Thus, according to his no-memory ideas, the summer pole
should be warmer than the tropics. Since this fact depends only
on the earths axial geometry, which he knew, he could have been aware
of this. [***check this sometime***]
[30.5] The "octogesimal division" or Reaumur temperature scale had 0 and 100 oC
as fixed points like the centigrade scale, but 80 divisions not 100.
See here for more (thanks to E Bard).
[31] Well go on then: tell us the result: how do the results up a
mountain compare with those on the plain (and where will you find
a mountain near Paris?). From what I know, I would expect higher
interior temperatures up a mountain (on the grounds that less solar
radiation would have been absorbed by the atmosphere at a height).
I remain somewhat uncertain as to the translation of "consequences"
from the french. As done here, as "consequences" (the EB translation
has "inferences", which would mean the same), it implies that
it is these remarkable consequences that matter; if so it is
odd that they are not specifically mentioned: on this reading,
it is the fact that IR cannot penetrate transparent things
(arbitrarily extrapolated to the atmosphere from glass, I've just
realised) that is the consequence. On the other hand,
"consequences" can be read as "results", and he may just be
commenting on the excellent repeatability of the experiment.
[31.5] This would only be the
first-order effect: in time, as heat was conducted up, (all?)
levels of the atmosphere would become warmer.
[32] Notice that he is being a bit imprecise here. He cannot solve
the problem as stated accurately, because he does not know
Stephans law, i.e. that
R=sT^4, i.e. that radiation is proportional to the fourth power of
temperature (and then it can only be done accurately
if you pretend the atmosphere doesn't exist).
I presume he is going to solve it assuming conductive
losses only, not particularly relevant to the earth in space.
This point should be remembered as the discussion progresses
(or repeats...) in the following pages: his much-vaunted exact
solution is the exact solution to an approximate problem.
[33] "There is no doubt as to the truth of the results, because
I have used the wrong values..." ;-)
Sorry, couldn't resist that. What he means is, that in practice
he can be sure that the real times would be longer, because the
earth is less conducting than the material he has assumed.
However, he appears to be wrong on two counts:
[34] This would appear to be the bit where one can say
"he anticipated the possibility of humans changing the climate".
However, from this section (unlike a previous glancing
ref, it is clear that he means modification of the
surface, not the atmosphere). The bit about "great movements
of the air" is unclear.
[35] But this marvellous result, sadly, does not have any
importance for determining the temperature of the
real world, heated as it is mostly by solar radiation.
[36] The fraction of solar heat that is conducted polewards through
the earth is so tiny that it is invariably ignored: most would be
transported through the atmosphere or ocean. If you suppressed both of
these, pole-to-equator temperature gradients would increase.
[37] The laws may not be the same, but the results are
indistinguishable, since the "original heat" nowadays has so little
effect. However, I think that what he is saying is that over
the continents the "original heat" problem is to solve for the cooling,
given an initial temperature and some law of cooling of the
surface (he is a bit coy about this latter part. He doesn't
know the law of radiative cooling, so I wonder what he did use.
Presumably one would have to read his Oeuvres to find out).
Whereas, over the oceans, the problem is to solve, given a fixed
boundary temperature at the top. An interesting question is whether
his maths allowed him to solve both-at-once for the earth, or if
he had to do all-land, then all-ocean problems separately.
[38] He keeps saying this and it just isn't true. Its a hangover
in his mind from him trying to decompose the problem. The interior of the
earth is hotter than the surface, so heat doesn't flow from the surface
to the interior, but the other way round. He knows this.
[39] In his discussion, the SW is assumed to penetrate the atmosphere
without hindrance, and its only the IR that the atmosphere affects.
That means that the atmosphere is just as relevant to, say, the original
heat loss, but he doesn't seem to have noticed this.
[39.5] The EB translation adds here: "For this reason, we heard with the
greatest interest the reading of the memoir presented by Prof Pouillet;
and if in the course of this article we have not mentioned his experimental
researches, it is simply from the wish not to anticipate the
report which will soon be made.". It would be interesting to know
why Prof Pouillets stuff was omitted 3 years later, when priority
was no longer a problem.
[40] Of course, this is only valid if you follow his rules. In the real
world, replacement of the interior by a body this hot (apart from,
probably, vapourising the rock) would cause convection to start which
would presumably lead to a shorter transfer time for the heat.
WMC | June, Lescun / July, Marcham and Coton / August, Coton.
The text
(1) Discours preliminaire de la Theorie de la chaleur
Footnotes
[1] This, for example, is a footnote.
Not to mention radioactive decay...