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liquids, but so large a space in gases that the volume of the atoms is utterly insignificant in comparison with that of the calorific envelopes. This greater and more uniform separation of the atoms by the calorific envelopes is supposed to account for the mobility of fluids. In different elastic Anids the calorific envelopes have different volumes: if the volume of the envelope surrounding an atom of sulphur = 1, the corresponding volumes in the other gases will be 3, 6, 9, 12, 18 or 24 (p. 55–67).

Of the correctness of the atomic theory, the following proof is adduced by Wollaston (Ann. Phil. 20, 251; Gilb. 72, 37). If matter were infinitely divisible, atmospheric air would by virtue of its elasticity expand into infinite space. The earth's atmosphere could not therefore have a definite limit, but must extend itself to the other heavenly bodies and form atmospheres around them, the density of which would be proportional to the mass and attractive power of these bodies. That no atmosphere is observed round the moon might perhaps be explained by the consideration that the lunar atmosphere, if it existed, must, on account of the small mass of the moon, be very rare and therefore imperceptible. But it may be astronomically demonstrated that the sun and Jupiter, whose masses are much larger than that of the earth, are likewise without atmospheres. Hence it follows that the air is not infinitely divisible, but that its atoms existing in the higher regions of the atmosphere do not separate from each other beyond that point at which their mutual repulsion is exactly balanced by their attraction towards the earth. Against this it may perhaps be alleged that even supposing the air to be infinitely divisible, its elasticity must at length be so much diminished by decrease of density that the earth's attraction will set bounds to the greater expan. sion which a further removal from the earth would involve. Moreover, if we admit, with Poisson and Dumas, that the uttermost parts of the air are, on account of the extreme cold there existing, in the solid or liquid state and surround the atmosphere in the form of svow-flakes of nitrogen and oxygen—the preceding demonstration will appear even less satisfactory.

6. Chemical Combination. A chemical compound is produced, when one or more atoms of one substance arrange themselves in the most symmetrical manner possible by the side of one or more atoms of another substance, or of several other substances, and thus form a compound atom.-—For the manner in which atoms arrange themselves one with another, vid. Gaudin (Bibl. univ. 52, 131).–Atoms are always more inclined to unite in simple than in complex numbers, and the more intimate compounds of the inorganic kingdom generally exhibit simple numerical proportions; while in organic compounds formed under the influence of the vital force, very complicated proportions are met with. Compound atoms again unite with compound atoms of a different kind to form compounds of the second order; and the compound atoms of the second order thus formed, by combining with others of the same order, give rise to compound atoms and combinations of the third order, and so on. The mode of conceiving the formation of the less intimate compounds of variable constitution, e. g. solutions of acids, alkalis or salts in arbitrary quantities of water--whether in such cases these bodies first form compound atoms of definite constitution by combining with a small quantity of water, and these are afterwards surrounded by the remaining atoms of the liquid, or whether the mixture takes place in some other way,—must for the present remain undecided,

A chemical combination therefore is a mixture continued as it were to the extreme of intimacy; in a mixture properly so called, whole masses of atoms of the one body are laid side by side with those of the other and these heterogeneous masses can be distinguished by the senses. But in chemical combination the individual heterogeneous atoms are laid side by side; and since atoms—even compound ones—are too small to be individually discernible, the eye perceives only the masses formed by the heaping together of these atoms by virtue of cohesion, and hence the chemical compound appears homogeneous. These masses may indeed be separated into smaller and smaller ones by mechanical force, but their compound atoms are not thereby resolved into simple atoms; only the cohesion is overcome which holds together the compound atoms, not the affinity by which the simple atoms are united into compound ones.

With regard to the innate force by which atoms are disposed to combine, three hypotheses have been laid down. By some, it is regarded as the same universal force of attraction which under different circumstances exhibits itself as gravitation, cohesion, and adhesion; by others, as an attractive force of a peculiar nature; by others again as electricity.

First Hypothesis. Chemical combinations are produced by universal attraction.

Although Newton was the first who regarded chemical combination as the result of an attractive force, he nevertheless supposed that this force was different from universal attraction, and that it diminished according to the inverse cube of the distance. Buffon was the first to consider both these forces as identical. Since tbe force of universal attraction depends wholly on the mass of the attracting bodies and not at all upon their quality, while in chemical combination the latter is of the utmost importance, Buffon endeavoured to explain this difference by supposing that the centres of gravity of the atoms of beterogeneous substances might, in consequence of their difference of form, approach one another within different distances—and therefore, since the force of gravitation varies inversely as the square of the distance, the attraction between such bodies would vary in amount with the shape of their atoms.Bergman also attributed these differences between the action of gravitation and that of affinity to the different forms of the atoms and likewise to their relative position. - Guyton-Morveau perceived that to explain the great difference in the strength of affinity depending on the nature of the bodies concerned, on the hypothesis of a difference of form in their atoms, was mathematically impossible: but he was nevertheless inclined-since, according to his view, strength of adhesion and strength of affinity follow the same laws—to regard affinity as a particular manifestation of the gravitation of the atoms, and to hope that the peculiar characteristics of affinity would be explained by the discovery of new facts.

Berthollet's Theory. Universal attraction is probably the cause of chemical combination. Its action in this respect exhibits peculiar characters, because it is exerted, not on masses, but on molecules placed at extremely small distances from each other, and differing in form, cohesion and elasticity. All bodies have affinity for all others: but the affinity is not always manifested, because other forces, such as gravitation, cohesion and elasticity overcome it (p. 35).

Two bodies are, by virtue of their affinity, essentially capable of uniting in all proportions; the exceptions to this law are to be attributed to the cohesion and elasticity, partly of the simple substances themselves, partly of the compound. Thus, water dissolves only a certain quantity of salt, because the cohesion of the salt ultimately balances the affinity: similarly, the elasticity of a gas prevents its absorption by water beyond a certain limit, and the elasticity of oxygen gas causes metals to combine with only a definite quantity of oxygen. Moreover, if a combination in certain definite proportions, e. g. that of 76.6 baryta and 40 sulphuric acid possesses very great cohesion, it separates from the state of solution in water, becomes thereby removed from the sphere of chemical action, and consequently takes up no more of the excess of baryta or sulphuric acid which may perhaps exist in the liquid. For a similar reason, hydrogen and oxygen combine only in the proportion which forms the most coherent compound, viz. water; (the more coherent peroxide of hydrogen was not known at that time). This state of greatest cohesion corresponds, in most combinations of acids and bases, with the proportion which produces the most complete neutralization : but in compounds of the more coherent substances oxalic acid and tartaric acid with ammonia, potash, and soda, it is found in the acid salt.

The smaller the quantity which any substance requires of another to produce neutralization, the greater is their natural affinity (p. 142). Since, for example, according to the later more exact determinations, 47-2 parts of potash require 40 of sulphuric and 54 of nitric acid to neutralize them, the affinities of sulphuric and nitric acid for potash are to one another as 54 : 40. But in the chemical actions of bodies, not only their force of affinity, but also their quantity must be taken into account. If we assume, according to what precedes, that the affinity of a molecule of potash for a molecule of sulphuric acid amounts to 54, and for a molecule of nitric acid to 40, and suppose that 1 molecule of sulphuric acid and 3 molecules of nitric acid act simultaneously on 1 molecule of potash,—the force with which the sulphuric acid tends to lay hold of the potash will be 1.54, and that exerted by the nitric acid 3.40 = 120. This product of the force of affinity into the quantity of the acting substance is called by Berthollet the Chemical Mass. Hence the chemical force of a body increases in direct proportion to its quantity; and a substance possessing but small affinity may, when its quantity is in excess, exert a stronger attraction on a third body than other substances possessing intrinsically greater affinity but present in smaller quantity.

When a body A comes in contact with two bodies B and C, both of which tend to combine with A, it does not combine exclusively with that one for which it has the greater affinity, not even when the quantity of the latter is sufficient for the complete saturation of A; neither does it combine exclusively with the one which acts with the greater chemical mass, but divides itself between the two in the proportion of their chemical masses. If, according to the preceding example, 1 molecule of sulphuric acid and 3 of nitric acid act on 1 of potash, the chemical mass of the sulphuric acid being 1.54 and that of the nitric acid 3.40 = 120, 14 of the quantity of potash present combines with the sulphuric acid, and i with the nitric.

This law—that a body divides itself between two others which are endeavouring to lay hold of it, in the proportion of their chemical masses -is subject to exceptions, only when in such conflicts of affinity, a change in the state of aggregation of one of the acting bodies or one of the compounds, is produced by cohesion or elasticity, and these bodies are thus removed from the sphere of chemical action. In such cases A may combine exclusively with B or C. Hence ar four following cases.

1. The cohesion of B effects its complete separation; e.g. When ammonia is added to an aqueous solution of sulphate of alumina, the sulphuric acid at first divides itself between the two bases in the ratio of their chemical masses; but since the alumina is thus deprived of a portion of its sulphuric acid, and the remainder is not sufficient to hold all the alumina in solution, a portion of it is precipitated and thus removed from the sphere of chemical action: now since by this precipitation, the quantity of alumina contained in the solution, and therefore also its chemical mass, is diminished, the ammonia is enabled to rob it of another portion of sulphuric acid, thereby precipitating more alumina, diminishing the chemical mass of that which remains dissolved, again removing sulphuric acid, and so on,—till at length it appropriates all the acid and throws down the whole of the alumina. These successive decompositions follow each other so quickly, that the whole action seems to take place in a moment.

2. The elasticity of B effects its complete separation ; e.g. When hydrochloric acid is added to a solution of carbonate of potash in water, the potash at first divides itself between the two acids: the compound thus formed of part of the potash with the whole of the carbonic acid allows however a part of the carbonic acid, now less intimately combined, to escape as gas and thus to remove itself from the sphere of action; the chemical mass of the carbonic acid in the solution being thus diminished, the hydrochloric acid takes from it a fresh portion of potash, and sets free another portion of carbonic acid-and thus the action is repeated, as in the former case, till the whole of the potash has combined with the hydrochloric acid, and the whole of the carbonic acid has escaped.

3. The cohesion of AC effects the complete separation of B; e. g. If baryta dissolved in water be brought in contact with a mixture of sulphuric and nitric acids, in such proportion that for every molecule of baryta present there shall be 1 molecule of sulphuric and 3 of nitric acid, the baryta will at the commencement be divided between the two acids in the same proportion as the potash in the example above given. But potash forms with both the acids soluble salts, which therefore remain mixed; whereas the compound of baryta with a certain quantity of sulphuric acid is insolable, falls down, and is removed from the sphere of action. The solution now contains, besides the combination of baryta with nitric acid, the excess of sulphuric acid which the precipitated sulphate of baryta was unable to take up. This free sulphuric acid takes from the nitric acid, in proportion to its chemical mass, a new quantity of baryta, which however is precipitated in combination with the proportional quantity of sulphuric acid; this sets free another portion of sulphuric acid, which again takes baryta from the nitric acid; and this repeated abstraction and precipitation goes on till all the baryta is thrown down in the form of sulphate and all the nitric acid is set free. In accordance with this explanation, Berthollet supposes that on bringing together two salts, whose acids as well as bases are different, four salts are always produced: thus nitrate of potash and sulphate of soda in solution produce a mixture which still contains a portion of these salts in the undecomposed state, together with sulphate of potash and nitrate of soda. In general therefore four salts are obtained; but if one of the two new salts is insoluble and separates itself from the sphere of action, the undecomposed salts yet remaining in solution produce, in consequence of the equal division of their elements, a new quantity of the insoluble salt; but as this always falls down, the decomposition goes on till the two original

salts are completely decomposed ;--.g., nitrate of baryta and sulphate of soda.

4. The elasticity of AC effects the complete separation of B; e.g. When peroxide of iron is heated to redness with charcoal, the oxygen ought to divide itself between the iron and the carbon in proportion to their chemical masses. But since the oxygen which combines with the carbon forms carbonic oxide, which escapes as gas and so becomes removed from the sphere of action, the remaining carbon continues to withdraw oxygen from the iron, till the latter is completely reduced to the metallic state.

Review of Berthollet's Theory.—1. This theory does not establish the identity between affinity and universal attraction. Berthollet himsel supposes that different bodies have very different degrees of affinity for one another, without specifying to what extent the individual qualities of the molecules may exert a peculiar influence on their mutual gravitation and thus modify the laws of universal attraction.

2. Unacquainted with our present system of stoïchiometry, Berthollet supposed that two bodies can combine in any proportions whatever, and endeavoured to explain the fact that combination generally takes place in a few definite proportions only, by assuming that precisely when these proportions hold good, the compound possesses the greatest density, cohesion, or elasticity. But why does chlorine gas combine with hydrogen gas in one proportion only, and then without any condensation or expansion produce hydrochloric acid gas?

3. It is true that the quantity of a substance exerts some influence on its manifestations of affinity (p. 125); but unless adhesion also comes into play, this influence is not exerted by any quantity beyond that which is still capable of entering into combination. For example, since one atom of oxygen cannot combine with more than one atom of carbon, 100 atoms of carbon will have no more effect on the combination of any substance with one atom of oxygen than a single atom of carbon would; if this one atom cannot abstract the oxygen, neither will 100 atoms do it.

4. Berthollet's theory—that a body A divides itself between the bodies B and C in the proportion of their chemical masses—has an appearance of truth in those cases only in which the substances which act upon each other are contained in a liquid in which both they and their possible compounds are soluble; because in such cases it cannot for the most part be directly shown what compounds are contained in the liquid, whether AC and B according to the ordinary view, or A B and AC according to Berthollet's. But in some cases even of this kind, the incorrectness of Berthollet's theory may be distinctly shown. Boracio acid colours litmus wine-red, sulphuric acid turns it bright red. Now if sulphuric acid be gradually added to a warm solution of borate of soda in water which has been coloured blue with litmus, the liquid at first remains blue, because a combination of soda with excess of boracic acid is produced; on the addition of more sulphuric acid, boracic acid is set free, and colours the liquid wine-red; and not till all the soda has entered into combination with the sulphuric acid does a further addition of that acid give the liquid a bright red colour; but if sulphuric acid were present at the commencement of the action, either in the free state or combined with sulphate of soda in the form of an acid salt, the bright red colour would appear at once. (Gay-Lussac, Ann. Chim. Phys. 49, 323; also Pogg. 25, 619.) From the same cause, a solution of sulphate of potash or soda to which boracic acid has been added colours litmus only wine-red; but the

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