Neumann first shewed that atoms of similar stoichiometrical composition have the same capacity for heat, e. g., metallic oxides and sulphurets,and salts of carbonic and sulphuric acid; and Regnault showed that the same law was further applicable to many other series of compounds. Hermann showed that in certain metallic sulphurets, the heat-capacity of the compound atom might be found by taking the sum of the capacities of the metal and of sulphur. [Comp. also L. Gmelin. (Gehler. Physik. Wörterbuch. 9, 141.)] The law upon which this is based may, with a few exceptions, be enunciated as generally applicable in the following terms: The simple atoms by which a compound atom is formed, retain therein the same capacity for heat that they possess when separate; and consequently, the heat-capacity of a compound atom is the sum of the heatcapacities of the simple atoms which compose it. Some cases however can only be explained by supposing that the heat-capacity of certain substances, especially carbon and oxygen, varies by simple multiples according to the compound in which they exist. Exact agreement is not to be expected, since as is shown by the great differences between the results obtained by different observers-it is only in the case of a few substances, that the specific heat has been exactly determined;-and moreover, the specific heat of the same body varies according to circumstances. It must be especially borne in mind that in all cases when the specific heat of a compound is determined in the liquid state, the heat-capacity of the atom thus found is greater than that which results from calculation,-undoubtedly because, as shown in the case of water, the passage of a body from the solid to the liquid state is attended with an increase of specific heat. Since then an approximation between the results of calculation and experiment (which latter will be taken from the foregoing table and annexed within brackets) is all that can be indicated, we may be allowed to shorten the numbers. According to the table (p. 243) the atoms of most simple substances have the same capacity for heat, viz. 3.2;-let this be called the normal capacity.-Carbon in the form of diamond seems to have (0-8) and oxygen (16) of this normal capacity: on the contrary, chlorine, iodine, bromine, phosphorus, arsenic, antimony, silver and gold (and judging from the specific heats of their compounds, likewise, potassium, sodium, and lithium) have twice the normal capacity, viz. 6·4. In many compounds however, oxygen appears to enter with 24 or of the normal capacity, and in ice to possess the normal capacity itself: similarly, carbon, sulphur, and nitrogen appear to possess different capacities for heat, according to the nature of the compound in which they are formed. 1.*2Cu 6·4 + 0 1·6 = 8·0 (7·68). 2. H 3.2 + 0 3·2 = 6·4 (6·48). 3. Metal 3.2 + O 2·4 = 5·6 (5·52). = = 4. 3Metal 96 +40 (at 2·4) 9.619-2 (19.66). 5. 2A1 64 + 30 (at 1·6) 4·8=11·2 (11·17). 6. 2 Metal 64+ 30 (at 2:4)=7.2 13.6 (13.95). 7. Metal 3.2 + 20 (at 1·6) 3·2 = 6·4 (6·59). 8. Mo 3.2+20 (at 2.4) 4'8 8.0 (8.33). 9. B 3230 (at 1.6) 4.8 8.0 (8.26). 10. Metal 3.2 + 30 (at 2·4) 7·2 = 10·4 (9∙51). 11. Metal 6-4 + 30 (at 2·4) 7·2 = 13·6 (14·26). 12. Sb 6.4 + 40 (at 2·4) 9'6 = 16·0 (15·3). 13. Ca 3-2 F 6·49·6 (8·16); accords but little. 14. 2Metal 64 + Cl 6·4 = 12·8 (12.04). = 15. Metal 6.4 + Cl 6·4 = 12·8 (12·40). 16. Metal 3.2 + Cl 6·4 = 17. Metal 3.2 + 2C1 12.8 18. P or As 6'4+3C1 19.2 9·6 (9.31). 160 (18-69, but liquid). 19. Metal 64 + Br. 6·4 = 12·8 (12·71). 20. Pb 3.2 + Br. 6·4 21. 2Metal 64 + I 6·4 9·6 (9.71). 12·8 (13·0). 22. Metal 6.4 + I 6·4 = 12·8 (13-6). 23. Metal 3.2 + I 6·4 = 9·6 (9·63). 24. 2Cu 64+ S 3·2 = 9·6 (9·65). 25. Metal 3-2 S 3.2 6.4 (5.7....63). This large variation makes it probable that sulphur enters into many of these compounds with a smaller capacity for heat, perhaps = 2.4. 26. Ag 64+ S 3·2 = 9·6 (9·26). 27. 2Bi 6·4 + 3S 9.6 = 16·0 (15-65). 28. If the carbon in this compound be supposed to possess 8 times the capacity for heat which it has in the diamond, or twice the normal capacity, we shall have: C 64 + 2S 6·4 12·8 (12.5). = 29. Metal 3.2 + 2S 6·4 = 9·6 (10·36). 30. Fe 3.2+28 (at 2·4) 4·88·0 (7·7). 31. As 64 + 2S 6·4 = 12·8 (11·9). 32. As 6'4 + 3S (at 2·4) 7·2 = 13·6 (13·95). 33. Sb 6:43S (at 3.2) 9.6 16.0 (16.05). 34. Co 3.2 + As 6·49·6 (9·64). 35. Sn 3.2 + Bi 3·2 = 6·4 (6·6). * These numbers refer to those in the first column of the table ( 249). 38. Like 35; 39 like 36. 40. KO (K 64+ O 2.4) 8.8 + CO2 (C 16+ 20 at 2:44.8) 5.6 144 (14.5....149). 41. Met. O (according to 3) 5'6 + CO2 (according to 40) 5'6 11·2 (1051): not sufficiently near. 42. Does not give a satisfactory result. 43. KO 8.8 B 03 (according to 9) 8.0 16.8 (16.8....16.9). 44. Pb O (according to 3) 5'6 + BO3 8·0 = 13·6 (13·27). 45. KO 88 + 2BŎ3 16·0 = 24·8 (24·0....25·7). 46. PbO 56+ 2B O3 16·021·6 (20·7). 47. KO 88+ Cr O3 (Cr 3.2 + 30, at 2.4 7.2) 10.4 48. KO 8.8+2Cr O3 20·8 = 29·6 (28·4). 19.2 (18'4). 49. HO (according to 2) 64+ SO3 (S 3.2 + 30 at 1.6 4.8) 8.0 =144 (17·1): does not agree. 50. KO 88+ SO3 8.0 16·8 (16·4....16·6). 51. Met. O 56+ SO3 8.0 13.6 (13·06). 52. 3PbO (3.56) 16·8 + PO3 (P 64+ 50 at 1·68·0) 14·4= 31.2 (32.46). 53. 2KO (2.8.8) 17.6 + PO 144 32·0 (30.5....317). 56. 3PbO (3.5.6) 16'8 + As 05 14.431·2 (32.8). 57. KO 88+ As O3 14·4 = 23·2 (254).—Since KO, C1 05 and K O, N 05 exhibit the same capacity, that of C1 05 and N 05 as well as that of As 05 must be 14.4: hence nitrogen in nitric acid must have twice the usual capacity. 58. Ba O 56+ N 05 14·4 20·0 (17.8 ... 19·9). 59. Ca O 56+ SO3 8.0 + 2H O (2.6.4) 12.826.4 (236) a very considerable difference. H. Schröder (Pogg. 52, 269) proceeds upon the same principles. He likewise supposes that certain substances may possess different atomic heat-capacities according to the compounds in which they exist, and brings this alteration of the capacity of a substance into connection with the change in its equivalent volume: so that the heat-capacity of a body is smallest in that compound into which it enters with the smallest equivalent volume (compare pp. 73-78). Oxygen, e. g. enters with a capacity of 24 into those compounds in which its equivalent volume is 2.7 (atomic weight of oxygen 8), viz. compounds of 1 atom of metal with 1 At. oxygen, of 2 At. metal with 3, and of 3 At. metal with 4 At. oxygen; and with the capacity of 1.8 (2 of 2.4) into those compounds in which its volume is 1:35, viz. compounds of 1 At. metal with 2 At. oxygen. Similarly, with the compounds of sulphur and other substances, as may be seen more in detail in the original memoir. = It may perhaps be regarded as certain that the heat-capacity of the atoms of compounds must be smaller, the more strongly their elements are condensed. This is likewise seen (not however in all cases) on applying the method of calculating condensation given on page 77. The smaller the divisor, the greater is the number of compound atoms in the same space, and the greater therefore is the condensation of the elements in the compound. According to page 77, the divisor for Fe S2, is 6; for Mo S2, 7; for Sn S2, 8;-and according to the table p. 249, the heat-capacity of Fe S2 is 7.702; of Mo S2, 9.864; and of Sn S2, 10 856.-These observa tions on the connection between the condensation and heat-capacity of elements in their compounds may suffice for the present, till the mode of calculating the condensation of elements in compounds shall have been determined with greater accuracy. Avogadro's method of calculating the heat-capacity of compound atoms appears to be founded on hypotheses of too bold a character, and therefore inadmissible. The capacity of bodies for heat may be attributed to their adhesion to that element; and this adhesion in the atoms of most bodies may be supposed to be of the same strength,-so that these atoms, when immersed in a uniform medium of heat and exposed to the same temperature, will absorb equal quantities of heat. Since the heat which is attached to bodies by adhesion and expands them has lost absolutely nothing of its elasticity, and leaves the bodies as soon the temperature of any neighbouring body becomes lower, even in the slightest degree, the heat thus retained in bodies is called Free, Uncombined, Sensible Heat*. CHEMICAL RELATIONS, I. Combinations of Heat with Ponderable Bodies, constituting Fluids. All ponderable fluids, whether liquids or gases, may be regarded as chemical combinations of ponderable substances with a certain excess of heat in the absence of heat, all ponderable bodies would exist in the solid state. Substances which are solid at comparatively low temperatures assume the liquid and gaseous states at higher temperatures. With this change in their state of aggregation, part of the heat becomes insensible, both to * Clement & Desormes consider that even a vacuum has a certain capacity for heat, and they estimate this capacity at 0·41, that of an equal bulk of air being assumed = 1. But Gay-Lussac has shown that if a Torricellian vacuum be produced in a tube 0.075 metres in width, and containing a delicate thermometer, no heating or cooling takes place on alternately contracting and enlarging the empty space by moving the mercury quickly up and down, unless a portion of air be present (Comp. Prevost, Ann. Chim. Phys. 31, 429). On the other hand, Clement & Desormes admitted air into an imperfect vacuum produced by the air-pump, and attributed the rise of temperature thereby produced to that portion of heat which was driven out of the empty space by the air which entered. But this rise of temperature may be better explained on the supposition that the air still contained in the vessel, as well as that which first enters, is compressed by the portion which follows, and thus its specific heat is diminished. Aug. de la Rive & F. Marcet have also shown (Bibl. unir. 22, 265) that when a thermometer is placed in the vacuum, close to the opening at which the air enters, it sinks during the first two or three seconds when the air enters, and afterwards rises, showing that the air which first enters absorbs heat in consequence of its expansion, and afterwards evolves it when compressed by the portions which subsequently enter. The following experiment likewise gives a similar result. When oil-gas, compressed to 30 atmospheres, is made to flow into a cylinder 3 feet long, and closed at the further end, that end becomes very warm, and the end at which the gas enters very cold (Qu. J. of Roy. Inst. N. S. 2, 474; also Schw. 51, 106).—If capacity for heat be due to the adhesion of heat to ponderable bodies, such capacity can scarcely be ascribed to a vacuum. On the other hand, the presence of a certain quantity of heat in the vacuum cannot be denied. For the adhesion of the heat to the solid walls of the empty space cannot overcome its expansive force to such an extent as to prevent any of it from remaining in the empty space; and the hotter the walls are, the greater will be the quantity of heat left in the free unabsorbed state; or, according to the ordinary view, the opposite walls of the vacuum emit and receive rays of heat through it, and, consequently, the vacuum must be filled with these rays of heat, crossing each other in all directions, the feelings and to the thermometer, being then in a state of chemical combination, and thereby deprived, to a certain extent, of its elasticity. When these bodies return to their former state of aggregation, this portion of heat is set free and again becomes sensible to the feelings and to the thermometer. The heat thus combined with ponderable bodies in the liquid state is thence called Combined or Latent Heat, inasmuch as its tendency to equilibrium is to a certain extent overcome by the adhesion of the ponderable substance; likewise Heat of Fluidity, inasmuch as it is regarded as the cause of fluidity in ponderable bodies. It is however probable that solid bodies also contain heat chemically combined with them, as will be seen by II.-It appears then that a body may contain heat in two states,-first, chemically combined,-secondly, retained by adhesion. 1. Formation of Liquids. A solid body, situated in a cold medium into which heat is gradually introduced, becomes capable, when the medium has attained a certain temperature, of fixing a portion of the heat, and, if subjected to external pressure, forms a liquid by combining with it. The temperature at which this fusion takes place the Melting Point as it is called,--is very different in different substances. The greater their affinity for heat, the sooner do they fix it even when diffused through the medium in very small quantity; the smaller the affinity, the greater must be the quantity of heat collected in and about the bodies in order that its expansive tendency may be overcome by that affinity.--Alcohol is liquid at 90°, mercury fuses at - 40°, ice above 0°, sulphur at + 109, many metals below a red heat, others not till raised to the highest attainable temperatures, and carbon probably not at any temperature hitherto produced. Hence the distinction between easily fusible and refractory substancesCorpora fusibilia and refractaria. Those compounds only are infusible which decompose below their melting point; e. g. wood. The liquefaction of many substances is preceded by a softening which renders their particles capable of sticking together: e. g. the welding of iron and other metals, baking of porcelain, softening of wax. The melting point of each individual body is perfectly constant: for as long as any of the substance remains to be fused, it renders latent any quantity of heat which may be added in excess; and it is not till the fusion is quite complete, that a further accession of heat causes the temperature to rise. If, on the contrary, the quantity of heat in the surrounding medium be diminished, the liquid previously formed first gives up to the medium merely that uncombined portion of heat by which its temperature had been raised above the melting point; but if the temperature of the medium ultimately falls below the melting point, the tendency of the heat to diffuse itself through the surrounding medium overcomes its affinity for the solid body, the heat leaves the ponderable matter, and the latter returns to the liquid state. The temperature at which a body solidifies, or the Freezing Point, generally coincides with the melting point: for just as when heat is communicated to a solid body, the temperature of that body does not rise above its melting point, till it has absorbed the quantity of heat required to melt it,-so, on the other hand, a liquid does not generally cool below the melting point until completely solidified, because, so long as any portion of the substance remains in the liquid state, the abstraction of heat from without is compen. sated by the conversion of latent into sensible heat. Nevertheless, some |