CHAPTER VII

MOLECULES AND ATOMS. THE LAWS OF GAY-LUSSAC AND AVOGADRO-GERHARDT

Hydrogen combines with oxygen in the proportion of two volumes to one. The composition by volume of nitrous oxide is exactly similar—it is composed of two volumes of nitrogen and one volume of oxygen. By decomposing ammonia by the action of an electric spark it is easy to prove that it contains one volume of nitrogen to three volumes of hydrogen. So, similarly, it is found, whenever a compound is decomposed and the volumes of the gases proceeding from it are measured, that the volumes of the gases or vapours entering into combination are in a very simple proportion to one another. With water, nitrous oxide, &c., this may be proved by direct observation; but in the majority of cases, and especially with substances which, although volatile—that is, capable of passing into a gaseous (or vaporous) state—are liquid at the ordinary temperature, such a direct method of observation presents many difficulties. But, then, if the densities of the vapours and gases be known, the same simplicity in their ratio is shown by calculation. The volume of a substance is proportional to its weight, and inversely proportional to its density, and therefore by dividing the amount by weight of each substance entering into the composition of a compound by its density in the gaseous or vaporous state we shall obtain factors which will be in the same proportion as the volumes of the substances entering into the composition of the compound.[1] So, for example, water contains eight parts by weight of oxygen to one part by weight of hydrogen, and their densities are 16 and 1, consequently their volumes (or the above-mentioned factors) are 1 and ½, and therefore it is seen without direct experiment that water contains two volumes of hydrogen for every one volume of oxygen. So also, knowing that nitric oxide contains fourteen parts of nitrogen and sixteen parts of oxygen, and knowing that the specific gravities of these last two gases are fourteen and sixteen, we find that the volumes in which nitrogen and oxygen combine for the formation of nitric oxide are in the proportion of 1 : 1. We will cite another example. In the last chapter we saw that the density of NO₂ only becomes constant and equal to twenty-three (referred to hydrogen) above 135°, and as a matterof fact a method of direct observation of the volumetric composition of this substance would be very difficult at so high a temperature. But it may be easily calculated. NO₂, as is seen from its formula and analysis, contains thirty-two parts by weight of oxygen to fourteen parts by weight of nitrogen, forming forty-six parts by weight of NO₂, and knowing the densities of these gases we find that one volume of nitrogen with two volumes of oxygen gives two volumes of nitrogen peroxide. Therefore, knowing the amounts by weight of the substances participating in a reaction or forming a given substance, and knowing the density of the gas or vapour,[2] the volumetric relations of the substances acting in a reaction or entering into the composition of a compound, may be also determined.

Such an investigation (either direct, or by calculation from the densities and composition) of every chemical reaction, resulting in the formation of definite chemical compounds, shows that the volumes of the reacting substances in a gaseous or vaporous state are either equal or are in simple multiple proportion.[3] This forms the first law of those discovered by Gay-Lussac. It may be formulated as follows: The amounts of substances entering into chemical reaction occupy under similar physical conditions, in a gaseous or vaporous state, equal or simple multiple volumes. This law refers not only to elements, but also to compounds entering into mutual chemical combination; thus, for example, one volume of ammonia gas combines with one volume of hydrogen chloride. For in the formation of sal-ammoniac, NH₄Cl, there enter into reaction 17 parts by weight of ammonia, NH₃, which is 8·5 times denser than hydrogen, and 36·5 parts by weight of hydrogen chloride, whose vapour density is 18·25 times that of hydrogen, as has been proved by direct experiment. By dividing the weights by the respective densities we find that the volume of ammonia, NH₃, is equal to two, and so also the volume of hydrogen chloride. Hence the volumes of the compounds which here combine together are equal to each other. Taking into consideration that the law of Gay-Lussac holds good, not only for elements, but also for compounds, it should be expressed as follows: Substances interact with one another in commensurable volumes of their vapours.[4]

The law of combining volumes and the law of multiple proportion were discovered independently of each other—the one in France by Gay-Lussac, the other in England by Dalton—almost simultaneously. In the language of the atomic hypothesis it may be said that atomic quantities of elements occupy equal or multiple volumes.

The first law of Gay-Lussac expresses the relation between the volumes of the component parts of a compound. Let us now consider the relation existing between the volumes of the component parts and of the compounds which proceed from them. This may sometimes be determined by direct observation. Thus the volume occupied by water, formed by two volumes of hydrogen and one volume of oxygen, may be determined by the aid of the apparatus shown in fig. 56. The long glass tube is closed at the top and open at the bottom, which is immersed in a cylinder containing mercury. The closed end is furnished with wires like a eudiometer. The tube is filled with mercury, and then a certain volume of detonating gas is introduced. This gas is obtained from the decomposition of water, and therefore in every three volumes contains two volumes of hydrogen and one volume of oxygen. The tube is surrounded by a second and wider glass tube, and the vapour of a substance boiling above 100°—that is, whose boiling point is higher than that of water—is passed through the annular space between them. Amyl alcohol, whose boiling point is 132°, may be taken for this purpose. The amyl alcohol is boiled in the vessel to the right hand and its vapour passed between the walls of the two tubes. In the case of amyl alcohol the outer glass tube should be connected with a condenser to prevent the escape into the air of the unpleasant-smelling vapour. The detonating gas is thus heated up to a temperature of 132°. When its volume becomes constant it is measured, the height of the column of mercury in the tube above the level of the mercury in the cylinder being noted. Let this volume equal v; it will therefore contain ⅓ v of oxygen and ⅔ v of hydrogen. The current of vapour is then stopped, and the gas exploded; water is formed, which condenses into a liquid. The volume occupied by the vapour of the water formed has now to be determined. For this purpose the vapour of the amyl alcohol is again passed between the tubes, and thus the whole of the water formed is converted into vapour at the same temperature as that at which the detonating gas was measured; and the cylinder of mercury being raised until the column of mercury in the tube stands at the same height above the surface of the mercury in the cylinder as it did before the explosion, it is found that the volume of the water formed is equal to ⅔ v—that is, it is equal to the volume of the hydrogen contained in it. Consequently the volumetric composition of water is expressed in the following terms: Two volumes of hydrogen combine with one volume of oxygen to form two volumes of aqueous vapour. For substances which are gaseous at the ordinary temperature, this direct method of observation is sometimes very easily conducted; for instance, with ammonia, nitric and nitrous oxides. Thus to determine the composition by volume of nitrous oxide, the above-described apparatus may be employed. Nitrous oxide is introduced into the tube, and after measuring its volume electric sparks are passed through the gas; it is then found that two volumes of nitrous oxide have given three volumes of gases—namely, two volumes of nitrogen and one volume of oxygen. Consequently the composition of nitrous oxide is similar to that of water; two volumes of nitrogen and one volume of oxygen give two volumes of nitrous oxide. By decomposing ammonia it is found to be composed in such a manner that two volumes give one volume of nitrogen and three volumes of hydrogen; also two volumes of nitric oxide are formed by the union of one volume of oxygen with one volume of nitrogen. The same relations may be proved by calculation from the vapour densities, as was described above.

Comparisons of various results made by the aid of direct observations or calculation, an example of which has just been cited, led Gay-Lussac to the conclusion that the volume of a compound in a gaseous or vaporous state is always in simple multiple proportion to the volume of each of the component parts of which it is formed (and consequently to the sum of the volumes of the elements of which it is formed). This is the second law of Gay-Lussac; it extends the simplicity of the volumetric relations to compounds, and is of the same nature as that presented by the elements entering into mutual combination. Hence not only the substances forming a given compound, but also the substances formed, exhibit a simple relation of volume when measured as vapour or gas.[5]

When a compound is formed from two or more components, there may or may not be a contraction; the volume of the reacting substances is in this case either equal to or greater than the volume of the resultant compound. The reverse is naturally observed in the case of decompositions, when from one substance there are produced several of simpler nature. Therefore in the future we shall term combination a reaction in which a contraction is observed—that is, a diminution in the volume of the component bodies in a state of vapour or gas; and we shall term decomposition a reaction in which an expansion is produced; while those reactions in which the volumes in a gaseous or vaporous state remain constant (the volumes being naturally compared at the same temperature and pressure) we shall term reactions of substitution or of double decomposition. Thus the transition of oxygen into ozone is a reaction of combination, the formation of nitrous oxide from oxygen and nitrogen will also be a combination, the formation of nitric oxide from the same will be a reaction of substitution, the action of oxygen on nitric oxide a combination, and so on.

The degree of contraction produced in the formation of chemical compounds not unfrequently leads to the possibility of distinguishing the degree of change which takes place in the chemical character of the components when combined. In those cases in which a contraction occurs, the properties of the resultant compound are very different from the properties of the substances of which it is composed. Thus ammonia bears no resemblance in its physical or chemical properties to the elements from which it is derived; a contraction takes place in a state of vapour, indicating a proximation of the elements—the distance between the atoms is diminished, and from gaseous substances there is formed a liquid substance, or at any rate one which is easily liquefied. For this reason nitrous oxide formed by the condensation of two permanent gases is a substance which is somewhat easily converted into a liquid; again, nitric acid, which is formed from elements which are permanent gases, is a liquid, whilst, on the contrary, nitric oxide, which is formed without contraction and is decomposed without expansion, remains a gas which is as difficult to liquefy as nitrogen and oxygen. In order to obtain a still more complete idea of the dependence of the properties of a compound on the properties of the component substances, it is further necessary to know the quantity of heat which is developed in the formation of the compound. If this quantity be large—as, for example, in the formation of water—then the amount of energy in the resultant compound will be considerably less than the energy of the elements entering into its composition; whilst, on the contrary, if the amount of heat evolved in the formation of a compound be small, or if there even be an absorption of heat, as in the formation of nitrous oxide, then the energy of the elements is not destroyed, or is only altered to a slight extent; hence, notwithstanding the contraction (compression) involved in its formation, nitrous oxide supports combustion.

The preceding laws were deduced from purely experimental and empirical data and as such evoke further consequences, as the law of multiple proportions gave rise to the atomic theory and the law of equivalents (Chapter IV.) In view of the atomic conception of the constitution of substances, the question naturally arises as to what, then, are the relative volumes proper to those physically indivisible molecules which chemically react on each other and consist of the atoms of elements. The simplest possible hypothesis in this respect would be that the volumes of the molecules of substances are equal; or, what is the same thing, to suppose that equal volumes of vapours and gases contain an equal number of molecules. This proposition was first enunciated by the Italian savant Avogadro in 1810. It was also admitted by the French physico-mathematician Ampère (1815) for the sake of simplifying all kinds of physico-mathematical conceptions respecting gases. But Avogadro and Ampère's propositions were not generally received in science until Gerhardt in the forties had applied them to the generalisation of chemical reactions, and had demonstrated, by aid of a series of phenomena, that the reactions of substances actually take place with the greatest simplicity, and more especially that such reactions take place between those quantities of substances which occupy equal volumes, and until he had stated the hypothesis in an exact manner and deduced the consequences that necessarily follow from it. Following Gerhardt, Clausius, in the fifties, placed this hypothesis of the equality of the number of molecules in equal volumes of gases and vapours on the basis of the kinetic theory of gases. At the present day the hypothesis of Avogadro and Gerhardt lies at the basis of contemporary physical, mechanical, and chemical conceptions; the consequences arising from it have often been subject to doubt, but in the end have been verified by the most diverse methods; and now, when all efforts to refute those consequences have proved fruitless, the hypothesis must be considered as verified,[6] and the law of Avogadro-Gerhardt must be spoken of as fundamental, and as of great importance for the comprehension of the phenomena of nature. The law may now be formulated from two points of view. In the first place, from a physical aspect: equal volumes of gases (or vapours) at equal temperatures and pressures contain the same number of molecules—or of particles of matter which are neither mechanically nor physically divisible—previous to chemical change. In the second place, from a chemical aspect, the same law may be expressed thus: the quantities of substances entering into chemical reactions occupy, in a state of vapour, equal volumes. For our purpose the chemical aspect is the most important, and therefore, before developing the law and its consequences, we will consider the chemical phenomena from which the law is deduced or which it serves to explain.

When two isolated substances interact with each other directly and easily—as, for instance, an alkali and an acid—then it is found that the reaction is accomplished between quantities which in a gaseous state occupy equal volumes. Thus ammonia, NH₃, reacts directly with hydrochloric acid, HCl, forming sal-ammoniac, NH₄Cl, and in this case the 17 parts by weight of ammonia occupy the same volume as the 36·5 parts by weight of hydrochloric acid.[7] Ethylene, C₂H₄, combines with chlorine, Cl₂, in only one proportion, forming ethylene dichloride, C₂H₄Cl₂, and this combination proceeds directly and with great facility, the reacting quantities occupying equal volumes. Chlorine reacts with hydrogen in only one proportion, forming hydrochloric acid, HCl, and in this case equal volumes interact with each other. If an equality of volumes is observed in cases of combination, it should be even more frequently encountered in cases of decomposition, taking place in substances which split up into two others. Indeed, acetic acid breaks up into marsh gas, CH₄, and carbonic anhydride, CO₂, and in the proportions in which they are formed from acetic acid they occupy equal volumes. Also from phthalic acid, C₈H₆O₄, there may be obtained benzoic acid, C₇H₆O₂, and carbonic anhydride, CO₂, and as all the elements of phthalic acid enter into the composition of these substances, it follows that, although they cannot re-form it by their direct action on each other (the reaction is not reversible), still they form the direct products of its decomposition, and they occupy equal volumes. But benzoic acid, C₇H₆O₂, is itself composed of benzene, C₆H₆, and carbonic anhydride, CO₂, which also occupy equal volumes.[8] There is an immense number of similar examples among those organic substances to whose study Gerhardt consecrated his whole life and work, and he did not allow such facts as these to escape his attention. Still more frequently in the phenomena of substitution, when two substances react on one another, and two are produced without a change of volume, it is found that the two substances acting on each other occupy equal volumes as well as each of the two resultant substances. Thus, in general, reactions of substitution take place between volatile acids, HX, and volatile alcohols, R(OH), with the formation of ethereal salts, RX, and water, H(OH), and the volume of the vapour of the reacting quantities, HX, R(OH), and RX, is the same as that of water H(OH), whose weight, corresponding with the formula, 18, occupies 2 volumes, if 1 part by weight of hydrogen occupy 1 volume and the density of aqueous vapour referred to hydrogen is 9. Such general examples, of which there are many,[9] show that the reaction of equal volumes forms a chemical phenomenon of frequent occurrence, indicating the necessity for acknowledging the law of Avogadro-Gerhardt.

But the question arises, What is the relation of volumes if the reaction of two substances takes place in more than one proportion, according to the law of multiple proportions? A definite answer can only be given in cases which have been very thoroughly studied. Thus chlorine, in acting on marsh gas, CH₄, forms four compounds, CH₃Cl, CH₂Cl₂, CHCl₃, and CCl₄, and it may be established by direct experiment that the substance CH₃Cl (methylic chloride) precedes the remainder, and that the latter proceed from it by the further action of chlorine. And this substance, CH₃Cl, is formed by the reaction of equal volumes of marsh gas, CH₄, and chlorine, Cl₂, according to the equation CH₄ + Cl₂ = CH₃Cl + HCl. A great number of similar cases are met with amongst organic—that is, carbon—compounds. Gerhardt was led to the discovery of his law by investigating many such reactions, and by observing that in them the reaction of equal volumes precedes all others.

But if nitrogen or hydrogen give several compounds with oxygen, the question proposed above cannot be answered with complete clearness, because the successive formations of the different combinations cannot be so strictly defined. It may be supposed, but neither definitely affirmed nor experimentally confirmed, that nitrogen and oxygen first give nitric oxide, NO, and only subsequently the brown vapours N₂O₃ and NO₂. Such a sequence in the combination of nitrogen with oxygen can only be supposed on the basis of the fact that NO forms N₂O₃ and NO₂ directly with oxygen. If it be admitted that NO (and not N₂O or NO₂) be first formed, then this instance would also confirm the law of Avogadro-Gerhardt, because nitric oxide contains equal volumes of nitrogen and oxygen. So, also, it may be admitted that, in the combination of hydrogen with oxygen, hydrogen peroxide is first formed (equal volumes of hydrogen and oxygen), which is decomposed by the heat evolved into water and oxygen. This explains the presence of traces of hydrogen peroxide (Chapter IV.) in almost all cases of the combustion or oxidation of hydrogenous substances; for it cannot be supposed that water is first formed and then the peroxide of hydrogen, because up to now such a reaction has not been observed, whilst the formation of H₂O from H₂O₂ is very easily reproduced.[10]

Thus a whole series of phenomena show that the chemical reaction of substances actually takes place, as a rule, between equal volumes, but this does not preclude the possibility of the frequent reaction of unequal volumes, although, in this case, it is often possible to discover a preceding reaction between equal volumes.[11]

The law of Avogadro-Gerhardt may also be easily expressed in an algebraical form. If the weight of a molecule, or of that quantity of a substance which enters into chemical reaction and occupies in a state of vapour, according to the law, a volume equal to that occupied by the molecules of other bodies, be indicated by the letters M₁, M₂ ... or, in general, M, and if the letters D₁, D₂, ... or, in general, D, stand for the density or weight of a given volume of the gases or vapours of the corresponding substances under certain definite conditions of temperature and pressure, then the law requires that

M₁ / D₁ = M₂ / D₂ ⋯ = M / D = C

where C is a certain constant. This expression shows directly that the volumes corresponding with the weights M₁, M₂ ... M, are equal to a certain constant, because the volume is proportional to the weight and inversely proportional to the density. The magnitude of C is naturally conditioned by and dependent on the units taken for the expression of the weights of the molecules and the densities. The weight of a molecule (equal to the sum of the atomic weights of the elements forming it) is usually expressed by taking the weight of an atom of hydrogen as unity, and hydrogen is now also chosen as the unit for the expression of the densities of gases and vapours; it is therefore only necessary to find the magnitude of the constant for any one compound, as it will be the same for all others. Let us take water. Its reacting mass is expressed (conditionally and relatively) by the formula or molecule H₂O, for which M = 18, if H = 1, as we already know from the composition of water. Its vapour density, or D, compared to hydrogen = 9, and consequently for water C = 2, and therefore and in general for the molecules of all substances M / D = 2.

Consequently the weight of a molecule is equal to twice its vapour density expressed in relation to hydrogen, and conversely the density of a gas is equal to half the molecular weight referred to hydrogen.

The truth of this may be seen from a very large number of observed vapour densities by comparing them with the results obtained by calculation. As an illustration, we may point out that for ammonia, NH₃, the weight of the molecule or quantity of the reacting substance, as well as the composition and weight corresponding with the formula, is expressed by the figures 14 + 3 = 17. Consequently M = 17. Hence, according to the law, D = 8·5. And this result is also obtained by experiment. The density, according to both formula and experiment, of nitrous oxide, N₂O, is 22, of nitric acid 15, and of nitric peroxide 23. In the case of nitrous anhydride, N₂O₃, as a substance which dissociates into NO + NO₂, the density should vary between 38 (so long as the N₂O₃ remains unchanged) and 19 (when NO + NO₂ is obtained). There are no figures of constant density for H₂O₂, NHO₃, N₂O₄, and many similar compounds which are either wholly or partially decomposed in passing into vapour. Salts and similar substances either have no vapour density because they do not pass into vapour (for instance, potassium nitrate, KNO₃) without decomposition, or, if they pass into vapour without decomposing, their vapour density is observed with difficulty only at very high temperatures. The practical determination of the vapour density at these high temperatures (for example, for sodium chloride, ferrous chloride, stannous chloride, &c.) requires special methods which have been worked out by Sainte-Claire Deville, Crafts, Nilson and Pettersson, Meyer, Scott, and others. Having overcome the difficulties of experiment, it is found that the law of Avogadro-Gerhardt holds good for such salts as potassium iodide, beryllium chloride, aluminium chloride, ferrous chloride, &c.—that is, the density obtained by experiment proves to be equal to half the molecular weight—naturally within the limits of experimental error or of possible deviation from the law.

Gerhardt deduced his law from a great number of examples of volatile carbon compounds. We shall become acquainted with certain of them in the following chapters; their entire study, from the complexity of the subject, and from long-established custom, forms the subject of a special branch of chemistry termed ‘organic’ chemistry. With all these substances the observed and calculated densities are very similar.

When the consequences of a law are verified by a great number of observations, it should be considered as confirmed by experiment. But this does not exclude the possibility of apparent deviations. They may evidently be of two kinds: the fraction M / D may be found to be either greater or less than 2—that is, the calculated density may be either greater or less than the observed density. When the difference between the results of experiment and calculation falls within the possible errors of experiment (for example, equal to hundredths of the density), or within a possible error owing to the laws of gases having an only approximate application (as is seen from the deviations, for instance, from the law of Boyle and Mariotte), then the fraction M / D proves but slightly different from 2 (between 1·9 and 2·2), and such cases as these may be classed among those which ought to be expected from the nature of the subject. It is a different matter if the quotient of M / D be several times, and in general a multiple, greater or less than 2. The application of the law must then be explained or it must be laid aside, because the laws of nature admit of no exceptions. We will therefore take two such cases, and first one in which the quotient M / D is greater than 2, or the density obtained by experiment is less than is in accordance with the law.

It must be admitted, as a consequence of the law of Avogadro-Gerhardt, that there is a decomposition in those cases where the volume of the vapour corresponding with the weight of the amount of a substance entering into reaction is greater than the volume of two parts by weight of hydrogen. Suppose the density of the vapour of water to be determined at a temperature above that at which it is decomposed, then, if not all, at any rate a large proportion of the water will be decomposed into hydrogen and oxygen. The density of such a mixture of gases, or of detonating gas, will be less than that of aqueous vapour; it will be equal to 6 (compared with hydrogen), because 1 volume of oxygen weighs 16, and 2 volumes of hydrogen 2; and, consequently, 3 volumes of detonating gas weigh 18 and 1 volume 6, while the density of aqueous vapour = 9. Hence, if the density of aqueous vapour be determined after its decomposition, the quotient M / D would be found to be 3 and not 2. This phenomenon might be considered as a deviation from Gerhardt's law, but this would not be correct, because it may be shown by means of diffusion through porous substances, as described in Chapter II., that water is decomposed at such high temperatures. In the case of water itself there can naturally be no doubt, because its vapour density agrees with the law at all temperatures at which it has been determined.[12] But there are many substances which decompose with great ease directly they are volatilised, and therefore only exist as solids or liquids, and not in a state of vapour. There are, for example, many salts of this kind, besides all definite solutions having a constant boiling point, all the compounds of ammonia for example, all ammonium salts—&c. Their vapour densities, determined by Bineau, Deville, and others, show that they do not agree with Gerhardt's law. Thus the vapour density of sal-ammoniac, NH₄Cl, is nearly 14 (compared with hydrogen), whilst its molecular weight is not less than 53·5, whence the vapour density should be nearly 27, according to the law. The molecule of sal-ammoniac cannot be less than NH₄Cl, because it is formed from the molecules NH₃ and HCl, and contains single atoms of nitrogen and chlorine, and therefore cannot be divided; it further never enters into reactions with the molecules of other substances (for instance, potassium hydroxide, or nitric acid) in quantities of less than 53·5 parts by weight, &c. The calculated density (about 27) is here double the observed density (about 13·4); hence M / D = 4 and not 2. For this reason the vapour density of sal-ammoniac for a long time served as an argument for doubting the truth of the law. But it proved otherwise, after the matter had been fully investigated. The low density depends on the decomposition of sal-ammoniac, on volatilising, into ammonia and hydrogen chloride. The observed density is not that of sal-ammoniac, but of a mixture of NH₃ and HCl, which should be nearly 14, because the density of NH₃ = 8·5 and of HCl = 18·2, and therefore the density of their mixture (in equal volumes) should be about 13·4.[13] The actual decomposition of the vapours of sal-ammoniac was demonstrated by Pebal and Than by the same method as the decomposition of water, by passing the vapour of sal-ammoniac through a porous substance. The experiment demonstrating the decomposition during volatilisation of sal-ammoniac may be made very easily, and is a very instructive point in the history of the law of Avogadro-Gerhardt, because without its aid it would never have been imagined that sal-ammoniac decomposed in volatilising, as this decomposition bears all the signs of simple sublimation; consequently the knowledge of the decomposition itself was forestalled by the law. The whole aim and practical use of the discovery of the laws of nature consists in, and is shown by, the fact that they enable the unknown to be foretold, the unobserved to be foreseen. The arrangement of the experiment is based on the following reasoning.[14] According to the law and to experiment, the density of ammonia, NH₃, is 8½, and of hydrochloric acid, HCl, 18¼, if the density of hydrogen = 1. Consequently, in a mixture of NH₃ and HCl, the ammonia will penetrate much more rapidly through a porous mass, or a fine orifice, than the heavier hydrochloric acid, just as in a former experiment the hydrogen penetrated more rapidly than the oxygen. Therefore, if the vapour of sal-ammoniac comes into contact with a porous mass, the ammonia will pass through it in greater quantities than the hydrochloric acid, and this excess of ammonia may be detected by means of moist red litmus paper, which should be turned blue. If the vapour of sal-ammoniac were not decomposed, it would pass through the porous mass as a whole, and the colour of the litmus paper would not be altered, because sal-ammoniac is a neutral salt. Thus, by testing with litmus the substances passing through the porous mass, it may be decided whether the sal-ammoniac is decomposed or not when passing into vapour. Sal-ammoniac volatilises at so moderate a temperature that the experiment may be conducted in a glass tube heated by means of a lamp, an asbestos plug being placed near the centre of the tube.[15] The asbestos forms a porous mass, which is unaltered at a high temperature. A piece of dry sal-ammoniac is placed at one side of the asbestos plug, and is heated by a Bunsen burner. The vapours formed are driven by a current of air forced from a gasometer or bag through two tubes containing pieces of moist litmus paper, one blue and one red paper in each. If the sal-ammoniac be heated, then the ammonia appears on the opposite side of the asbestos plug, and the litmus there turns blue. And as an excess of hydrochloric acid remains on the side where the sal-ammoniac is heated, it turns the litmus at that end red. This proves that the sal-ammoniac, when converted into vapour, splits up into ammonia and hydrochloric acid, and at the same time gives an instance of the possibility of correctly conjecturing a fact on the basis of the law of Avogadro-Gerhardt.[15 bis]

So also the fact of a decomposition may be proved in the other instances where M / D proved greater than 2, and hence the apparent deviations appear in reality as an excellent proof of the general application and significance of the law of Avogadro-Gerhardt.

In those cases where the quotient M / D proves to be less than 2, or the observed density greater than that calculated, by a multiple number of times, the matter is evidently more simple, and the fact observed only indicates that the weight of the molecule is as many times greater as that taken as the quotient obtained is less than 2. So, for instance, in the case of ethylene, whose composition is expressed by CH₂, the density was found by experiment to be 14, and in the case of amylene, whose composition is also CH₂, the density proved to be 35, and consequently the quotient for ethylene = 1, and for amylene = ⅖. If the molecular weight of ethylene be taken, not as 14, as might be imagined from its composition, but as twice as great—namely, as 28—and for amylene as five times greater—that is as 70—then the molecular composition of the first will be C₂H₄, and of the second C₅H₁₀, and for both of them M / D will be equal to 2. This application of the law, which at first sight may appear perfectly arbitrary, is nevertheless strictly correct, because the amount of ethylene which reacts—for example, with sulphuric and other acids—is not equal to 14, but to 28 parts by weight. Thus with H₂SO₄, Br₂, or HI, &c., ethylene combines in a quantity C₂H₄, and amylene in a quantity C₅H₁₀, and not CH₂. On the other hand, ethylene is a gas which liquefies with difficulty (absolute boiling point = +10°), whilst amylene is a liquid boiling at 35° (absolute boiling point = +192°), and by admitting the greater density of the molecules of amylene (M = 70) its difference from the lighter molecules of ethylene (M = 28) becomes clear. Thus, the smaller quotient M / D is an indication of polymerisation, as the larger quotient is of decomposition. The difference between the densities of oxygen and ozone is a case in point.

On turning to the elements, it is found in certain cases, especially with metals—for instance, mercury, zinc, and cadmium—that that weight of the atoms which must be acknowledged in their compounds (of which mention will be afterwards made) appears to be also the molecular weight. Thus, the atomic weight of mercury must be taken as = 200, but the vapour density = 100, and the quotient = 2. Consequently the molecule of mercury contains one atom, Hg. It is the same with sodium, cadmium, and zinc. This is the simplest possible molecule, which necessarily is only possible in the case of elements, as the molecule of a compound must contain at least two atoms. However, the molecules of many of the elements prove to be complex—for instance, the weight of an atom of oxygen = 16, and its density = 16, so that its molecule must contain two atoms, O₂, which might already be concluded by comparing its density with that of ozone, whose molecule contains O₃ (Chapter IV.) So also the molecule of hydrogen equals H₂, of chlorine Cl₂, of nitrogen N₂, &c. If chlorine react with hydrogen, the volume remains unaltered after the formation of hydrochloric acid, H₂ + Cl₂ = HCl + HCl. It is a case of substitution between the one and the other, and therefore the volumes remain constant. There are elements whose molecules are much more complex—for instance, sulphur, S₆—although, by heating, the density is reduced to a third, and S₂ is formed. Judging from the vapour density of phosphorus (D = 62) the molecule contains four atoms P₄. Hence many elements when polymerised appear in molecules which are more complex than the simplest possible. In carbon, as we shall afterwards find, a very complex molecule must be admitted, as otherwise its non-volatility and other properties cannot be understood. And if compounds are decomposed by a more or less powerful heat, and if polymeric substances are depolymerised (that is, the weight of the molecule diminishes) by a rise of temperature, as N₂O₄ passes into NO₂, or ozone, O₃, into ordinary oxygen, O₂, then we might expect to find the splitting-up of the complex molecules of elements into the simplest molecule containing a single atom only—that is to say, if O₂ be obtained from O₃, then the formation of O might also be looked for. The possibility but not proof of such a proposition is indicated by the vapour of iodine. Its normal density = 127 (Dumas, Deville, and others), which corresponds with the molecule I₂. At temperatures above 800° (up to which the density remains almost constant), this density distinctly decreases, as is seen from the verified results obtained by Victor Meyer, Crafts, and Troost. At the ordinary pressure and 1,000° it is about 100, at 1,250° about 80, at 1,400° about 75, and apparently it strives to reduce itself to one-half—that is, to 63. Under a reduced pressure this splitting-up, or depolymerisation, of iodine vapour actually reaches a density[16] of 66, as Crafts demonstrated by reducing the pressure to 100 mm. and raising the temperature to 1,500°. From this it may be concluded that at high temperatures and low pressures the molecule I₂ gradually passes into the molecule I containing one atom like mercury, and that something similar occurs with other elements at a considerable rise of temperature, which tends to bring about the disunion of compounds and the decomposition of complex molecules.[17]

Besides these cases of apparent discrepancy from the law of Avogadro-Gerhardt there is yet a third, which is the last, and is very instructive. In the investigation of separate substances they have to be isolated in the purest possible form, and their chemical and physical properties, and among them the vapour density, then determined. If it be normal—that is, if D = M/2—it often serves as a proof of the purity of the substance, i.e. of its freedom from all foreign matter. If it be abnormal—that is, if D be not equal to M/2—then for those who do not believe in the law it appears as a new argument against it and nothing more; but to those who have already grasped the important significance of the law it becomes clear that there is some error in the observation, or that the density was determined under conditions in which the vapour does not follow the laws of Boyle or Gay-Lussac, or else that the substance has not been sufficiently purified, and contains other substances. The law of Avogadro-Gerhardt in that case furnishes convincing evidence of the necessity of a fresh and more exact research. And as yet the causes of error have always been found. There are not a few examples in point in the recent history of chemistry. We will cite one instance. In the case of pyrosulphuryl chloride, S₂O₅Cl₂, M = 215, and consequently D should = 107·5, instead of which Ogier and others obtained 53·8—that is, a density half as great; and further, Ogier (1882) demonstrated clearly that the substance is not dissociated by distillation into SO₃ and SO₂Cl₂, or any other two products, and thus the abnormal density of S₂O₅Cl₂ remained unexplained until D. P. Konovaloff (1885) showed that the previous investigators were working with a mixture (containing SO₃HCl), and that pyrosulphuryl chloride has a normal density of approximately 107. Had not the law of Avogadro-Gerhardt served as a guide, the impure liquid would have still passed as pure; the more so since the determination of the amount of chlorine could not aid in the discovery of the impurity. Thus, by following a true law of nature we are led to true deductions.

All cases which have been studied confirm the law of Avogadro-Gerhardt, and as by it a deduction is obtained, from the determination of the vapour density (a purely physical property), as to the weight of the molecule or quantity of a substance entering into chemical reaction, this law links together the two provinces of learning—physics and chemistry—in the most intimate manner. Besides which, the law of Avogadro-Gerhardt places the conceptions of molecules and atoms on a firm foundation, which was previously wanting. Although since the days of Dalton it had become evident that it was necessary to admit the existence of the elementary atom (the chemical individual indivisible by chemical or other forces), and of the groups of atoms (or molecules) of compounds, indivisible by mechanical and physical forces; still the relative magnitude of the molecule and atom was not defined with sufficient clearness. Thus, for instance, the atomic weight of oxygen might be taken as 8 or 16, or any multiple of these numbers, and nothing indicated a reason for the acceptation of one rather than another of these magnitudes;[18] whilst as regards the weights of the molecules of elements and compounds there was no trustworthy knowledge whatever. With the establishment of Gerhardt's law the idea of the molecule was fully defined, as well as the relative magnitude of the elementary atom.

The chemical particle or molecule must be considered as the quantity of a substance which enters into chemical reaction with other molecules, and occupies in a state of vapour the same volume as two parts by weight of hydrogen.

The molecular weight (which has been indicated by M) of a substance is determined by its composition, transformations, and vapour density.

The molecule is not divisible by the mechanical and physical changes of substances, but in chemical reaction it is either altered in its properties, or quantity, or structure, or in the nature of the motion of its parts.

An agglomeration of molecules, which are alike in all chemical respects, makes up the masses of homogeneous substances in all states.[19]

Molecules consist of atoms in a certain state of distribution and motion, just as the solar system[20] is made up of inseparable parts (the sun, planets, satellites, comets, &c.) The greater the number of atoms in a molecule, the more complex is the resultant substance. The equilibrium between the dissimilar atoms may be more or less stable, and may for this reason give more or less stable substances. Physical and mechanical transformations alter the velocity of the motion and the distances between the individual molecules, or of the atoms in the molecules, or of their sum total, but they do not alter the original equilibrium of the system; whilst chemical changes, on the other hand, alter the molecules themselves, that is, the velocity of motion, the relative distribution, and the quality and quantity of the atoms in the molecules.

Atoms are the smallest quantities or chemically indivisible masses of the elements forming the molecules of elements and compounds.

Atoms have weight, the sum of their weights forms the weight of the molecule, and the sum of the weights of the molecules forms the weight of masses, and is the cause of gravity, and of all the phenomena which depend on the mass of a substance.

The elements are characterised, not only by their independent existence, their incapacity of being converted into each other, &c., but also by the weight of their atoms.

Chemical and physical properties depend on the weight, composition, and properties of the molecules forming a substance, and on the weight and properties of the atoms forming the molecules.

This is the substance of those principles of molecular mechanics which lie at the basis of all contemporary physical and chemical constructions since the establishment of the law of Avogadro-Gerhardt. The fecundity of the principles enunciated is seen at every step in all the particular cases forming the present store of chemical data. We will here cite a few examples of the application of the law.

As the weight of an atom must be understood as the minimum quantity of an element entering into the composition of all the molecules formed by it, therefore, in order to find the weight of an atom of oxygen, let us take the molecules of those of its compounds which have already been described, together with the molecules of certain of those carbon compounds which will be described in the following chapter:

The number of substances taken might be considerably increased, but the result would be the same—that is, the molecules of the compounds of oxygen would never be found to contain less than 16 parts by weight of this element, but always n16, where n is a whole number. The molecular weights of the above compounds are found either directly from the density of their vapour or gas, or from their reactions. Thus, the vapour density of nitric acid (as a substance which easily decomposes above its boiling point) cannot be accurately determined, but the fact of its containing one part by weight of hydrogen, and all its properties and reactions, indicate the above molecular composition and no other. In this manner it is very easy to find the atomic weight of all the elements, knowing the molecular weight and composition of their compounds. It may, for instance, be easily proved that less than n12 parts of carbon never enters into the molecules of carbon compounds, and therefore C must be taken as 12, and not as 6 which was the number in use before Gerhardt. In a similar manner the atomic weights now accepted for the elements oxygen, nitrogen, carbon, chlorine, sulphur, &c., were found and indubitably established, and they are even now termed the Gerhardt atomic weights. As regards the metals, many of which do not give a single volatile compound, we shall afterwards see that there are also methods by which their atomic weights may be established, but nevertheless the law of Avogadro-Gerhardt is here also ultimately resorted to, in order to remove any doubt which may be encountered. Thus, for instance, although much that was known concerning the compounds of beryllium necessitated its atomic weight being taken as Be = 9—that is, the oxide as BeO and the chloride BeCl₂—still certain analogies gave reason for considering its atomic weight to be Be = 13·5, in which case its oxide would be expressed by the composition Be₂O₃, and the chloride by BeCl₃.[21] It was then found that the vapour density of beryllium chloride was approximately 40, when it became quite clear that its molecular weight was 80, and as this satisfies the formula BeCl₂, but does not suit the formula BeCl₃, it therefore became necessary to regard the atomic weight of Be as 9 and not as 13½.

With the establishment of a true conception of molecules and atoms, chemical formulæ became direct expressions, not only of composition,[22] but also of molecular weight or vapour density, and consequently of a series of fundamental chemical and physical data, inasmuch as a number of the properties of substances are dependent on their vapour density, or molecular weight and composition. The vapour density D = M/2. For instance, the formula of ethyl ether is C₄H₁₀O, corresponding with the molecular weight 74, and the vapour density 37, which is the fact. Therefore, the density of vapours and gases has ceased to be an empirical magnitude obtained by experiment only, and has acquired a rational meaning. It is only necessary to remember that 2 grams of hydrogen, or the molecular weight of this primary gas in grams, occupies, at 0° and 760 mm. pressure, a volume of 22·3 litres (or 22,300 cubic centimetres), in order to directly determine the weights of cubical measures of gases and vapours from their formulæ, because the molecular weights in grams of all other vapours at 0° and 760 mm. occupy the same volume, 22·3 litres. Thus, for example, in the case of carbonic anhydride, CO₂, the molecular weight M = 44, hence 44 grams of carbonic anhydride at 0° and 760 mm. occupy a volume of 22·3 litres—consequently, a litre weighs 1·97 gram. By combining the laws of gases—Gay-Lussac's, Mariotte's, and Avogadro-Gerhardt's—we obtain[23] a general formula for gases

6200s(273 + t) = Mp

where s is the weight in grams of a cubic centimetre of a vapour or gas at a temperature t and pressure p (expressed in centimetres of mercury) if the molecular weight of the gas = M. Thus, for instance, at 100° and 760 millimetres pressure (i.e. at the atmospheric pressure) the weight of a cubic centimetre of the vapour of ether (M = 74) is s = 0·0024.[24]

As the molecules of many elements (hydrogen, oxygen, nitrogen, chlorine, bromine, sulphur—at least at high temperatures) are of uniform composition, the formulæ of the compounds formed by them directly indicate the composition by volume. So, for example, the formula HNO₃ directly shows that in the decomposition of nitric acid there is obtained 1 vol. of hydrogen, 1 vol. of nitrogen, and 3 vols. of oxygen.

And since a great number of mechanical, physical, and chemical properties are directly dependent on the elementary and volumetric composition, and on the vapour density, the accepted system of atoms and molecules gives the possibility of simplifying a number of most complex relations. For instance, it may be easily demonstrated that the vis viva of the molecules of all vapours and gases is alike. For it is proved by mechanics that the vis viva of a moving mass = (½) mv², where m is the mass and v the velocity. For a molecule, m = M, or the molecular weight, and the velocity of the motion of gaseous molecules = a constant which we will designate by C, divided by the square root of the density of the gas[25] = C/√D, and as D = M/2, the vis viva of molecules = C²—that is, a constant for all molecules. Q.E.D.[26] The specific heat of gases (Chapter XIV.), and many other of their properties, are determined by their density, and consequently by their molecular weight. Gases and vapours in passing into a liquid state evolve the so-called latent heat, which also proves to be in connection with the molecular weight. The observed latent heats of carbon bisulphide, CS₂ = 90, of ether, C₄H₁₀O, = 94, of benzene, C₆H₆, = 109, of alcohol, C₂H₆O, = 200, of chloroform, CHCl₃, = 67, &c., show the amount of heat expended in converting one part by weight of the above substances into vapour. A great uniformity is observed if the measure of this heat he referred to the weight of the molecule. For carbon bisulphide the formula CS₂ expresses a weight 76, hence the latent heat of evaporation referred to the molecular quantity CS₂ = 76 x 90 = 6,840, for ether = 9,656, for benzene = 8,502, for alcohol = 9,200, for chloroform = 8,007, for water = 9,620, &c. That is, for molecular quantities, the latent heat varies comparatively little, from 7,000 to 10,000 heat units, whilst for equal parts by weight it is ten times greater for water than for chloroform and many other substances.[27]

Generalising from the above, the weight of the molecule determines the properties of a substance independently of its composition—i.e. of the number and quality of the atoms entering into the molecule—whenever the substance is in a gaseous state (for instance, the density of gases and vapours, the velocity of sound in them, their specific heat, &c.), or passes into that state, as we see in the latent heat of evaporation. This is intelligible from the point of view of the atomic theory in its present form, for, besides a rapid motion proper to the molecules of gaseous bodies, it is further necessary to postulate that these molecules are dispersed in space (filled throughout with the luminiferous ether) like the heavenly bodies distributed throughout the universe. Here, as there, it is only the degree of removal (the distance) and the masses of substances which take effect, while those peculiarities of a substance which are expressed in chemical transformations, and only come into action on near approach or on contact, are in abeyance by reason of the dispersal. Hence it is at once obvious, in the first place, that in the case of solids and liquids, in which the molecules are closer together than in gases and vapours, a greater complexity is to be expected, i.e. a dependence of all the properties not only upon the weight of the molecule but also upon its composition and quality, or upon the properties of the individual chemical atoms forming the molecule; and, in the second place, that, in the case of a small number of molecules of any substance being disseminated through a mass of another substance—for example, in the formation of weak (dilute) solutions (although in this case there is an act of chemical reaction—i.e. a combination, decomposition, or substitution)—the dispersed molecules will alter the properties of the medium in which they are dissolved, almost in proportion to the molecular weight and almost independently of their composition. The greater the number of molecules disseminated—i.e. the stronger the solution—the more clearly defined will those properties become which depend upon the composition of the dissolved substance and its relation to the molecules of the solvent, for the distribution of one kind of molecules in the sphere of attraction of others cannot but be influenced by their mutual chemical reaction. These general considerations give a starting point for explaining why, since the appearance of Van't Hoff's memoir (1886), ‘The Laws of Chemical Equilibrium in a Diffused Gaseous or Liquid State’ (see Chapter I., Note 19), it has been found more and more that dilute (weak) solutions exhibit such variations of properties as depend wholly upon the weight and number of the molecules and not upon their composition, and even give the means of determining the weight of molecules by studying the variations of the properties of a solvent on the introduction of a small quantity of a substance passing into solution. Although this subject has been already partially considered in the first chapter (in speaking of solutions), and properly belongs to a special (physical) branch of chemistry, we touch upon it here because the meaning and importance of molecular weights are seen in it in a new and peculiar light, and because it gives a method for determining them whenever it is possible to obtain dilute solutions. Among the numerous properties of dilute solutions which have been investigated (for instance, the osmotic pressure, vapour tension, boiling point, internal friction, capillarity, variation with change of temperature, specific heat, electroconductivity, index of refraction, &c.) we will select one—the ‘depression’ or fall of the temperature of freezing (Raoult's cryoscopic method), not only because this method has been the most studied, but also because it is the most easily carried out and most frequently applied for determining the weight of the molecules of substances in solution, although here, owing to the novelty of the subject there are also many experimental discrepancies which cannot as yet be explained by theory.[27 bis]

If 100 gram-molecules of water, i.e. 1,800 grms, be taken and n gram-molecules of sugar, C₁₂H₂₂O₁₁, i.e. n 342 grms., be dissolved in them, then the depression d, or fall (counting from 0°) of the temperature of the formation of ice will be (according to Pickering)

which shows that for high degrees of dilution (up to 0·25n) d approximately (estimating the possible errors of experiment at ±0°·005) = n1·10, because then d = 0°, 0°·0110, 0°·0275, 0°·1100, 0°·2750, 1°·1000, and the difference between these figures and the results of experiment for very dilute solutions is less than the possible errors of experiment (for n = 1 the difference is already greater) and therefore for dilute solutions of sugar it may be said that n molecules of sugar in dissolving in 100 molecules of water give a depression of about 1°·1n. Similar data for acetone (Chapter I., Note 49) give a depression of 1°·006n for n molecules of acetone per 100 molecules of water. And in general, for indifferent substances (the majority of organic bodies) the depression per 100H₂O is nearly n1°·1 to n1°·0 (ether, for instance, gives the last number), and consequently in dissolving in 100 grms. of water it is about 18°·0n to 19°·0n, taking this rule to apply to the case of a small number of n (not over 0·2n). If instead of water, other liquid or fused solvents (for example, benzene, acetic acid, acetone, nitrobenzene or molten naphthaline, metals, &c.) be taken and in the proportion of 100 molecules of the solvent to n molecules of a dissolved indifferent (neither acid nor saline) substance, then the depression is found to be equal to from 0°·62n to 0°·65n and in general Kn. If the molecular weight of the solvent = m, then 100 gram-molecules will weigh 100m grms., and the depression will be approximately (taking 0·63n) equal to m0·63n degrees for n molecules of the substance dissolved in 100 grms. of the solvent, or in general the depression for 100 grms. of a given solvent = kn where k is almost a constant quantity (for water nearly 18, for acetone nearly 37, &c.) for all dilute solutions. Thus, having found a convenient solvent for a given substance and prepared a definite (by weight) solution (i.e. knowing how many grms. r of the solvent there are to q grms. of the substance dissolved) and having determined the depression d—i.e. the fall in temperature of freezing for the solvent—it is possible to determine the molecular weight of the substance dissolved, because d = kn where d is found by experiment and k is determined by the nature of the solvent, and therefore n or the number of molecules of the substance dissolved can be found. But if r grms. of the solvent and q grms. of the substance dissolved are taken, then there are 100q/r of the latter per 100 grms. of the former, and this quantity = nX, where n is found from the depression and = d / k and X is the molecular weight of the substance dissolved. Hence X = 100qk / rd , which gives the molecular weight, naturally only approximately, but still with sufficient accuracy to easily indicate, for instance, whether in peroxide of hydrogen the molecule contains HO or H₂O₂ or H₃O₃, &c. (H₂O₂ is obtained). Moreover, attention should be drawn to the fact that a great many substances taken as solvents give per 100 molecules a depression of about 0·63n, whilst water gives about 1·05n, i.e. a larger quantity, as though the molecules of liquid water were more complex than is expressed by the formula H₂O.[28] A similar phenomenon which repeats itself in the osmotic pressure, vapour tension of the solvent, &c. (see Chapter I., Notes 19 and 49), i.e. a variation of the constant (k for 100 grms. of the solvent or K for 100 molecules of it), is also observed in passing from indifferent substances to saline (to acids, alkalis and salts) both in aqueous and other solutions as we will show (according to Pickering's data 1892) for solutions of NaCl and CuSO₄ in water. For

n = 0·01 0·03 0·05 0·1 0·5

molecules of NaCl the depression is

d = 0°·0177 0°·0598 0°·0992 0°·1958 0°·9544

which corresponds to a depression per molecule

K = 1·77 1·96 1·98 1·96 1·91

i.e. here in the most dilute solutions (when n is nearly 0) d is obtained about 1·7n, while in the case of sugar it was about 1·1n. For CuSO₄ for the same values of n, experiment gave:

i.e. here again d for very dilute solutions is nearly 1·7n, but the value of K falls as the solution becomes more concentrated, while for NaCl it at first increased and only fell for the more concentrated solutions. The value of K in the solution of n molecules of a body in 100H₂O, when d = Kn, for very dilute solutions of CaCl₂ is nearly 2·6, for Ca(NO₃)₂ nearly 2·5, for HNO₃, KI and KHO nearly 1·9–2·O, for borax Na₂B₄O₇ nearly 3·7, &c., while for sugar and similar substances it is, as has been already mentioned, nearly 1·0–1·1. Although these figures are very different[28 bis] still k and K may be considered constant for analogous substances, and therefore the weight of the molecule of the body in solution can be found from d. And as the vapour tension of solutions and their boiling points (see Note 27 bis and Chapter I., Note 51) vary in the same manner as the freezing point depression, so they also may serve as means for determining the molecular weight of a substance in solution.[29]

Thus not only in vapours and gases, but also in dilute solutions of solid and liquid substances, we see that if not all, still many properties are wholly dependent upon the molecular weight and not upon the quality of a substance, and that this gives the possibility of determining the weight of molecules by studying these properties (for instance, the vapour density, depression of the freezing point, &c.) It is apparent from the foregoing that the physical and even more so the chemical properties of homogeneous substances, more especially solid and liquid, do not depend exclusively upon the weights of their molecules, but that many are in definite (see Chapter XV.) dependence upon the weights of the atoms of the elements entering into their composition, and are determined by their quantitative and individual peculiarities. Thus the density of solids and liquids (as will afterwards be shown) is chiefly determined by the weights of the atoms of the elements entering into their composition, inasmuch as dense elements (in a free state) and compounds are only met with among substances containing elements with large atomic weights, such as gold, platinum, and uranium. And these elements themselves, in a free state, are the heaviest of all elements. Substances containing such light elements as hydrogen, carbon, oxygen and nitrogen (like many organic substances) never have a high specific gravity; in the majority of cases it scarcely exceeds that of water. The density generally decreases with the increase of the amount of hydrogen, as the lightest element, and a substance is often obtained lighter than water. The refractive power of substances also entirely depends on the composition and the properties of the component elements.[29 bis] The history of chemistry presents a striking example in point—Newton foresaw from the high refractive index of the diamond that it would contain a combustible substance since so many combustible oils have a high refractive power. We shall afterwards see (Chapter XV.) that many of those properties of substances which are in direct dependence not upon the weight of the molecules but upon their composition, or, in other words, upon the properties and quantities of the elements entering into them, stand in a peculiar (periodic) dependence upon the atomic weight of the elements; that is, the mass (of molecules and atoms), proportional to the weight, determines the properties of substances as it also determines (with the distance) the motions of the heavenly bodies.