Mayer's spiritual kin are not to be found among the heat-theorists of his time, such as Helmholtz and others, but among thinkers of the stamp of Goethe, Howard and Ruskin. His basic idea of the inner connexion between all forms of energy in nature corresponds entirely with Goethe's idea of metamorphosis. Just as Goethe saw in the ur-plant the Idea common to all plant-forms or, in the various plant-organs, the metamorphosis of one and the same ur-organ, so was Mayer convinced of the existence of an ur-force which expressed itself in varying guises in the separate energy-forms of nature. In the picture of the physical universe which hovered before him, the transformation of one form of energy into another - such as mechanical energy into electrical, this into chemical and so on - was somewhat similar to Goethe's picture of the organic life of the earth, in which the metamorphosis of one living form into another constantly occurred. 'There is in nature', said Mayer, 'a specific dimension of immaterial constitution which preserves its value in all changes taking place among the objects observed, whereas its form of appearance alters in the most manifold ways.'
For the physicist, accustomed to a purely quantitative observation of nature, it is difficult to comprehend that Mayer could have arrived at the thought of a constant quantitative relation between the various manifestations of natural energy, without deriving from it the conviction of their qualitative indentity - i.e., without concluding from the existence of the mechanical heat - equivalent that heat is itself nothing else than a certain form of spatial movement. Mayer actually had a picture directly contrary to the mechanistic conception. For him, the arising of heat represented a disappearance of mechanical energy.
If this, then, was Mayer's belief, what was it that convinced him of the existence of a numerical balance between appearing and vanishing energy, even before he had any experimental proof?
Later in this book there will be occasion to introduce a concept of number in tune with our qualitative world-outlook. What led Mayer to look upon number as an expression of existing spiritual associations in nature will then become clear. Let this much be said here, that number in the universe has quite different functions from that of serving merely as an expression for a total of calculable items, or as a means of comparing spatial distances. It is in the nature of the onlooker-consciousness that it is unable to interpret numerical equality between natural phenomena save as indicating the presence of an equal number of calculable objects or of spatial movements of equal magnitude. It was therefore consistent for such a consciousness to regard the discovery by Mayer of the mechanical heat-equivalent as a confirmation of the existing mechanical conception of heat.
For Mayer such an interpretation was not necessary. His conviction of the existence of an ur-force, manifesting through metamorphosis in all natural forces, led him to expect a constant numerical relation amongst these, without requiring him to deny the objective existence of qualitative differences, as these displayed themselves in the field of phenomena. He was spiritually akin to Goethe, also, in that he guarded himself strictly against substituting for the contents of our perception conveyed by nature purely hypothetical entities which, while fashioned after the world of the senses, are, in principle, imperceptible. Mayer sought after a truly empirically founded concept of force, and his method was that of reading from all the various manifestations of force which were open to sense observation. One such manifestation, capable of empirical determination, was the balance between appearing and disappearing energy.
Science treated Mayer in the same way as it treated Howard. It took from him what it wanted for its purpose without concerning itself with the epistemological principle which had led him to his discovery. Thus it was that Mayer's discovery led to most important consequences for the development of modern technical devices, whereas it was the fate of his guiding idea to be first derided, then misunderstood and finally forgotten. The consequence was that the knowledge of the numerical equilibrium between created and expended energy in the economy of nature has widened more and more the abyss separating spirit and matter in human life, instead of leading, as indeed it might have done, to a bridging of the abyss. The thought, therefore, regarding the appearing and disappearing of measurable cosmic substance, to which we are led when following Goethe's method of observing nature, stands in no sort of contradiction to what Mayer himself conceived as the relation of the various forms of energy to one another, and the maintenance of the numerical balance between them.
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Having thus determined our standpoint with regard to the thermodynamic theory of heat and the law of conservation, we may proceed to the study, first of the phenomenon of thermal expansion, and then of the effect of heat on the various states of physical matter, by applying to them, unimpeded by any preconceived mechanistic idea, what we have learnt through our previous studies. We must start by developing a proper picture of the dynamic condition of matter in the solid state.
In a solid body the material substance is centred on an inner point, the so-called centre of gravity - a characteristic which such a body shares with the earth as a whole. Likewise, two such bodies exert on one another the same influence that the earth exerts on each of them: they try to assume the shortest possible distance from each other. Since the days of Faraday science has been accustomed to ascribe these phenomena to the existence of certain fields of force, connected with each body and working on one another through the intermediary space. It is to this concept of the field of force that we must now give special attention. For the field-concept, in the form introduced by Faraday into scientific thinking, is one of the few scientific concepts which have been obtained by being 'read' from the corresponding phenomena themselves, and which therefore retain their validity in a science which is based on the method of reading.
According to the field-concept, terrestrial manifestations of gravity are due to the earth's being the bearer of a gravitational field centred within the globe, and extending thence in all directions through space, across and beyond the earth's body. Every point in space, both inside and outside the earth, is characterized by a definite intensity of this field, the so-called gravitational potential. This is subject to variations due to the presence of other physical masses, which carry their own fields of gravity. What happens between such masses and that of the earth, as well as mutually between such masses themselves, is brought about by the particular conditions in space resulting from the interpenetration of the various fields.