Galileo and Hooke demonstrated that every sound is characterized by a precise number of vibrations per second, but the full understanding of even the simplest... vibrators requires... calculus. ...Leonard Euler, Daniel Bernoulli, Jean le Rond d'Alembert, and Joseph Louis Lagrange all studied the vibrating string.... In 1747 d'Alembert found... the wave equation and in 1753 Bernoulli stated the... decomposition of every motion of a string as a sum of elementary sinusoidal motions. Then at the beginning of the following century Fourier developed "harmonic analysis."

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.

If all the strata of air of... the atmosphere... preserved their density with their transparency, and lost only the mobility... peculiar to them, this mass of air, thus become solid, on being exposed to the rays of the sun, would produce an effect the same in kind... as just described.

It is difficult to know how far the atmosphere influences the mean temperature of the globe... It is to... M. de Saussure that we are indebted for a capital experiment which appears to throw... light on this... The theory of the instrument is... 1st... the acquired heat is concentrated, because it is not dissipated immediately by renewing the air; 2d, that the heat of the sun, has properties different from those of invisible heat... The rays... are transmitted in considerable quantity through the glass plates... They heat the air and the partitions which contain it. Their heat thus communicated ceased to be luminous, and preserves only the properties of non-luminous radiating heat. In this state it cannot pass through the plate of glass covering the vessel. ...It is necessary to consider attentively this order of facts, and the results of the calculus when we would ascertain the influence of the atmosphere and waters upon the thermometrical state of our globe.

From the constitution of the solar system it is... probable that the temperature of the poles... are a little less than that of space... the same for all... although the distances from the sun may be unequal.

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... The 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...

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... Any point of space whatever which contains these bodies acquires a fixed temperature.

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.

We... now consider the second cause of terrestrial heat, which... resides in the planetary spaces. ...Ascertain what would be the thermometrical state of the terrestrial mass, if it received only the heat of the sun. To facilitate... first leave the atmosphere out of the account. ...If the earth and all the bodies of the solar system, were placed in space deprived of all heat ...The polar regions would be subject to intense cold and the decrease of temperature from... equator to... poles would be incomparably more rapid and extended.In this hypothesis of the absolute cold of space, all the effects of heat... at the surface of the earth, should be attributed to... the sun. The least variance in... its distance... from the earth, would occasion... considerable changes in temperature. The interruption of day and night would produce effects sudden... Bodies, would be exposed... at commencement of night, to a cold of infinite intensity. Animals and vegetables could not resist... the sudden and powerful change... produced at the rising of the sun.