Joseph Fourier Quotes

Letter, quoted by Vladimir Dobrushkin, "Biography of Joseph Fourier" & Elena Presitini, The Evolution of Applied Harmonic Analysis (2004) p. 42.

The heat of the earth is derived from three sources...
1. ...[S]olar rays; the unequal distribution of which causes diversities of climate.
2. ...[T]he common temperature of the planetary spaces; being exposed to the radiation from the innumerable stars which surround the solar system.
3. The earth preserves in its interior that primitive heat which it had at the time of the first formation of the planets. ...We will show ...the principle features of these phenomena.

The solar system is situated in a region of the universe, every point of which has a common and constant temperature, determined by the rays of light and heat which proceed from the surrounding stars. This low temperature is a little below that of the polar regions of the earth.

We conclude... that there exists a physical cause always present which modifies the temperature at the surface of the earth, and gives this planet a fundamental heat, which is... independent of the action of the sun and that internal heat preserved... It is to be attributed to the radiation from all the bodies in the universe, whose light and heat can reach us... rays which penetrate every part of the planetary regions... [A]ny point of space whatever which contains these bodies acquires a fixed temperature.

This temperature of space is not the same in different regions of the universe; but it does not vary in the regions... [of] planetary bodies... [T]he planets of our system... equally participate in the common temperature... augmented for each... by the rays of the sun, according to the distance of the planet from... [it]. ...The intensity and distribution of heat on the surface of these bodies results from the distance from the sun, the inclination of the axes of rotation to the orbit, and the state of the surface...

The interposition of the air very much modifies the effects of the heat upon the surface of the globe. The solar rays traversing the atmospheric strata, which are condensed by their own weight [at decreasing altitudes], heat them very unequally; those which are rarest are likewise coldest, because they... absorb a smaller part of the rays. The heat of the sun... in the form of light, possesses the property of penetrating transparent solids or liquids, and loses this property... when by... terrestrial bodies, it is turned into heat radiating without light.

Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy. Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.

This distinction of luminous and non-luminous heat, explains the elevation of temperature caused by transparent bodies.

The analytical equations, unknown to the ancient geometers, which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics; they extend to all general phenomena. There cannot be a language more universal and more simple, more free from errors and from obscurities, that is to say more worthy to express the invariable relations of natural things.
Considered from this point of view, mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
Its chief attribute is clearness; it has no marks to express confused notions. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.

We shall now consider that peculiar heat which our globe had at the time of the formation of the planets, and which continues to be dissipated at the surface under the influence of the low temperature of the planetary space.

The mobility of the air, which is rapidly displaced... and... rises when heated... diminish the intensity of the effects... [of] a transparent and solid atmosphere, but do not entirely change their character.

I am sorry not to have known the mathematician who first made use of this method because I would have cited him. Regarding the researches of d'Alembert and Euler could one not add that if they knew this expansion they made but a very imperfect use of it. They were both persuaded that an arbitrary and discontinuous function could never be resolved in series of this kind, and it does not seem that anyone had developed a constant in cosines of multiple arcs, the first problem which I had to solve in the theory of heat.

If we consider further the manifold relations of this mathematical theory to civil uses and the technical arts, we shall recognize completely the extent of its applications. It is evident that it includes an entire series of distinct phenomena, and that the study of it cannot be omitted without losing a notable part of the science of nature. The principles of the theory are derived, as are those of rational mechanics, from a very small number of primary facts, the causes of which are not considered by geometers, but which they admit as the results of common observations confirmed by all experiment.

The primitive heat... in the interior of the earth would not increase the external temperature of space... for... the effect of this central heat has long since become insensible at the surface, although it may be very great at a moderate depth.

Liquids are very poor conductors of heat; but they have, like aeriform media, the property of carrying it rapidly in certain directions. This is the same property which, combining with, combining with the centrifugal force, displaces and mingles all parts of the atmosphere... [and] ocean, and maintains in them, regular and immense currents.