|Jane Marcet's 1805 sand-marble illustrative model of capacity of a body for caloric (see: heat capacity), in which the sand represents the "caloric" and the ping pong balls represent the atoms, according to which a given body will have so much capacity for caloric, i.e. heat as it was viewed in that period.  This visual is based on Antoine Lavoisier's 1789 Elements of Chemistry (pg. 16) description of "spherical lead bullets and sand" model of bodies and caloric.|
In 1783, Antoine Lavoisier and Pierre Laplace, in their Memoir on Heat, building on the latent heat theories of Joseph Black, stated the following, which is the essential origin of the caloric model of heat, in basics:
“If heat is a fluid, it is possible that during the combination of various substances, it combines with them or is evolved from them. Thus, nothing indicates a priori that the ‘free heat’ is the same before and after the combination; nothing, moreover, suggests in the hypothesis that heat is only the vis viva [kinetic energy] of the particles of bodies, for in substances that combine together, acting on one another by virtue of their mutual affinities, their particles are subjected to the action of attractive forces that can alter the amount of their vis viva, and, subsequently, the amount of heat. But one should accept the following principals being common to the two hypotheses:‘If, in any combination or change of state, there is a decrease in free heat, this heat will reappear completely whenever the substances return to their original state; and conversely, if in the combination or in the change of state there is an increase in free heat, this new heat will disappear on the return of the substances to their original state.’
This principle, moreover, is confirmed by experiment, and in what follows the detonation of saltpeter [gunpowder] will furnish us with visible proof. We can generalize it further, and extend it to all the phenomena of heat, in the following way:‘All changes in heat, whether real or apparent, suffered by a system of bodies during a change of state of recur in the opposite sense when the system returns to its original state.’
Thus, the changes of ice into water and of water into vapor, cause the thermometer to show the disappearance of a very considerable amount of heat which reappears in the change of water into ice and in the condensing of vapors.”— Antoine Lavoisier (1783), Memoir on Heat (co-author: Pierre Laplace) (pgs. 5-6)
The term "calorique" (caloric) was introduced in 1787 by French chemist Guyton de Morveau, working in coordination with French chemist Antoine Lavoisier, Savoyard chemist Claude Berthollet, and French chemist Antoine de Fourcroy in a paper presenting the suggestions on the reformulation of the chemical nomenclature.  Lavoisier, in 1777, had formerly used the names igneous fluid and matter of heat for the hypothetical fluid.  The postulate of the caloric particle came to be known as the "caloric theory".
In a 1780 memoir titled “On Combustion in General”, Lavoisier presented his new theory of combustion, with five key points:
(a) In combustion, there is disengagement of the matter of fire (caloric) or of light.
(b) A body can burn only in pure air [oxygen gas].
(c) There is “destruction or decomposition of pure air” and the increase in weight of the body burnt is exactly equal to the weight of the air “destroyed or decomposed”.
(d) The body burnt changes into an acid by addition of the substance which increases its weight.
(e) Pure air is compound of the matter of heat (caloric) or of light with a base; where in combustion, the burning body removes the base, which it attracts more strongly than does the matter of heat, and sets free the combined matter of heat, which appears as flame, heat, and light.
In this theory, as contrasted with the older phlogiston theory, which situated the matter of fire (phlogiston) in the combustible, the matter of heat was theorized to be located in pure air. 
In 1789, Lavoisier, in his Elements of Chemistry, published the following listing what he considered to be the 33 known elements, including caloric:
In 1799, English chemist William Jackson, in his “A Synopsis of the Chemical Characters: Adapted to the New Nomenclature”, presented the following basic chemical elements or what he referred to as “examples of simple characters” (left) and “examples of compound characters” (right), i.e. chemical compounds: 
Accordingly, we have the following conception of ice (solid) to water (liquid) to vapor (gas) transitions:
which seems to signify or conceptualize the logic that ice is a chemical compound of oxygen and hydrogen with no caloric (no vertical line), water that of oxygen and hydrogen with some caloric added, signified by the caloric character (vertical line) on top, and vapor of water that of oxygen and hydrogen with more caloric, signified by the caloric character (vertical line) at the bottom of the compound symbol.
In 1805, English introductory science writer Jane Marcet, in her Conversations on Chemistry, gave the following Q&A summary conception of caloric: 
Mrs B: Your reasoning is very good, as far as conducting power is concerned; but facts, as established by decisive experiments, overturn your theory, and leave no doubt that the quantity of caloric which enters into various substances to produce in them the same thermometric effect, is very different; and hence they are said to possess different capacities for caloric.
Caroline: What do you mean by the capacity of a body for caloric [see: heat capacity]?
Mrs B: I mean a certain disposition of bodies to require more or less caloric for raising their temperature to any given degree of heat. Perhaps the fact may be illustrated thus:Let us put as many marbles into this glass as it will contain, and pour some sand over them; observe how the sand penetrates and lodges between them. We shall now fill another glass with pebbles of various forms; you see that they arrange themselves in a more compact manner than the marbles, which, being globular, can touch each other by a single point only. The pebbles, therefore, will not admit so much sand between them; and consequently one of these glasses will necessarily contain more sand than the other, though both of them be equally full.
Caroline: This I understand perfectly. The marbles and the pebbles represent two bodies of different kinds, and the sand the caloric contained in them; and it appears very plain, from this comparison, that one body may admit of more caloric between its particles than another.
● Re-establishment of equilibrium in the caloric
1. Caloric (definition) - Merriam-Webster Collegiate Dictionary, 2000, version 2.5.
2. Lavoisier, Antoine. (1789). Elements of Chemistry, (pg. 5). London: G.G. and J.J. Robinsons.
3. Morveau, Guyton de. (1787). Méthode de Nomenclature Chimique (Method of Chemical Nomenclature), 31.
4. Collection of the French Academy of Sciences for that year, pg. 420.
5. Partington, J.R. (1957). A Short History of Chemistry, 3rd ed. (pg. 131-35). New York: Dover Reprint.
6. Jackson, William. (1799). “A Synopsis of the Chemical Characters: Adapted to the New Nomenclature” (Ѻ), by Jean-Henri Hassenfratz and Pierre-Auguste Adet, Systematically Arranged by William Jackson, Practical Chemist. London: Harry Ashby & Son Engineers & Printer.
7. (a) Marcet, Jane. (1805). Conversations on Chemistry (pg. 66). Philadelphia: Grigg & Elliot, 1846.
(b) Jane Marcet – Wikipedia.
● Metcalfe, Samuel L. (1859). Caloric: its Mechanical, Chemical and Vital Agencies in the Phenomena of Nature (Volume 1). J.B. Lippincott & Co.