been hammered. Finally, one body expands more by heat than another. All these disturbing causes, which prevent the existence of any exact relation between atomic weight and specific gravity, are absent in gaseous bodies: in these the size of the atoms is so small in comparison with that of the heat-spheres that it need not be taken into consideration; moreover, cohesion is in gases completely overcome, and they all expand equally with equal increments of heat. The following table is arranged in the same manner as the last.Column A: the simple substances taken in order according as their atomic numbers for the same volume diminish. Column B: their atomic weights. Column C: their specific gravities in the liquid or solid state, that of water = 1000; in the case of the metals the sp. gr. are those which they possess after fusion and solidification, not after hammering. Column D: the quotient obtained by dividing the specific gravity by the atomic weight, that is to say, the atomic number. Column E: the quotients in column D multiplied by 770 (air being 770 times lighter than water) in order to render the atomic numbers of this table comparable with those of the former, in which the sp. gr. of air was assumed 1.000. Column F: the atomic numbers of column E divided by 0.0693; the column F of the present table is thus made to harmonize with column E of the preceding: it gives the number of atoms of a liquid or solid body contained in a space which would include 1 atom of hydrogen. Column G: the numbers taken from column F of the former table, and giving the reduced atomic number of a body in the gaseous state, 1 volume of hydrogen gas being supposed to contain 1 atom of hydrogen. By examining this table we arrive at the following results : 1. Equal volumes of different liquid and solid bodies contain very different numbers of atoms. If 1 cubic inch of hydrogen gas contains 1.x At. hydrogen, then 1 cub. in. potassium contains 245. x At. potassium, and 1 cub. in. diamond 6481. x At. carbon. Of all liquid and solid bodies potassium has the smallest and carbon the greatest (27 times as great) atomic number. This great diversity in the atomic numbers is perhaps to be explained; (a) from difference of magnitude in the atoms themselves.-The greater the weight, and therefore also the magnitude of the atoms, the smaller must be the number of them which at equal intervals can be disposed in a given space. This is perhaps one of the causes why uranium which has so large an atomic weight should have so small an atomic number; why sodium, whose atomic weight is not much more than half that of potassium, has an atomic number nearly twice as great. The great atomic number of carbon may likewise partly arise from the smallness of its atoms. (b.) From difference in the force of attraction (Cohesion) between the atoms.-The hardest of all substances, the diamond, is precisely that which contains the greatest number of atoms in a given volume either then its great cohesion is the consequence of the close approximation of its atoms, or this close approximation a consequence of their great cohesion; or possibly, the strong attraction of the particles for one another, together with the close approximation thereby produced, may be the cause of the great tenacity and hardness of the diamond. The other bodies likewise follow nearly in the order of their cohesion, and the soft metal potassium terminates the series. (c.) From the different affinities of the atoms for heat.-The stronger this affinity, the greater will be the quantity of heat collected in the pores, and the more widely therefore will the atoms be kept asunder. A greater attraction for heat implies also a greater inclination to assume the gaseous state. Accordingly, the less volatile bodies, those namely which have the smallest attraction for heat, such as carbon and the more refractory metals, exhibit larger atomic numbers than sulphur, selenium, phosphorus, iodine, bromine, chlorine, and the volatile metals. The only exceptions to this rule are zinc and the very refractory metals, uranium, gold, silver, and osmium. In a similar manner, as will afterwards be shown (vid. Heat), the specific heat of bodies is greater, cæteris paribus, in proportion as they have fewer atoms in a given space and therefore greater intervals between them. Lastly, the exceptions just noticed and others also show that the three causes here considered, viz., the size of the atoms, their cohesion, and their attraction for heat, are not the only ones by which the atomic numbers are affected. 2. Many elements possessed of similar properties have their atomic numbers nearly equal; e. g., nickel, manganese, cobalt, and iron (of which that of the diamond is double); platinum, palladium, and rhodium; titanium and chromium; tungsten and molybdenum; silver and gold; phosphorus and antimony; iodine, bromine, and chlorine. The atomic numbers of some substances are also simple multiples of others of similar nature; that of copper is nearly double that of mercury: that of zinc double that of lead; of arsenic 14 times that of antimony; of sodium nearly twice that of potassium. 3. On comparing the atomic numbers of one and the same substance in its gaseous (column G) and in its liquid or solid state (column F), we have the following results:-A space which contains 1 At. chlorine in the gaseous state will hold 418 atoms of liquid chlorine; hence chlorine in passing from the liquid to the gaseous state at a temperature 0° C. and a pressure of 0.76 metres (= 30 inches) is expanded to 418 times its volume. In the case of bromine the expansion amounts to 422 times, of iodine 437, of phosphorus 309, of arsenic 440, of sulphur 231, of mercury 1485, and of carbon (if its vapour be regarded as a monatomic gas) to 6481 times its volume. The great differences between these numbers show the utter groundlessness of the law which Persoz (Chim. Molec. 254) thought he had discovered, viz., that all substances both simple and compound, in passing from the gaseous to the liquid or solid state, undergo the same amount of condensation. The specific gravities calculated according to this law appear to coincide with the results of observation, only because Persoz regarded the vapours of sulphur and phosphorus as monatomic gases, and supposed that the sp. gr. of sulphur determined by experiment was not 2 but 1.8, taking also for that of arsenic the totally incorrect number 83 determined by Bergman, and long since rectified by Lavoisier, Guibourt, Karsten, and Herapath. 4. Since liquid and solid bodies rarely contain equal numbers of atoms in equal volumes, they exhibit no tendency to combine in those simple proportions by volume which invariably hold good in the combination of gases. If, for example, we would combine 1 cub. in. of sulphur with 1 cub. in. of lead, we should have to bring together 1388.x At. sulphur and 1218. At. lead, and since these bodies combine in equal numbers of atoms there would remain 170. At. sulphur uncombined. The differences of the atomic numbers in the table are such that even by multiplying the volume of a body by 13, 14, 2, 24, 3, 4, &c., no exact relations would result. If, moreover, it be considered that the same metal according as its density has or has not been increased by hammering must have a different atomic number, and again that different substances when heated expand in various degrees, so that a proportion by volume correctly determined at one temperature would be incorrect at every other, it will be evident that the endeavours of Meinecke (Chemische Messkunst) and of Frère de Montizon (Ann. Chim. Phys. 7, 7,) to discover simple relations by volume in the combinations of liquid and solid bodies must necessarily have led to no result whatever. The so-called Atomic volume. It is inconsistent with the atomic theory to suppose that the space which a body occupies is completely filled by it. For the laws of gravitation oblige us to assign the same specific gravity to the atoms of different substances, and consequently to suppose that the different weights of these atoms are due to difference of magnitude; e. g., that an atom of double weight must also be of double volume. It follows from this that the specific gravities of different substances must depend upon the magnitude of the spaces existing between their atoms. These atoms must be regarded as impenetrable and of unalterable volume, and the expansion of a body by heat or by diminution of external pressure, as well as its contraction by cooling or increase of pressure, as proceeding from an enlargement or diminution of the intervening spaces. In opposition to this view, which follows almost of necessity from the hypothesis of atoms, Le Royer and Dumas (J. Phys. 92, 409) and more lately Graham and Kopp, conceive that the space which a body occupies is completely filled by atoms without any intervening spaces. According to this hypothesis, the specific gravity of a body multiplied by the volume of its atoms, must give the atomic weight (for the greater the sp. gr. of any substance and therefore-according to this view of its atoms, and the greater their volume, the greater also must be their weight). Conversely, when the atomic weight and specific gravity are known, the volume of the atoms will be found by dividing the first by the second. Thus the atomic weight of carbon = 6 divided by the specific gravity of the diamond = 35 will give the atomic volume of carbon = 1.714; and the atomic weight of potassium 39.2 divided by its sp. gr. 0.865 gives its atomic volume = 45:32. If now these numbers be compared with the atomic numbers of carbon and potassium in column D, it will be found that the so-called atomic volume is exactly the reciprocal of the atomic number; for 1714. 0.5833 = 1, and 45:32. 0.0221 = = 1. (It is scarcely necessary to observe that these numbers will come out differently if instead of assuming the atomic weight of hydrogen 1, we take that of oxygen = 100, as is commonly done). That the atomic volume is necessarily the reciprocal of the atomic number is easily seen: for according to the view first laid down (which must be regarded as the correct one) the specific gravity is the product of the atomic number and the atomic weight (page 52): so that if S specific gravity, G = atomic weight and Zatomic number, we have SG. Z. If now, according to Leroyer, &c., we divide the atomic weight G by the sp. gr. which according to the above is G. Z., we have the atomic volume = 1 G = Hence the atomic volume is the reciprocal of the atomic number. It is easy to see from this that the expression atomic volume must lead to erroneous views and inferences: for we can understand by it nothing else than an atom of a body together with the adjacent and surrounding interstices; since, however, these interstices vary according to external circumstances, such as pressure and temperature, the atomic volume must be variable also. This is allowed by Pol. Boullay (Ann. Chim. Phys. 43, 266, extr. Pogg. 19, 107; also N. Tr. 23, 1, 208) who advanced similar views. If this mode of calcu lation be adopted, it is better to leave the atomic theory out of the question and adopt the nomenclature of H. Schröder, who calls these quotients equivalent volumes. Since 16 parts of sulphur are the equivalent of 126 iodine, a volume of sulphur which takes up 16: 2000 = 8 cubic measures, is the equivalent of 1 vol. iodine which occupies 126: 4048 25.46 cubic measures; for 1 vol. sulphur of 8 cubic measures, whose sp. gr. = 2 contains 2. 8 = 16 parts by weight, and 1 vol. iodine whose sp. gr. 4946 contains 4.946. 25.46 126 parts by weight. (For further development of this matter, vid. Density of Compounds.) Atomic weight of Compounds. The two laws above laid down (page 41) apply to compounds as well as to simple substances. If one compound substance A is capable of com bining with another compound substance B in different proportions, the smallest quantity of B with which A can combine, multiplied by 1, 2, 3, 4.... gives the other quantities of B which can enter into combination with A. Thus, 47.2 parts of potash are united in carbonate of potash with 22, and in bicarbonate with 44 parts of carbonic acid:111.8 oxide [of lead can combine with 9, 18, 27 and 54 parts of nitric acid. The second law is also applicable from the proportions in which one compound substance combines with two others may likewise be determined the proportion according to which these two combine with one another. Hydrate of magnesia contains 20.7 magnesia and 9 water; sulphate of magnesia, 207 magnesia and 40 sulphuric acid: and accordingly 9 water and 40 sulphuric acid are exactly the proportions of these two bodies contained in oil of vitriol. In this manner the atomic weights or equivalents of compound bodies may be determined quite independently of those of simple substances. For example, we might assume the atom of sulphuric acid = 1000, and then determine that of water = 225, of magnesia 517-5, and oxide of lead 2795, these being the quantities of these several substances, which combine with 1000 parts of sulphuric acid: moreover, since these quantities of the several bases saturate 1350 nitric acid, this number 1350 would, on the same hypothesis, express the atomic weight of nitric acid. Numbers so determined would not, however, be in accordance with those of the simple substances obtained on the supposition of hydrogen 1 or oxygen 100. = = = The atomic weight of any compound is equal to the sum of the atomic weights of the simple substances which compose it. This is in exact accordance with the atomic theory; for the atom of a compound must weigh as much as the individual atoms of the simple substances composing it taken together. 1 At. hydrogen = 1 and 1 At. oxygen 8 form 1 At. water 1+8=9; 1 At. lead= 103.8 and 1 At. oxygen = 8 form 1 At. oxide of lead= 111'8; 1 At. sulphur = 16 and 3 At. oxygen = 24 form 1 At. sulphuric acid = 16+ 24 = 40. Hence 111.8 parts of oxide of lead combine with exactly 40 parts of sulphuric acid, because this is the proportion in which 1 At. oxide of lead combines with 1 At. sulphuric acid. If 111.8 parts of oxide of lead be heated to redness with an excess of aqueous sulphuric acid, that part of the acid not taken up by the oxide of lead evaporates together with the water, and there remain exactly 151-8 parts of sulphate of lead, containing 1118 oxide of lead and 40 sulphuric acid. When galena, a compound of 1 At. lead with 1 At. sulphur is digested with nitric acid, which gives to the lead and the sulphur the quantities of oxygen required for converting them respectively into oxide of lead and sulphuric acid, and the liquid is evaporated to dryness, there remains the same compound of 1118 oxide of lead and 40 sulphuric acid, so that no excess of sulphuric acid can be removed by water or of oxide of lead by acetic acid, because 1 At. lead by combining with oxygen forms exactly 1 At. oxide of lead, and 1 At. sulphur by combining with oxygen forms exactly 1 At. sulphuric acid, and moreover oxide of lead and sulphuric acid combine precisely in the proportion of 1 atom to 1 atom. It is a necessary concomitant of this law, |