Comte divides barology into two parts: static and dynamic barology. Static barology investigates the effects of weight with bodies in a state of equilibrium. In the case of solid bodies, Comte notes, this investigation began already with the discovery of the Archimedian principle.
In the case of liquids, static barology, Comte thinks, did not begin until modern times. He divides this part of barology into two studies. First of them concerns the case of a small portion of liquid within a vessel: here Comte emphasises especially Stevin’s investigation of the pressure of liquid on the vessel. The second study concerns great amounts of liquid, like oceans, where we have to take into account that the direction of gravity varies significantly from one place to another. This study, Comte thinks, is intrinsically linked with the more astronomical questions of the shape of the Earth and of the theory of tides.
Static barology of gases, Comte continues, has the added difficulty of determining the weight of the gas in case. This was first made possible, he explains, by the invention of a method for creating vacuum, which allowed measuring the difference in the weight of a container with gas and without any gas at all. This discovery made it possible to apply methods of static barology of liquids to gases.
Comte notes that an important addition to static barology would be a study of capillary phenomena, especially as they are important to explaining organic processes. Unfortunately, he laments, this part of barology is still hindered by the metaphysical notion of attraction,
Dynamic barology, Comte states, should then investigate the involvement of weight in the movement of bodies. This investigation began, in his opinion, with Galileo’s study of freely falling bodies and curves of projectiles. Comte thinks that this part of barology is still far from perfect, since the laws governing air resistance are still not determined. Even more insufficient dynamic barology becomes, when we move from solid bodies to liquids and gases.
Heat, Comte suggests, is after gravity the most universal phenomena in physics. He backs up this claim with the statement that heat affects organic and inorganic nature as much as gravity, being the foremost agent acting against the effects of gravity. While gravity affects geometry and mechanics of bodies, Comte continues, heat affects the constitution of molecules and especially living organisms. Indeed, he continues, heat is the primary method by which humans affect nature. Thus, after barology, Comte concludes, thermology is the next part of physics.
Although the investigation of heat began around the time of Galileo with the invention of the thermometer, Comte notes, it was always many steps behind barology. The greatest difference between the two disciplines, according to him, was that while barology already investigated laws of weight, thermology still concentrated on metaphysical questions like the nature of fire. Comte still sees vestiges of metaphysics especially in the so-called caloric theory of heat, which assumes the existence of a fluid causing thermal phenomena.
Comte divides his account of thermology to physical and mathematical thermology, the former of which provides the basis for the latter. He then divides physical thermology into two parts, first of which studies interaction of bodies influencing their temperature, that is, warmer body warming the cooler and the cooler body cooling the warmer. He notes that there are two different cases of this interaction, in the first of which bodies radiate their heat and thus affect one another at distance, while in the other the bodies are in contact with one another.
The other part of physical thermology, Comte says, studies reversible changes in the physical constitution of the body through heat – thus, all chemical changes and inconvertible changes, like a body losing its elasticity due to heat, are excluded from this investigation. Such changes include changes in the volume of the body and changes between solid, liquid, and gaseous states of a substance. Comte also suggests the study of evaporation and hygrometry as an appendix to this part of thermology.
Comte singles out the mathematical study of thermology, because he thinks that it holds a unique position among the physical disciplines: barology and acoustics merely apply mechanics, while optics and electrology are still mired in the metaphysics of luminous and electric fluids. Comte refers especially to Fourier’s account of heat flux, the mathematical part of which he had already applauded in the first volume. Comte notes that Fourier’s work concerns only the first part of the physical thermology, that of transmission of heat, while the account of other physical changes involving heat still await their scientifically mathematical treatment. Comte also suggests the study of the global changes of temperatures as a more practical application of Fourier’s theory.
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