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. 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, NH{4}Cl, 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 NH{4}Cl, because it is formed from the molecules NH{3} 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 NH{3} and HCl, which should be nearly 14, because the density of NH{3} = 8·5 and of HCl = 18·2, and therefore the density of their mixture (in equal volumes) should be about 13·4. 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. According to the law and to experiment, the density of ammonia, NH{3}, is 8-1/2, and of hydrochloric acid, HCl, 18-1/4, if the density of hydrogen = 1. Consequently, in a mixture of NH_{3} 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. 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]

As the density of aqueous vapour remains constant within the limits of experimental accuracy, even at 1,000°, when dissociation has certainly commenced, it would appear that only a very small amount of water is decomposed at these temperatures. If even 10 p.c. of water were decomposed, the density would be 8·57 and the quotient M/D = 2·1, but at the high temperatures here concerned the error of experiment is not greater than the difference between this quantity and 2. And probably at 1,000° the dissociation is far from being equal to 10 p.c. Hence the variation in the vapour density of water does not give us the means of ascertaining the amount of its dissociation.

This explanation of the vapour density of sal-ammoniac, sulphuric acid, and similar substances which decompose in being distilled was the most natural to resort to as soon as the application of the law of Avogadro-Gerhardt to chemical relations was begun; it was, for instance, given in my work on Specific Volumes, 1856, p. 99. The formula, M/D = 2, which was applied later by many other investigators, had already been made use of in that work.

The beginner must remember that an experiment and the mode in which it is carried out must be determined by the principle or fact which it is intended to illustrate, and not vice versa, as some suppose. The idea which determines the necessity of an experiment is the chief consideration.

It is important that the tubes, asbestos, and sal-ammoniac should be dry, as otherwise the moisture retains the ammonia and hydrogen chloride.

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 CH{2}, the density was found by experiment to be 14, and in the case of amylene, whose composition is also CH{2}, the density proved to be 35, and consequently the quotient for ethylene = 1, and for amylene = 2/5. 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 C{2}H{4}, and of the second C{5}H{10}, 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 H{2}SO{4}, Br{2}, or HI, &c., ethylene combines in a quantity C{2}H{4}, and amylene in a quantity C{5}H{10}, and not CH{2}. 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, O{2}, which might already be concluded by comparing its density with that of ozone, whose molecule contains O{3} (Chapter IV.) So also the molecule of hydrogen equals H{2}, of chlorine Cl{2}, of nitrogen N{2}, &c. If chlorine react with hydrogen, the volume remains unaltered after the formation of hydrochloric acid, H{2} + Cl{2} = 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, S{6}--although, by heating, the density is reduced to a third, and S{2} is formed. Judging from the vapour density of phosphorus (D = 62) the molecule contains four atoms P{4}. 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 N{2}O{4} passes into NO{2}, or ozone, O{3}, into ordinary oxygen, O{2}, 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 O{2} be obtained from O{3}, 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 I{2}. 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 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 I_{2} 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.

Just as we saw (Chapter VI. Note 46) an increase of the dissociation of N{2}O{4} and the formation of a large proportion of NO{2}, with a decrease of pressure. The decomposition of I{2} into I + I is a similar dissociation.

Although at first there appeared to be a similar phenomenon in the case of chlorine, it was afterwards proved that if there is a decrease of density it is only a small one. In the case of bromine it is not much greater, and is far from being equal to that for iodine.

As in general we very often involuntarily confuse chemical processes with physical, it may be that a physical process of change in the coefficient of expansion with a change of temperature participates with a change in molecular weight, and partially, if not wholly, accounts for the decrease of the density of chlorine, bromine, and iodine. Thus, I have remarked (Comptes Rendus, 1876) that the coefficient of expansion of gases increases with their molecular weight, and (Chapter II., Note 26) the results of direct experiment show the coefficient of expansion of hydrobromic acid (M = 81) to be 0·00386 instead of 0·00367, which is that of hydrogen (M = 2). Hence, in the case of the vapour of iodine (M = 254) a very large coefficient of expansion is to be expected, and from this cause alone the relative density would fall. As the molecule of chlorine Cl_{2} is lighter (= 71) than that of bromine (= 160), which is lighter than that of iodine (= 254), we see that the order in which the decomposability of the vapours of these haloids is observed corresponds with the expected rise in the coefficient of expansion. Taking the coefficient of expansion of iodine vapour as 0·004, then at 1,000° its density would be 116. Therefore the dissociation of iodine may be only an apparent phenomenon. However, on the other hand, the heavy vapour of mercury (M = 200, D = 100) scarcely decreases in density at a temperature of 1,500° (D = 98, according to Victor Meyer); but it must not be forgotten that the molecule of mercury contains only one atom, whilst that of iodine contains two, and this is very important. Questions of this kind which are difficult to decide by experimental methods must long remain without a certain explanation, owing to the difficulty, and sometimes impossibility, of distinguishing between physical and chemical changes.

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, S{2}O{5}Cl{2}, 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 SO{3} and SO{2}Cl{2}, or any other two products, and thus the abnormal density of S{2}O{5}Cl{2} remained unexplained until D. P. Konovaloff (1885) showed that the previous investigators were working with a mixture (containing SO{3}HCl), 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; 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.

And so it was in the fifties. Some took O = 8, others O = 16. Water in the first case would be HO and hydrogen peroxide HO{2}, and in the second case, as is now generally accepted, water H{2}O and hydrogen peroxide H{2}O{2} or HO. Disagreement and confusion reigned. In 1860 the chemists of the whole world met at Carlsruhe for the purpose of arriving at some agreement and uniformity of opinion. I was present at this Congress, and well remember how great was the difference of opinion, and how a compromise was advocated with great acumen by many scientific men, and with what warmth the followers of Gerhardt, at whose head stood the Italian professor, Canizzaro, followed up the consequences of the law of Avogadro. In the spirit of scientific freedom, without which science would make no progress, and would remain petrified as in the middle ages, and with the simultaneous necessity of scientific conservatism, without which the roots of past study could give no fruit, a compromise was not arrived at, nor ought it to have been, but instead of it truth, in the form of the law of Avogadro-Gerhardt, received by means of the Congress a wider development, and soon afterwards conquered all minds. Then the new so-called Gerhardt atomic weights established themselves, and in the seventies they were already in general use.

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.

A bubble of gas, a drop of liquid, or the smallest crystal, presents an agglomeration of a number of molecules, in a state of continual motion (like the stars of the Milky Way), distributing themselves evenly or forming new systems. If the aggregation of all kinds of heterogeneous molecules be possible in a gaseous state, where the molecules are considerably removed from each other, then in a liquid state, where they are already close together, such an aggregation becomes possible only in the sense of the mutual reaction between them which results from their chemical attraction, and especially in the aptitude of heterogeneous molecules for combining together. Solutions and other so-called indefinite chemical compounds should be regarded in this light. According to the principles developed in this work we should regard them as containing both the compounds of the heterogeneous molecules themselves and the products of their decomposition, as in peroxide of nitrogen, N{2}O{4} and NO_{2}. And we must consider that those molecules A, which at a given moment are combined with B in AB, will in the following moment become free in order to again enter into a combined form. The laws of chemical equilibrium proper to dissociated systems cannot be regarded in any other light.

Molecules consist of atoms in a certain state of distribution and motion, just as the solar system 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.

This strengthens the fundamental idea of the unity and harmony of type of all creation and is one of those ideas which impress themselves on man in all ages, and give rise to a hope of arriving in time, by means of a laborious series of discoveries, observations, experiments, laws, hypotheses, and theories, at a comprehension of the internal and invisible structure of concrete substances with that same degree of clearness and exactitude which has been attained in the visible structure of the heavenly bodies. It is not many years ago since the law of Avogadro-Gerhardt took root in science. It is within the memory of many living scientific men, and of mine amongst others. It is not surprising, therefore, that as yet little progress has been made in the province of molecular mechanics; but the theory of gases alone, which is intimately connected with the conception of molecules, shows by its success that the time is approaching when our knowledge of the internal structure of matter will be defined and established.

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:

Molecular Amount of Molecular Amount of Weight Oxygen Weight Oxygen

H{2}O 18 16 HNO{3} 63 48 N{2}O 44 16 CO 28 16 NO 30 16 CO{2} 44 32 NO_{2} 46 32

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 BeCl{2}--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 Be{2}O{3}, and the chloride by BeCl{3}. 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 BeCl{2}, but does not suit the formula BeCl{3}, it therefore became necessary to regard the atomic weight of Be as 9 and not as 13-1/2.

If Be = 9, and beryllium chloride be BeCl{2}, then for every 9 parts of beryllium there are 71 parts of chlorine, and the molecular weight of BeCl{2} = 80; hence the vapour density should be 40 or n{4}0. If Be = 13·5, and beryllium chloride be BeCl{3}, then to 13·5 of beryllium there are 106·5 of chlorine; hence the molecular weight would be 120, and the vapour density 60 or n60. The composition is evidently the same in both cases, because 9 : 71 :: 13·5 : 106·5. Thus, if the symbol of an element designate different atomic weights, apparently very different formulæ may equally well express both the percentage composition of compounds, and those properties which are required by the laws of multiple proportions and equivalents. The chemists of former days accurately expressed the composition of substances, and accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6, Si = 14, &c. The Gerhardt equivalents are also satisfied by them, because O = 16, C = 12, Si = 28, &c., are multiples of them. The choice of one or the other multiple quantity for the atomic weight is impossible without a firm and concrete conception of the molecule and atom, and this is only obtained as a consequence of the law of Avogadro-Gerhardt, and hence the modern atomic weights are the results of this law (see_ Note 28).

With the establishment of a true conception of molecules and atoms, chemical formulæ became direct expressions, not only of composition, 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 C{4}H{10}O, 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, CO_{2}, 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 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.

The percentage amounts of the elements contained in a given compound may be calculated from its formula by a simple proportion. Thus, for example, to find the percentage amount of hydrogen in hydrochloric acid we reason as follows:--HCl shows that hydrochloric acid contains 35·5 of chlorine and 1 part of hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1 part by weight of hydrogen, consequently 100 parts by weight of hydrochloric acid will contain as many more units of hydrogen as 100 is greater than 36·5; therefore, the proportion is as follows--x : 1 :: 100 : 36·5 or x = 100/36·5 = 2·739. Therefore 100 parts of hydrochloric acid contain 2·739 parts of hydrogen. In general, when it is required to transfer a formula into its percentage composition, we must replace the symbols by their corresponding atomic weights and find their sum, and knowing the amount by weight of a given element in it, it is easy by proportion to find the amount of this element in 100 or any other quantity of parts by weight. If, on the contrary, it be required to find the formula from a given percentage composition, we must proceed as follows: Divide the percentage amount of each element entering into the composition of a substance by its atomic weight, and compare the figures thus obtained--they should be in simple multiple proportion to each other. Thus, for instance, from the percentage composition of hydrogen peroxide, 5·88 of hydrogen and 94·12 of oxygen, it is easy to find its formula; it is only necessary to divide the amount of hydrogen by unity and the amount of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained, which are in the ratio 1 : 1, which means that in hydrogen peroxide there is one atom of hydrogen to one atom of oxygen.

The following is a proof of the practical rule given above that to find the ratio of the number of atoms from the percentage composition, it is necessary to divide the percentage amounts by the atomic weights of the corresponding substances, and to find the ratio which these numbers bear to each other. Let us suppose that two radicles (simple or compound), whose symbols and combining weights are A and B, combine together, forming a compound composed of x atoms of A and y atoms of B. The formula of the substance will be AxBy. From this formula we know that our compound contains xA parts by weight of the first element, and yB of the second. In 100 parts of our compound there will be (by proportion) (100. xA)/(xA + yB) of the first element, and (100. yB)/(xA + yB) of the second. Let us divide these quantities, expressing the percentage amounts by the corresponding combining weights; we then obtain 100x/(xA + yB) for the first element and 100y/(xA + yB) for the second element. And these numbers are in the ratio x : y--that is, in the ratio of the number of atoms of the two substances.

It may be further observed that even the very language or nomenclature of chemistry acquires a particular clearness and conciseness by means of the conception of molecules, because then the names of substances may directly indicate their composition. Thus the term 'carbon dioxide' tells more about and expresses CO{2} better than carbonic acid gas, or even carbonic anhydride. Such nomenclature is already employed by many. But expressing the composition without an indication or even hint as to the properties, would be neglecting the advantageous side of the present nomenclature. Sulphur dioxide, SO{2}, expresses the same as barium dioxide, BaO{2}, but sulphurous anhydride indicates the acid properties of SO{2}. Probably in time one harmonious chemical language will succeed in embracing both advantages.

This formula (which is given in my work on 'The Tension of Gases,' and in a somewhat modified form in the 'Comptes Rendus,' Feb. 1876) is deduced in the following manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is the molecular weight and D the density referred to hydrogen. But it is equal to the weight s{0} of a cubic centimetre of a gas in grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the weight s of a cubic centimetre of a gas at a temperature t and under a pressure p (in centimetres) is equal to s_{0}p/76(1 + at). Therefore, s_{0} = s.76(1 + at)/p; hence D = 76.s(1 + at)/0·0000898p, whence M = 152s(1 + at)/0·0000898p, which gives the above expression, because 1/a = 273, and 152 multiplied by 273 and divided by 0·0000898 is nearly 6200. In place of s, m/v may be taken, where m is the weight and v_ the volume of a vapour.

The above formula may be directly applied in order to ascertain the molecular weight from the data; weight of vapour m grms., its volume v c.c., pressure p cm., and temperature t°; for s = the weight of vapour m, divided by the volume v, and consequently M = 6,200m(273 + t)/pv. Therefore, instead of the formula (see Chapter II., Note 34), pv = R(273 + t), where R varies with the mass and nature of a gas, we may apply the formula pv = 6,200(m/M)(273 + t). These formulæ simplify the calculations in many cases. For example, required the volume v occupied by 5 grms. of aqueous vapour at a temperature t = 127° and under a pressure p = 76 cm. According to the formula M = 6,200m(273 + t)/pv, we find that v = 9,064 c.c., as in the case of water M = 18, m in this instance = 5 grms. (These formulæ, however, like the laws of gases, are only approximate.)

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 HNO_{3} 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 = (1/2) mv^2, 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 = C/D, and as D = M/2, the vis viva of molecules = C^2--that is, a constant for all molecules. Q.E.D. 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, CS{2} = 90, of ether, C{4}H{10}O, = 94, of benzene, C{6}H{6}, = 109, of alcohol, C{2}H{6}O, = 200, of chloroform, CHCl{3}, = 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 CS{2} expresses a weight 76, hence the latent heat of evaporation referred to the molecular quantity CS{2} = 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.

Chapter I., Note 34.

The velocity of the transmission of sound through gases and vapours closely bears on this. It = (Kpg)/D(1 + [Greek: a]t), where K is the ratio between the two specific heats (it is approximately 1·4 for gases containing two atoms in a molecule), p the pressure of the gas expressed by weight (that is, the pressure expressed by the height of a column of mercury multiplied by the density of mercury), g the acceleration of gravity, D the weight of a cubic measure of the gas, [Greek: a] = 0·00367, and t the temperature. Hence, if K be known, and as D can he found from the composition of a gas, we can calculate the velocity of the transmission of sound in that gas. Or if this velocity be known, we can find K. The relative velocities of sound in two gases can he easily determined (Kundt).

If a horizontal glass tube (about 1 metre long and closed at both ends) be full of a gas, and be firmly fixed at its middle point, then it is easy to bring the tube and gas into a state of vibration, by rubbing it from centre to end with a damp cloth. The vibration of the gas is easily rendered visible, if the interior of the tube be dusted with lycopodium (the yellow powder-dust or spores of the lycopodium plant is often employed in medicine), before the gas is introduced and the tube fused up. The fine lycopodium powder arranges itself in patches, whose number depends on the velocity of sound in the gas. If there be 10 patches, then the velocity of sound in the gas is ten times slower than in glass. It is evident that this is an easy method of comparing the velocity of sound in gases. It has been demonstrated by experiment that the velocity of sound in oxygen is four times less than in hydrogen, and the square roots of the densities and molecular weights of hydrogen and oxygen stand in this ratio.

If the conception of the molecular weights of substances does not give an exact law when applied to the latent heat of evaporation, at all events it brings to light a certain uniformity in figures, which otherwise only represent the simple result of observation. Molecular quantities of liquids appear to expend almost equal amounts of heat in their evaporation. It may be said that the latent heat of evaporation of molecular quantities is approximately constant, because the vis viva of the motion of the molecules is, as we saw above, a constant quantity. According to thermodynamics the latent heat of evaporation is equal to ((t + 273)/E)(n´-n)dp/dT × 13·59, where t is the boiling point, n´ the specific volume (i.e. the volume of a unit of weight) of the vapour, and n the specific volume of the liquid, dp/dT the variation of the tension with a rise of temperature per 1°, and 13·89 the density of the mercury according to which the pressure is measured. Thus the latent heat of evaporation increases not only with a decrease in the vapour density (i.e. the molecular weight), but also with an increase in the boiling point, and therefore depends on different factors.

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]

Van't Hoff, starting from the second law of thermodynamics, showed that the dependence of the rise of pressure (dp) upon a rise of temperature (dT) is determined by the equation dp = (kmp/2T^2)dT, where k is the latent heat of evaporation of the solvent, m its molecular weight, p the tension of the saturated vapour of the solvent at T, and T the absolute temperature (T = 273 + t), while Raoult found that the quantity (p-p´)/p (Chapter I., Note 50) or the measure of the relative fall of tension (p the tension of the solvent or water, and p´ of the solution) is found by the ratio of the number of molecules, n of the substance dissolved, and N of the solvent, so that (p-p´)/p = Cn/(N + n) where C is a constant. With very dilute solutions p -p´ may be taken as equal to dp, and the fraction n/(N + n) as equal to n/N (because in that case the value of N is very much greater than n), and then, judging from experiment, C is nearly unity--hence: dp/p = n/N or dp = np/N, and on substituting this in the above equation we have (kmp/2T^2)dT = np/N. Taking a weight of the solvent m/N = 100, and of the substance dissolved (per 100 of the solvent) q, where q evidently = nM, if M be the molecular weight of the substance dissolved, we find that n/N = qm/100M, and hence, according to the preceding equation, we have M = (0·02T^2/k)·(q/dT), that is, by taking a solution of q grms. of a substance in 100 grms. of a solvent, and determining by experiment the rise of the boiling point dT, we find the molecular weight M of the substance dissolved, because the fraction 0·02T^2/k is (for a given pressure and solvent) a constant; for water at 100° (T = 373°) when k = 534 (Chapter I., Note 11), it is nearly 5·2, for ether nearly 21, for bisulphide of carbon nearly 24, for alcohol nearly 11·5, &c. As an example, we will cite from the determinations made by Professor Sakurai, of Japan (1893), that when water was the solvent and the substance dissolved, corrosive sublimate, HgCl{2}, was taken in the quantity q = 8·978 and 4·253 grms., the rise in the boiling point dT was = O°·179 and 0°·084, whence M = 261 and 263, and when alcohol was the solvent, q = 10·873 and 8·765 and dT = 0°·471 and 0°·380, whence M = 266 and 265, whilst the actual molecular weight of corrosive sublimate = 271, which is very near to that given by this method. In the same manner for aqueous solutions of sugar (M = 342), when q varied from 14 to 2·4, and the rise of the boiling point from 0°·21 to 0°·035, M was found to vary between 339 and 364. For solutions of iodine I{2} in ether, the molecular weight was found by this method to be between 255 and 262, and I_{2} = 254. Sakurai obtained similar results (between 247 and 262) for solutions of iodine in bisulphide of carbon.

We will here remark that in determining M (the molecular weight of the substance dissolved) at small but increasing concentrations (per 100 grms. of water), the results obtained by Julio Baroni (1893) show that the value of M found by the formula may either increase or decrease. An increase, for instance, takes place in aqueous solutions of HgCl{2} (from 255 to 334 instead of 271), KNO{3} (57-66 instead of 101), AgNO{3} (104-107 instead of 170), K{2}SO{4} (55-89 instead of 174), sugar (328-348 instead of 342), &c. On the contrary the calculated value of M decreases as the concentration increases, for solutions of KCl (40-39 instead of 74·5), NaCl (33-28 instead of 58·5), NaBr (60-49 instead of 103), &c. In this case (as also for LiCl, NaI, C{2}H{3}NaO{2}, &c.) the value of i (Chapter I., Note 49), or the ratio between the actual molecular weight and that found by the rise of the boiling point, was found to increase with the concentration, i.e. to be greater than 1, and to differ more and more from unity as the strength of the solution becomes greater. For example, according to Schlamp (1894), for LiCl, with a variation of from 1·1 to 6·7 grm. LiCl per 100 of water, i varies from 1·63 to 1·89. But for substances of the first series (HgCl{2}, &c.), although in very dilute solutions i is greater than 1, it approximates to 1 as the concentration increases, and this is the normal phenomenon for solutions which do not conduct an electric current, as, for instance, of sugar. And with certain electrolytes, such as HgCl{2}, MgSO{4}, &c., i exhibits a similar variation; thus, for HgCl{2} the value of M is found to vary between 255 and 334; that is, i (as the molecular weight = 271) varies between 1·06 and 0·81. Hence I do not believe that the difference between i and unity (for instance, for CaCl{2}, i is about 3, for KI about 2, and decreases with the concentration) can at present be placed at the basis of any general chemical conclusions, and it requires further experimental research. Among other methods by which the value of i is now determined for dilute solutions is the study of their electroconductivity, admitting that i = 1 + a(k-1), where a = the ratio of the molecular conductivity to the limiting conductivity corresponding to an infinitely large dilution (see Physical Chemistry), and k is the number of ions into which the substance dissolved can split up. Without entering upon a criticism of this method of determining i, I will only remark that it frequently gives values of i very close to those found by the depression of the freezing point and rise of the boiling point; but that this accordance of results is sometimes very doubtful. Thus for a solution containing 5·67 grms. CaCl{2} per 100 grms. of water, i, according to the vapour tension = 2·52, according to the boiling point = 2·71, according to the electroconductivity = 2·28, while for solutions in propyl alcohol (Schlamp 1894) i is near to 1·33. In a word, although these methods of determining the molecular weight of substances in solution show an undoubted progress in the general chemical principles of the molecular theory, there are still many points which require explanation.

We will add certain general relations which apply to these problems. Isotonic (Chapter I., Note 19) solutions exhibit not only similar osmotic pressures, but also the same vapour tension, boiling point and freezing temperature. The osmotic pressure bears the same relation to the fall of the vapour tension as the specific gravity of a solution does to the specific gravity of the vapour of the solvent. The general formulæ underlying the whole doctrine of the influence of the molecular weight upon the properties of solutions considered above, are: 1. Raoult in 1886-1890 showed that

((p-p´)/p) × (100/a) × (M/m) = a constant C

where p and p´ are the vapour tensions of the solvent and substance dissolved, a the amount in grms. of the substance dissolved per 100 grms. of solvent, M and m the molecular weights of the substance dissolved and solvent. 2. Raoult and Recoura in 1890 showed that the constant above C = the ratio of the actual vapour density d´ of the solvent to the theoretical density d calculated according to the molecular weight. This deduction may now be considered proved, because both the fall of tension and the ratio of the vapour densities d´/d give, for water 1·03, for alcohol 1·02, for ether 1·04, for bisulphide of carbon 1·00, for benzene 1·02, for acetic acid 1·63. 3. By applying the principles of thermodynamics and calling L{1} the latent heat of fusion and T{1} the absolute (= t + 273) temperature of fusion of the solvent, and L{2} and T{2} the corresponding values for the boiling point, Van't Hoff in 1886-1890 deduced:--

(Depression of freezing point)/(Rise of boiling point) = (L{2}/L{1}) × (T{1}^2/T{2}^2)

Depression of freezing point = (AT{1}^{2}a)/(L{1}M_{1})

Rise of boiling point = (AT{2}^{2}a)/(L{2}M_{1})

where A = 0·01988 (or nearly 0·02 as we took it above), a is the weight in grms. of the substance dissolved per 100 grms. of the solvent, M{1} the molecular weight of the dissolved substance (in the solution), and M the molecular weight of this substance according to its composition and vapour density, then i = M/M{1}. The experimental data and theoretical considerations upon which these formulæ are based will be found in text-books of physical and theoretical chemistry.

If 100 gram-molecules of water, i.e. 1,800 grms, be taken and n gram-molecules of sugar, C{12}H{22}O{11}, 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)

n = 0 0·010 0·025 0·100 0·250 1·000 d = 0° 0°·0103 0°·0280 0°·1115 0°·2758 1°·1412

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 100H{2}O 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 H{2}O{2} or H{3}O{3}, &c. (H{2}O{2} 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 H{2}O. 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 CuSO_{4} 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 CuSO{4} for the same values of n_, experiment gave:

d = 0°·0164 0°·0451 0°·0621 0°·1321 0°·5245 K = 1·64 1·50 1·44 1·32 1·05

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 100H{2}O, when d = Kn, for very dilute solutions of CaCl{2} is nearly 2·6, for Ca(NO{3}){2} nearly 2·5, for HNO{3}, KI and KHO nearly 1·9-2·O, for borax Na{2}B{4}O{7} 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.

A similar conclusion respecting the molecular weight of liquid water (i.e. that its molecule in a liquid state is more complex than in a gaseous state, or polymerized into H{8}O{4}, H{6}O{3} or in general into nH{2}O) is frequently met in chemico-physical literature, but as yet there is no basis for its being fully admitted, although it is possible that a polymerization or aggregation of several molecules into one takes place in the passage of water into a liquid or solid state, and that there is a converse depolymerization in the act of evaporation. Recently, particular attention has been drawn to this subject owing to the researches of Eötvös (1886) and Ramsay and Shields (1893) on the variation of the surface tension N with the temperature (N = the capillary constant a^2 multiplied by the specific gravity and divided by 2, for example, for water at 0° and 100° the value of a^2 = 15·41 and 12·58 sq. mm., and the surface tension 7·92 and 6·04). Starting from the absolute boiling point (Chapter II., Note 29) and adding 6°, as was necessary from all the data obtained, and calling this temperature T, it is found that AS = kT, where S is the surface of a gram-molecule of the liquid (if M is its weight in grams, s its sp. gr., then its sp. volume = M/s, and the surface S = [3root](M/s)^2), A the surface tension (determined by experiment at T), and k a constant which is independent of the composition of the molecule. The equation AS = kT is in complete agreement with the well-known equation for gases vp = RT (p. 140) which serves for deducing the molecular weight from the vapour density. Ramsay's researches led him to the conclusion that the liquid molecules of CS{2}, ether, benzene, and of many other substances, have the same value as in a state of vapour, whilst with other liquids this is not the case, and that to obtain an accordance, that is, that k shall be a constant, it is necessary to assume the molecular weight in the liquid state to be n times as great. For the fatty alcohols and acids n varies from 1-1/2 to 3-1/2, for water from 2-1/4 to 4, according to the temperature (at which the depolymerization takes place). Hence, although this subject offers a great theoretical interest, it cannot be regarded as firmly established, the more so since the fundamental observations are difficult to make and not sufficiently numerous; should, however, further experiments confirm the conclusions arrived at by Professor Ramsay, this will give another method of determining molecular weights.

We will cite one more example, showing the direct dependence of the properties of a substance on the molecular weight. If one molecular part by weight of the various chlorides--for instance, of sodium, calcium, barium, &c.--be dissolved in 200 molecular parts by weight of water (for instance, in 3,600 grams) then it is found that the greater the molecular weight of the salt dissolved, the greater is the specific gravity of the resultant solution.

Molecular Sp. gr. Molecular Sp. gr. weight at 15° weight at 15° HCl 36·5 1·0041 CaCl{2} 111 1·0236 NaCl 58·5 1·0106 NiCl{2} 130 1·0328 KCl 74·5 1·0121 ZnCl{2} 136 1·0331 BeCl{2} 80 1·0138 BaCl{2} 208 1·0489 MgCl{2} 95 1·0203

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.

It has long been known that the coefficient of refraction n for a given substance decreases with the density of a substance D, so that the magnitude (n-1) ÷ D = C is almost constant for a given ray (having a definite wave length) and for a given substance. This constant is called the refractive energy, and its product with the atomic or molecular weight of a substance the refraction equivalent. The coefficient of refraction of oxygen is 1·00021, of hydrogen 1·00014, their densities (referred to water) are 0·00143 and 0·00009, and their atomic weights, O = 16, H = 1; hence their refraction equivalents are 3 and 1·5. Water contains H{2}O, consequently the sum of the equivalents of refraction is (2 × 1·5) + 3 = 6. But as the coefficient of refraction of water = 1·331, its refraction equivalent = 5·958, or nearly 6. Comparison shows that, approximately, the sum of the refraction equivalents of the atoms forming compounds (or mixtures) is equal to the refraction equivalent of the compound. According to the researches of Gladstone, Landolt, Hagen, Brühl and others, the refraction equivalents of the elements are--H = 1·3, Li = 3·8, B = 4·0, C = 5·0, N = 4·1 (in its highest state of oxidation, 5·3), O = 2·9, F = 1·4, Na = 4·8, Mg = 7·0, Al = 8·4, Si = 6·8, P = 18·3, S = 16·0, Cl = 9·9, K = 8·1, Ca = 10·4, Mn = 12·2, Fe = 12·0 (in the salts of its higher oxides, 20·1), Co = 10·8, Cu = 11·6, Zn = 10·2, As = 15·4, Bi = 15·3, Ag = 15·7, Cd = 13·6, I = 24·5, Pt = 26·0, Hg = 20·2, Pb = 24·8, &c. The refraction equivalents of many elements could only be calculated from the solutions of their compounds. The composition of a solution being known it is possible to calculate the refraction equivalent of one of its component parts, those for all its other components being known. The results are founded on the acceptance of a law which cannot be strictly applied. Nevertheless the representation of the refraction equivalents gives an easy means for directly, although only approximately, obtaining the coefficient of refraction from the chemical composition of a substance. For instance, the composition of carbon bisulphide is CS{2} = 76, and from its density, 1·27, we find its coefficient of refraction to be 1·618 (because the refraction equivalent = 5 + 2 × 16 = 37), which is very near the actual figure. It is evident that in the above representation compounds are looked on as simple mixtures of atoms, and the physical properties of a compound as the sum of the properties present in the elementary atoms forming it. If this representation of the presence of simple atoms in compounds had not existed, the idea of combining by a few figures a whole mass of data relating to the coefficient of refraction of different substances could hardly have arisen. For further details on this subject, see works on Physical Chemistry.