Physics of the Terrestrial Environment, Subtle Matter and Height of the Atmosphere. Eric Chassefiere

we inhabit, and which is bounded by the reflection of the Sun’s rays. It is sometimes cold and sometimes warm, depending on the diversity of climates and seasons. The middle region of the air is the air space from the top of the highest mountains to the lower region of the air we breathe. It is cold, and humid, because of the vapors and exhalations that the Sun raises there. The upper region of the air is that which extends from the top of the mountains to the region of the elemental fire; it is purer, rarer, and lighter than the others.

      Air is certainly an “element” in the sense of the ancients: “the ancient philosophers recognized four elements, fire, air, water, and earth. These four popular elements are not elements, strictly speaking, because they are composed bodies; and not simple, unmixed bodies” (F1727). But, as is most important to note, it was considered at the beginning of the 18th century to be a physical matter that can be characterized by measurement, and whose distribution according to height can be predicted by applying the law of expansion, still known today as the law of Boyle-Mariotte. And this matter is subject to being mixed, as shown, for example, by the fact that air contains a certain degree of humidity. The stratification of the atmosphere expressed above is inherited from the Aristotelian design, but relatively precise criteria are provided to define the boundaries between layers. The middle region is the region that contains vapors and clouds, and which gives rise to the reflection of the Sun’s rays. The atmosphere thus consists of the union of the lower and middle regions, and extends from the Earth’s surface to the tops of the highest mountains. The supreme region, that of “pure” and “rare” air, above the highest mountains, extends to the elemental fire, therefore to the element fire, which fills, in the Aristotelian conception, the sub-lunar space above the air.

      Diderot and d’Alembert’s Encyclopédie (which we will refer to simply as the “Encyclopédie”) shows a significant evolution in the definition of the atmosphere. This word is presented as the name “given to the air that surrounds the Earth, that is, to this rare and elastic fluid with which the Earth is covered everywhere at a considerable height, which gravitates towards the center of the Earth and weighs on its surface, which is carried along with the Earth around the Sun, and which shares its annual as well as diurnal movement.” The elasticity of the air is emphasized, and the air no longer rises there only “at a certain distance”, but “at a considerable height”. The atmosphere has become, for most scientists, “the entire mass of air surrounding the Earth”, even if some writers call the atmosphere only “that part of the air close to the Earth which receives vapors and exhalations, and which substantially breaks up the rays of light” (by refraction). The atmosphere is not bounded at its top by elemental fire, but by “a more subtle matter called ether”, and “the space above the coarse air, though perhaps not entirely empty of air, […] is called the ethereal region or ethereal space.” Thus, we cannot exclude, upwards in the atmosphere, henceforth the whole mass of air, the existence of pure air, that of the “supreme region”, as defined in the DUF.

The definition of air in the Encyclopédie also shows a notable evolution. It is defined there as “a light, fluid, transparent body, capable of compression and expansion”. This body cannot be considered as an element, “although it may have parts that deserve this name”. There are two types of air: (i) vulgar or heterogeneous air and (ii) clean or elementary air: “Heterogeneous or vulgar air is an assembly of corpuscles of different kinds, which together constitute a fluid mass, in which we live and move, and which we inhale and exhale alternately.” We find air loaded with vapors and clouds (“coarse air”), composed of heterogeneous substances, which it is said can be reduced to two kinds:

      1. The matter of light or fire, which emanates perpetually from celestial bodies. To this, some physicists add the magnetic emanations of the Earth, true or alleged.

      2. This infinite number of particles that rise in the form of vapors or dry exhalations from the Earth, water, minerals, plants, animals, etc. either by the heat of the Sun, or by that of underground fires, or by that of fireplaces.

      What is called “elemental air” is air itself, “a subtle, homogeneous and elastic matter, which is the basis, so to speak, and the fundamental ingredient of all the air in the atmosphere, and which gives it its name”. It is therefore pure air from above, mixed in the lower part of the atmosphere with the vapors and exhalations emanating from the Earth. We also see appearing among the heterogeneous substances various subtle matters, to which we will return.

      The entry ATMOSPHERE found in the Encyclopédie devotes several paragraphs to the question of the height of the atmosphere, which we will address at length in the following chapters. The lower limit to the height of the atmosphere can be calculated by assuming that the air is homogeneous, without elastic force, and therefore of the same density everywhere. The measurement of the height of mercury in the barometer provides the weight of the air column, and knowing the ratio of the density of mercury to that of the “air we breathe here below”, namely 10,800, the height of the atmosphere, assumed homogeneous, is estimated to be 2 leagues ¼ (≈8.5 km). This value is a lower limit, by virtue of the elasticity of the air:

Air, by its elasticity, has the virtue of compressing and expanding: it has been found by various experiments frequently repeated in France, England and Italy, that the different spaces it occupies, when compressed by different weights, are reciprocally proportional to these weights: that is, the air occupies less space at the same time as it is more compressed; hence, it follows that in the upper part of the atmosphere, where the air is much less compressed, it must be much more rarefied than it is close to the surface of the Earth; and that consequently the height of the atmosphere must be much greater than that which we have just found.

      The consideration of the dilatation in the calculation of the vertical structure of the density of the air was carried out by Edme Mariotte, and others, in the second half of the 17th century, leading to a density which forms, with the height, a “continuous geometrical proportion”, that is, which decreases exponentially with the altitude. It follows that “the rule of compression according to the weights cannot give the height of the atmosphere; for this height would have to be infinite, and the density of the air would have to be zero at its upper surface”. But another obstacle prevented the height of the atmosphere from being estimated by this method. Jacques Cassini, during his campaign of measurements intended to extend the meridian of Observatoire de Paris, precisely measured the heights of several mountains, as well as the pressures prevailing at the top of these mountains. He found laws of variation with height that do not correspond to Boyle-Mariotte’s law of expansion. Expansion increases faster than the inverse of the compressive weight at altitude (as the inverse of the square of this weight, according to him). The Academy conducted numerous laboratory experiments at reduced pressure, experimenting with air dilatation much greater than that at work on mountain tops, and found no deviation from Boyle-Mariotte’s law. Hence:

      Some physicists have concluded that the air on the mountain tops is of a different nature from the air we breathe down here, and apparently follows other laws in its expansion and compression.

      The reason for this difference must be attributed to the amount of coarse vapors and exhalations with which the air is laden, and which is much greater in the lower part of the atmosphere than above. Since these vapors are less elastic and therefore less capable of rarefaction than pure air, the rarefactions of pure air must necessarily increase in greater proportion than the weight decreases.

      Thus, the elemental air at the top would by nature be different from the heterogeneous air at the bottom; less elastic, because of the vapors and exhalations it contains, which does not conclude on the height of the atmosphere from pressure measurements made at different heights, since it is not possible to extrapolate at great heights the measurements made near the surface of the Earth from a single law of air expansion:

In any case, it is constant that the rarefactions of the air at different heights do not follow the proportion of the weights with which the air is loaded; therefore the barometer experiments, made at the foot and on the top of the mountains, cannot give us the height of the atmosphere, since these experiments are done only within the lowest part of the air. The atmosphere extends far beyond this; and its rarefactions are all the further away from the previous law, the farther