Journal de Physique, 73, 58-76 (1811)
Setting out from this hypothesis, it is apparent that we have the means of determining very easily the relative masses of the molecules of substances obtainable in the gaseous state, and the relative number of these molecules in compounds; for the ratios of the masses of the molecules are then the same as those of the densities of the different gases at equal temperature and pressure, and the relative number of molecules in a compound is given at once by the ratio of the volumes of the gases that form it. For example, since the numbers 1.10359 and 0.07321 express the densities of the two gases oxygen and hydrogen compared to that of atmospheric air as unity, and the ratio of the two numbers consequently represents the ratio between the masses of equal volumes of these two gases, it will also represent on our hypothesis the ratio of the masses of their molecules. Thus the mass of the molecule of oxygen will be about 15 times that of the molecule of hydrogen, or, more exactly as 15.074 to 1. In the same way the mass of the molecule of nitrogen will be to that of hydrogen as 0.96913 to 0.07321, that is, as 13, or more exactly 13.238, to 1. On the other hand, since we know that the ratio of the volumes of hydrogen and oxygen in the formation of water is 2 to 1, it follows that water results from the union of each molecule of oxygen with two molecules of hydrogen. Similarly, according to the proportions by volume established by M. Gay-Lussac for the elements of ammonia, nitrous oxide, nitrous gas, and nitric acid, ammonia will result from the union of one molecule of nitrogen with three of hydrogen, nitrous oxide from one molecule of oxygen with two of nitrogen, nitrous gas from one molecule of nitrogen with one of oxygen, and nitric acid from one of nitrogen with two of oxygen.
On reviewing the various compound gases most generally known, I only find examples of duplication of the volume relatively to the volume of that one of the constituents which combines with one or more volumes in the other. We have already seen this for water. In the same way, we know that the volume of ammonia gas is twice that of the nitrogen which enters into it. M. Gay-Lussac has also shown that the volume of nitrous oxide is equal to that of the nitrogen which forms part of it, and consequently is twice that of the oxygen. Finally, nitrous gas, which contains equal volumes of nitrogen and oxygen, has a volume equal to the sum of the two constituent gases, that is to say, double that of each of them. Thus in all these cases there must be a division of the molecule into two; but it is possible that in other cases the division might be into four, eight, &c. The possibility of this division of compound molecules might have been conjectured à priori; for otherwise the integral molecules of bodies composed of several substances with a relatively large number of molecules, would come to have a mass excessive in comparison with the molecules of simple substances. We might therefore imagine that nature had some means of bringing them back to the order of the latter, and the facts have pointed out to us the existence of such means. Besides, there is another consideration which would seem to make us admit in some cases the division in question; for how could one otherwise conceive a real combination between two gaseous substances uniting in equal volumes without condensation, such as takes place in the formation of nitrous gas? Supposing the molecules to remain at such a distance that the mutual attraction of those of each gas could not be exercised, we cannot imagine that a new attraction could take place between the molecules of one gas and those of the other. But on the hypothesis of division of the molecule, it is easy to see that the combination really reduces two different molecules to one, and that there would be contraction by the whole volume of one of the gases if each compound molecule did not split up into two molecules of the same nature. M. Gay-Lussac clearly saw that, according to the facts, the diminution of volume on the combination of gases cannot represent the approximation of their elementary molecules. The division of molecules on combination explains to us how these two things may be made independent of each other.
Thus Dalton supposes  that water is formed by the union of hydrogen and oxygen, molecule to molecule. From this, and from the ratio by weight of the two components, it would follow that the mass of the molecule of oxygen would be to that of hydrogen as 7 1/2 to 1 nearly, or, according to Dalton's evaluation, as 6 to 1. This ratio on our hypothesis is, as we saw, twice as great, namely, as 15 to 1. As for the molecule of water, its mass ought to be roughly expressed by 15+2=17 (taking for unity that of hydrogen), if there were no division of the molecule into two; but on account of this division it is reduced to half, 8 1/2, or more exactly 8.537, as may also be found by dividing the density of aqueous vapour 0.625 (Gay-Lussac) by the density of hydrogen 0.0732. This mass differs from 7, that assigned to it by Dalton, by the difference in the values for the composition of water; so that in this respect Dalton's result is approximately correct from the combination of two compensating errors,--the error in the mass of the molecule of oxygen, and his neglect of the division of the molecule.
Dalton supposes that in nitrous gas the combination of nitrogen and oxygen is molecule to molecule: we have seen on our hypothesis that this is actually the same. Thus Dalton would have found the same molecular mass for nitrogen as we have, always supposing that of hydrogen to be unity, if he had not set out from a different value for that of oxygen, and if he had taken precisely the same value for the quantities of the elements in nitrous gas by weight. But supposing the molecule of oxygen to be less than half what we find, he has been obliged to make that of nitrogen also equal to less than half the value we have assigned to it, viz., 5 instead of 13. As regards the molecule of nitrous gas itself, his neglect of the division of the molecule again makes his result approach ours; he has made it 6+5=11, whilst according to us it is about (15+13)/2 = 14, or more exactly (15.074+13.238)/2 = 14.156, as we also find by dividing 1.03636, the density of nitrous gas according to Gay-Lussac, by 0.07321. Dalton has likewise fixed in the same manner as the facts has given us, the relative number of molecules in nitrous oxide and in nitric acid, and in the first case the same circumstance has rectified his result for the magnitude of the molecule. He makes it 6 + 2x5 = 16, whilst according to our method it should be (15.074+2x13.238)/2 = 20.775, a number which is also obtained by dividing 1.52092, Gay-Lussac's value for the density of nitrous oxide, by the density of hydrogen.
In the case of ammonia, Dalton's supposition as to the relative number of molecules in its composition is on our hypothesis entirely at fault. He supposes nitrogen and hydrogen to be united in it molecule to molecule, whereas we have seen that one molecule of nitrogen unites with three molecules of hydrogen. According to him the molecule of ammonia would be 5+1=6; according to us it should be (13+3)/2 = 8, or more exactly 8.119, as may also be deduced directly from the density of ammonia gas. The division of the molecule, which does not enter into Dalton's calculations, partly corrects in this case also the error which would result from his other suppositions.
All the compounds we have just discussed are produced by the union of one molecule of one of the components with one or more molecules of the other. In nitrous acid we have another compound of two of the substances already spoken of, in which the terms of the ratio between the number of molecules both differ from unity. From Gay-Lussac's experiments (Société d'Arcueil, same volume) it appears that this acid is formed from 1 part by volume of oxygen and 3 of nitrous gas, or, what comes to the same thing, of 3 parts of nitrogen and 5 of oxygen; hence it would follow, on our hypothesis, that its molecule should be composed of 3 molecules of nitrogen and 5 of oxygen, leaving the possibility of division out of account. But this mode of combination can be referred to the preceding simpler forms by considering it as the result of the union of 1 molecule of oxygen with 3 of nitrous gas, i.e. with 3 molecules, each composed of a half-molecule of oxygen and a half-molecule of nitrogen, which thus already included the division of some of the molecules of oxygen which enter into that of nitrous acid. Supposing there to be no other division, the mass of this last molecule would be 57.542, that of hydrogen being taken as unity, and the density of nitrous acid gas would be 4.21267, the density of air being taken as unity. But it is probable that there is at least another division into two, and consequently a reduction of the density to half: we must wait until this density has been determined by experiment.
M. Gay-Lussac has shown that if we assume that dry sulphuric acid is composed of 100 parts of sulphur and 138 of oxygen by weight, as the most recent work of chemists has established, and that the density of sulphurous acid gas is 2.265 referred to air as unity (Kirwan's determination), and if we admit, as the result of Gay-Lussac's experiments, that sulphuric acid is composed of two parts by volume of sulphurous acid is nearly equal to that of the oxygen which entered into it; and this equality would be exact if the bases on which the calculation rests were the same. If we suppose Kirwan's determination to be exact, throwing the whole error on the analysis of sulphuric acid, we find that in sulphurous acid 100 parts of sulphur take 95.02 of oxygen, and consequently in sulphuric acid 95.02 + (95.02/2) = 142.53, instead of 138. If, on the contrary, we suppose the analysis of sulphuric acid to be exact, it follows that sulphurous acid contains 92 of oxygen for 100 of sulphur, and that its specific gravity should be 2.30314, instead of 2.265.
One consideration would appear to weigh in favour of the first assumption until the density of sulphurous acid gas has been confirmed or rectified by fresh experiments,--namely, that there must have been in the determination of the composition of sulphuric acid, a source of error tending to increase the quantity of the radical, or, what is the same thing, diminish the quantity of oxygen. The determination was made from the quantity of dry sulphuric acid produced. Now it seems almost certain that ordinary sulphur contains hydrogen; the weight of this hydrogen, which must have been converted into water in the operation, has therefore been added to the true weight of the radical. I shall therefore assume sulphurous acid to be composed of 95.02  of oxygen to 100 of sulphur, or rather of sulphuric radical, instead of 92. 
In order now to determine the mass of the molecule of the sulphuric radical, it would be necessary to know what proportion by volume this radical in the gaseous state would bear to the oxygen in the formation of sulphurous acid. The analogy with other combinations already discussed, where there is in general a doubling of the volume or halving of the molecule, leads us to suppose that it is the same in this case also, i.e. that the volume of the sulphur as gas is half that of the sulphurous acid, and consequently also half that of the oxygen with which it combines. On this supposition the density of sulphur gas will be to that of oxygen as 100 to 95.02/2, or 47.51; which gives 2.323 for the density of gaseous sulphur, taking that of air as unity. The masses of the molecules being according to our hypothesis in the same ratio as the densities of the gases to which they belong, the mass of the molecule of the sulphuric radical will be to that of hydrogen as 2.323 to 0.07321, or as 31.73 to 1. One of these molecules combined, as we have said, with two of oxygen, will form sulphurous acid (division of the molecule being left out of account), and combined with yet another molecule of oxygen, will form sulphuric acid. Accordingly, sulphurous acid should be analogous to nitric acid, with regard to the relative number of molecules of its constituents, sulphuric acid having no analogue amongst the nitrogen compounds. The molecule of sulphurous acid, having regard to division, will be equal to (31.73 + 2 x 15.074)/2, or 30.94, as would also be obtained directly by dividing the density 2.265 of sulphurous acid gas by that of hydrogen gas. As for the molecule of sulphuric acid, it cannot be determined, for we do not know whether there is further division of the molecule on its formation, or not. 
Dalton had supposed that sulphuric acid was composed of two molecules of oxygen to one of radical, and sulphurous acid of one molecule of oxygen to one of sulphur. These two assumptions are incompatible, for according to Gay-Lussac's results the quantities of oxygen in these two acids for a given quantity of radical, are represented by 1 and 1 1/2. Besides, in his determination of the molecule he set out from a wrong value for the composition of sulphuric acid, and it is only by chance that the mass 15 which he assigns to it, bears to his value for the mass of the oxygen molecule a ratio which approaches that presented by these two substances on our hypothesis.
Phosphorus has as much analogy with sulphur that we might apparently assume that phosphoric acid also is composed of three molecules of oxygen to one of radical, and phosphorous acid of only two of oxygen to one of radical. On this assumption we may calculate approximately the mass of the molecule of the phosphoric radical. Rose found by a method analogous to that which had been employed for sulphuric acid, that phosphoric acid contains about 115 parts by weight of oxygen to 100 of phosphorous. There ought to be a little more oxygen in it if we suppose that phosphorus, like sulphur, contains hydrogen. As an approximation we can make this increase in the same proportion as we have seen holds good for sulphuric acid in accordance with the specific gravity of sulphurous acid, and thus bring the quantity of oxygen up to 120. We then find from our hypotheses that the mass of the molecule of the phosphoric radical is about 38, that of hydrogen being taken as unity. Dalton also has adopted for phosphorous and phosphoric acids, hypotheses analogous to those he had made for sulphurous and sulphuric acids; but since he used different values for the elements of these acids by weight, he arrived at a determination of the molecule of phosphorus, which does not bear the same ratio to his determination of the molecule of sulphur as ought to exist, according to us, between these molecules: he has fixed that of phosphorus as 8, hydrogen being unity. 
Let us now see what conjecture we may form as to the mass of the molecule of a substance which plays in nature a far greater part than sulphur or phosphorus, namely, that of carbon. As it is certain that the volume of carbonic acid is equal to that of the oxygen which enters into it, then, if we admit that the volume of carbon, supposed gaseous, which forms the other element, is doubled by the division of its molecules into two, as in several combinations of that sort, it will be necessary to suppose that this volume is the half of that of the oxygen with which it combines, and that consequently carbonic acid results from the union of one molecule of carbon and two of oxygen, and is therefore analogous to sulphurous and phosphorous acids, according to the preceding suppositions. In this case we find from the proportion by weight between the oxygen and the carbon, that the density of carbon as gas would be 0.832 with respect to that of air as unity, and the mass of its molecule 11.36 with respect to hydrogen. There is, however, one difficulty in this supposition, for we give to the molecule of carbon a mass less than that of nitrogen and oxygen, whereas one would be inclined to attribute the solidity of its aggregation at the highest temperatures to a higher molecular mass, as is observed in the case of the sulphuric and phosphoric radicals. We might avoid this difficulty by assuming a division of the molecule into four, or even into eight, on the formation of carbonic acid; for in that way we should have the molecule of carbon twice or four times as great as that we had just fixed. But such a composition would not be analogous to that of the other acids; and, besides, according to other known examples, the assumption or not of the gaseous state does not appear to depend solely on the magnitude of the molecule, but also on some other unknown property of substances. Thus we see sulphurous acid in the form of a gas at the ordinary temperature and pressure of the atmosphere not withstanding its large molecule, which is almost equal to that of the solid sulphuric radical. Oxygenated muriatic acid gas has a density, and consequently a molecular mass, still more considerable. Mercury, which as we shall see further on, should have an extremely large molecule, is nevertheless gaseous at a temperature infinitely lower than would be necessary to vaporise iron the molecule of which is smaller. Thus there is nothing to prevent us from regarding carbonic acid to be composed in the manner indicated above,--and therefore analogous to nitric, sulphuric, and phosphoric acids,--and the molecule of carbon to have a mass expressed by 11.36.
Dalton has made the same supposition as we have done regarding the composition of carbonic acid, and has consequently been led to attribute to carbon a molecule equal to 4.4, which is almost in the name ratio to his value for that of oxygen as 11.36 is to 15, the mass of the molecule of oxygen according to us.
Assuming the values indicated for the mass of the molecule of carbon and the density of its gas, carbonic oxide will be formed, according to the experiments of M. Gay-Lussac, of equal parts by volume of carbon gas and oxygen gas; and its volume will be equal to the sum of the volumes of its constituents: it will accordingly be formed of carbon and oxygen united molecule to molecule, with subsequent halving--all in perfect analogy to nitrous gas.
The mass of the molecule of carbonic acid will be:
(11.36+2 x 15.074)/2 = 20.75 = 1.5196/0.07321,and that of carbonic oxide will be:
(11.36 + 15.074)/2 = 13.22 = 0.96782/0.07321
The density of oxymuriatic acid according to MM. Gay-Lussac and Thenard is 2.470 referred to atmospheric air as unity; this gives for its molecule referred to that of hydrogen as unity, 33.74, adopting the density of hydrogen determined by MM. Biot and Arago. According to Davy 100 English cubic inches of oxymuriatic gas weigh 74.5 grains, and an equal volume of hydrogen gas 2.27. This would give for the molecule of the former 74.5/2.27 = 32.82. These two estimates differ very little from the mass that Davy himself, from other considerations, assigns to this substance, viz., 32.9. It follows from the experiments both of Gay-Lussac and Thenard, and of Davy, that muriatic acid gas is formed by the combination of equal volumes of oxymuriatic gas and hydrogen, and that its volume is equal to their sum. This means, according to our hypothesis, that muriatic acid is formed of these two substances united molecule to molecule, with halving of the molecule, of which we have already had so many examples. Accordingly the density of muriatic acid gas, calculating from that given above for oxymuriatic gas, should be 1.272; it is 1.278 according to the experiments of MM. Biot and Gay-Lussac. If we suppose this last determination to be exact, the density of oxymuriatic gas should be 2.483, and the mass of its molecule 33.91. Should we prefer to adopt this value, the mass of the molecule of muriatic acid will be 34.91/2 = 17.45 = 1.278/0.07321. The determination of the specific gravity of the muriatic acid gas by Davy, according to which 100 cubic inches of that gas weigh 39 grains, would give numbers only slightly different, viz., 33.36 for the mass of the molecule of oxymuriatic acid, and 17.18 for that of muriatic acid.
In the same way the other metals present for the most part two oxides in which the quantities of oxygen are as 1 to 2, so that from the proportions of their elements by weight, we may determine in the same manner the mass of their molecules. I find for example, 206 for the molecule of lead, 198 for that of silver, 123 for copper etc. 
M. Gay-Lussac has suspected that the equality of volume between a gaseous alkali and acid, which by their union from a neutral salt, may be general. That is as much as to say on our hypothesis, that neutral salts are composed of acid and alkali united molecules to molecule; but certain considerations appear to be opposed to the admission of this principle in all its generality. The idea of acidity, alkalinity, and neutrality, which still seems to me the most comformable to the phenomena, is that which I have given in my Memoir on this subject (Journal de Physique, tome lxix.). According to it, all substances form amongst themselves a series, in which they play in part of acid or alkali with respect to one another; and this series is the same as that on which depends the positive or negative electricity they develop on mutual contact. I express by the term of oxygenicity the property in virtue of which substances are ranked in the scale, placing first those which play the part of an acid with respect to the others. In this scale there is a point about which are placed the substances we term neutral, above it are those which are absolutely acid, below it are those which are alkaline, when their state of aggregation permits them to exhibit these qualities. Lastly, composite substances occupy in this scale a place intermediate between those of which they are composed, having regard to the degree of oxygenicity and to the proportion by weight of these constituents substances; so that a neutral substance results from the combination of two substances, one acid, the other alkaline, in a certain proportion (see the Memoir referred to).  The recognition of the simple ratios observed on combination, and in particular in cases where neutral substances are the result, leads us now to a more exact manner of conceiving the state of neutrality. The oxygenicity in two bodies which combine, cannot be supposed to have such a relation to the masses of their molecules, that from the union of certain definite numbers of these molecules there should result a certain definite degree of oxygenicity which would be that of neutrality, and would only depend, as we have already assumed for oxygenicity in general, on the proportion by weight and the degree of oxygenicity of the components. It appears, then, that we must admit that the degree of oxygenicity which corresponds to neutrality is not quite fixed, although approximating more or less to a fixed limit, and that this state depends on the excess of mass of one of the components (from which the acid or alkaline quality might result) being prevented from exercising these qualities by the simple combination with the contrary principle which retains it by its attraction, although the compound otherwise might have a state of aggregation permitting it to act as an acid or an alkali, if it were endowed with these qualities. The excess of mass thus held back is that which is necessary to complete a certain simple relation between the number of combining molecules. Thus amongst the different simple ratios in which molecules can combine, there is one which gives neutrality; that, namely, which gives the compound approximating most closely to the definite point of oxygenicity mentioned above, so that if in the compound formed according to this ratio, one of the component principles let one molecule of the other escape, or took up one in addition, the compound would diverge further from this precise point, about which there oscillate, as it were, the oxygenicities of the various neutral compounds; and it is this point which would give the neutral state in the combination of two substances which could combine in all proportions, or in ratios expressible by any number of molecules whatever. It is evident that this way of regarding the neutrality of compound substances reconciles the theory given in the Memoir quoted with the ideas put forward by M. Haüy in his Traité de Physique.
According to this theory it is evident that if the oxygenicity of two acids and two alkalies which combine respectively in pairs, is not extremely different, and if at the same time the mass of the molecule of one of the acids is not in a different ratio to its alkali from that of the other acid with regard to its own alkali, the ratio between the numbers of molecules which gives neutrality may be the same in both compounds; but in the contrary case, the ratio may vary in such a way that instead of the equality of volumes, or of combination molecule to molecule which we see between carbonic and a few other acids on the one hand and ammonia on the other, there may be other simple ratios such as 1 to 2, &c., which give the neutral state. Nevertheless, the simplicity which will always exist amongst these ratios, in conjunction with the information we may obtain from other sources as to the mass of the molecules and the degree of oxygenicity of the components, will sometimes put us in a position to determine, or at least conjecture, what are the simple ratios which may occur in a given case; but it is the task of experiment to confirm or correct these theoretical estimates.
He finds nearly the same mass, viz., 13.4, by taking as his starting-point the density of sulphuretted hydrogen; which his experiments make equal to 1.0645, a result only slightly different from Kirwan's, and by assuming that this gas (which contains, as we know, its own volume of hydrogen combined with sulphur) is composed of one molecule of sulphur and one of hydrogen. As we suppose the molecule of sulphur to be nearly twice as great, we must assume that this gas is the product of the union of one molecule of the radical with two at least of hydrogen, and that its volume is twice that of the gaseous radical, as in so many other cases. I say at least with two molecules of hydrogen, for if there were hydrogen already in ordinary sulphur, as known experiments on this substance indicate, its quantity also must be added. If, for instance, ordinary sulphur were composed of one molecule of sulphuric radical and one of hydrogen. Sulphuretted hydrogen would be composed of three molecules of hydrogen and one of radical. This could be decided by the comparison of the specific gravities of sulphuretted hydrogen and sulphurous acid gas, if both were known exactly. For example, supposing Davy's determination for sulphuretted hydrogen to be exact, the molecule of the sulphuric radical, on the supposition of only two molecules of hydrogen, would be 27.08, that of hydrogen being taken as unity; but on the supposition of three molecules of hydrogen, 27.08 would still be the sum of one molecule of radical and one of hydrogen, so that the former would be reduced to 26.08. If the exact density of sulphurous acid gas confirmed one or the other of these results, it would confirm by that means one or other of these hypotheses: but we are not sufficiently agreed about these densities to be able to draw any conclusion is this respect from the determinations hitherto existing.
It is on the assumption of this last value for the molecule of potassium that Davy finds 32.9 for that of oxymuriatic acid, calculating from the composition of muriate of potash, and assuming that this salt is formed of one molecule of potassium with one of acid. If we suppose the molecule of potassium to have a different mass, we must admit another relative number of molecules in the muriate, since both from our hypothesis and from the density of the gas, 32.9 is very nearly the molecule of oxymuriatic acid. On the supposition that the molecule of potassium is 81, and that in sulphide of potassium the combination is molecule to molecule, the molecule of sulphur will be about 27 instead of 13 1/2 as found by Davy on the later assumption, which will bring about between this result and that derived from sulphurous acid according to our calculations the agreement which exist between Davy's values.