With little to no explanation, Comte places acoustics as the next physical discipline after thermology. Indeed, one might even doubt if acoustics deserves a place on the list, because it seems more of an applied science, which Comte has usually excluded from his account of abstract physics. Yet, what he conceives as the topic of acoustics is not so much sound, but all vibrations. This topic has been studied positively, Comte thinks, at least as long as weight, although it is far less known. It seems that it is only the highly intricate mathematical analysis of heat by Fourier that has given reason for Comte to put thermology before acoustics.
Comte sees the importance of acoustics in that sonorous vibrations have revealed – and might be the only method to reveal – the internal molecular structure on inorganic bodies. Thus, he insists, it is through these vibrations that we know the inorganic bodies can acquire dispositions, just like living things. Acoustics is also important for physiology, Comte thinks, for the study of hearing and vocalisation, excluding what happens in nerves and brains. Yet, he emphasises, the study of these phenomena should not be left to physicists, who do not understand the peculiarities of physiology.
According to Comte acoustics is, after barology, physical science using mathematics most. It investigates, he explains, minute molecular oscillations near a state of equilibrium, where perturbation of the order is immediately followed by a return to the original state. Now, since these oscillations can be transmitted through an elastic medium, like waves on water, acoustics become an application of mechanics. Still, Comte notes, acoustics is far more difficult to study than barology, since it requires much more complicated mathematical tools: for instance, we can calculate only movement of vibrations in one dimension, but not in three dimensions. Even so, he assures the reader mathematical theory gives at least guidance for finding approximations and allows use of analogies in calculations.
Comte divides acoustics into three different topics, although he mentions also fourth, the timbre of each peculiar body, but then quickly discards it, because it is more a part of concrete physics. The first topic of acoustic proper, according to Comte, is the propagation of the sound. He notes that the velocity of the sound in air is known, but propagation in other substances or such intricate questions like the behaviour of echo have not been studied conclusively.
The second topic of acoustics would be the intensity of the sound. Yet, Comte thinks, we have not advanced much beyond what we know by common observation, the only fact he considers scientific being the effect of the density of the atmosphere on the intensity. The main reason for this poor state, according to him, is that we have not yet been able to measure this intensity.
The most satisfying part of acoustics, for Comte, are the laws regulating the musical tones. Yet, even here he sees insufficiency, since only the one-dimensional case has been studied, while the behaviour of a full three-dimensional instrument has not yet been investigated.
In an even worse condition Comte sees optics, which he regards as being plagued by the two hypotheses about the nature of light, whether it is supposed to be a material emission or a vibration. Comte thinks that both hypotheses try to reduce optics to a different science: emission theory to barology and vibration theory to acoustics. He is not enthusiastic about such an attempt to unify sciences: even physiology proves that vision is quite different from hearing and feeling weight and pressure. Since both hypotheses work as well, Comte suggests rejecting both of them and concentrating in a description of the laws governing optical phenomena.
Just like acoustics does not explain the physiological phenomena of hearing, Comte insists that optics does not explain vision. Furthemore, he thinks, optics – and indeed, no science – can explain the natural colours that different objects have: any explanation would be metaphysical and always more complicated to understand than what is to be explained. Somewhat ironically, Comte thinks it would be equally ridiculous to attempt to explain why different substances have different specific gravities of substances (periodic table had not yet been discovered).
Comte’s division of optics is quite traditional. First part should study direct light, and just like with acoustics, Comte mentions that we still have no tool for measuring the intensity of light. The second part is catoptrics that deals with reflection, while the third part, dioptrics, studies refraction, and the topic of the fourth part is diffraction. Beyond these general topics, Comte also mentions double refraction and polarisation as important particular issues.
The final physical discipline, in Comte’s opinion, is electrology. It is the most complex and thus had to be developed last, he explains, and due to this late blooming it is the least developed as science: although it has many curious facts, it still lacks laws to make the facts into a scientific system. Comte sees a clear sign of its unscientific nature in the abundance of hypotheses about various fluids that should explain electric phenomena. He thinks they are not as detrimental as in optics, since no true scientist takes them seriously and uses them as mere mnemonic devices. Still, Comte warns, they have had bad influence especially on physiology, where they have inspired such ridiculous notions as animal magnetism.
Since all bodies are not at all times electrical, the first topic investigated in electrology, Comte says, should be the investigation of methods to introduce bodies into an electric state. He also includes in this part the recognition and measurement of an electric state in a body. The second part of electrology, for Comte, is electrostatics, by which he means what he describes a state of an electric equilibrium: this part includes e.g. study of distribution of electrical state in a single body or in a set of contiguous bodies. The third part is then, naturally, electrodynamics, which studies movements generated by an electrical state, for instance, repulsions and attractions of two electrified bodies. Fourth part, finally, studies magnetism and its connection to electricity.
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