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nFe,Og; as this formula is quite in keeping with analyses it is assigned to ferric oxide. On comparing these crystallographically equivalent quantities of the two oxides it is found that 52:4x2 parts of chromium are replaced by 55'9 x 2 parts of iron, but as 52'4 has been determined to be the atomic weight of chromium it is argued that the atomic weight of iron is represented by the number 55'9. As the specific heat of iron multiplied into 55'9 gives the product 6:4, 55'9 is almost certainly the true atomic weight of iron. Again, the formulæ of potassium perchlorate and permanganate were at one time written KO.Clo, and KO.MnO, Berzelius proposed the formulæ KO.C10, and KO.MnO,, which on the system of notation now adopted became KCIO, and KMnO respectively: these formulæ represent crystallographically equivalent quantities of the two salts; if it is assumed that Cl represents the weight of the atom of chlorine (35-37), then Mn (55) probably represents the weight of the atom of manganese.

Observations of crystalline form have sometimes led the way to correct determinations of atomic weights or to changes in the received values of such weights. Thus H. Rose' gave the name of hyponiobium to a supposed allotropic form of the metal niobium ; but Marignac shewed that compounds of the hypothetical metal were identical in crystalline form with certain compounds of tin and titanium, and concluded that Rose's hyponiobium was itself isomorphous with the atomic groups SnF and TiF, and was therefore probably a compound. Further experiments shewed that the hyponiobium of Rose was really composed of niobium and oxygen in the proportions expressed by the formula NbO, provided that this group was regarded as crystallographically equivalent to SnF and TiF; if this were admitted it followed, from the analyses of the various compounds, that one atom of tin or titanium (117.8 or 48 parts by weight respectively) was replaced by 94 parts by weight of niobium, and that this number therefore represented the weight of the atom of niobium.

1 Pogg. Ann. 108. 273.

2 Ann. Chim. Phys. 60. 257. 3 Marignac's conclusions were afterwards confirmed by determinations, by

The facts, of which an outline has been given, shew that until more extended and precise knowledge of the law expressing the connections between crystalline form and chemical constitution is obtained, that method for determining the atomic weights of elements which is founded on these connections can be applied only tentatively and in a limited number of cases. The method may however now be of considerable service in suggesting lines of research bearing on the problems connected with atomic weight determinations.

It appears probable that the crystalline form of a substance is connected at once with the internal structure of the molecules of the substance and with the configuration of the molecules themselves. No attempt has been made, nor can in the present state of knowledge hopefully be made in any but the broadest manner, to apply to the facts of crystallography the dynamical theory of the molecular structure of matter.

36. I have endeavoured to shew that the most trustworthy method for determining molecular and atomic weights is founded on Avogadro's law, which is itself an outcome of the application of dynamical reasoning to a physical theory. Formerly it was supposed that strictly chemical evidence must be of paramount importance in determining these quantities. Although the superior importance of Avogadro's law

. is now admitted, this law can only be applied to a limited number of substances, hence we are frequently obliged to have recourse to purely chemical evidence in support of this or that molecular weight. The nature of this evidence must now be shortly illustrated.

In 1850 Brodie' endeavoured to shew that there exists no difference of kind between those reactions wherein elementary bodies are produced, or react, and those in which compound bodies are alone concerned. He supposed that the small Deville and Troost, of the specific gravity of gaseous chloride and oxychloride of niobium : see Compt, rend. 60. 122 I.

Roscoe's researches on the atomic weight of vanadium afford a very instructive example of the employnient of the results of crystallographic measurements in fixing atomic weights. Phil. Trans. for 1868, 1. et seq.

1 Phil. Trans. for 1860, 759, and also C. S. Journal, 4. 194.

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particles of elementary substances set free during reactions, or taking part in reactions, are composed of smaller parts which exhibit certain mutual polar relations. Silver chloride is not decomposed by oxygen, but it is readily acted on by potassium oxide with production of silver oxide and potassium chloride; hydriodic and iodic acids decompose one another with production of free iodine; silver oxide decomposes hydrogen peroxide to form silver, water, and free oxygen, half of the oxygen coming from the silver oxide and half from the peroxide; iodine decomposes barium peroxide with production of barium iodide and oxygen. These reactions were thus written by Brodie (translating into the new notation):

(1) AgAgcici+KKO=AGAGO+KKCICI
(2) #10,+5#1 = 38,7 +317
(3) Ħ,00+Aggo=#,+AgAg+00

(4) Baoo+1T=BaĪ1 + oo That part of Brodie's hypothesis which supposed a polar condition of atoms in molecules was not generally adopted by other chemists, but it was admitted that his researches established a general similarity of function and composition between elementary and compound molecules.

In the same year Williamson' distinguished between the atom of zinc in combination, and the free metal zinc (that is to say, he recognised that the atom of an element is not possessed of the same properties as the molecule of that element): he said it is not quite accurate to speak of 'zinc' as existing in zinc sulphate.

Recognising then that chemical reactions took place between molecules, chemists defined the molecule as the smallest part of a substance capable of taking part in a chemical change, or as the acting chemical unit. Supposing the atomic weights of the elements forming a compound to be known, the best method of determining the molecular weight of the compound appeared to be to find that formula which should express the atomic constitution in the simplest manner.

1 C. S. Journal, 4. 355.

Thus hydrogen and nitrogen are combined in ammonia in the proportion of 3 parts by weight of the former to 14 of the latter; assuming the atomic weights of these elements to be 1 and 14 respectively, the atomic composition of ammonia may be represented by the formula NH,; and as the reactions in which this substance takes part might all be represented as involving 17, or a whole multiple of 17 parts by weight of this compound, and moreover as the hydrogen in 17 parts by weight of ammonia was demonstrably divisible by chemical reactions into 3 parts, 17 was taken as the molecular weight of ammonia. An instructive illustration of this method of fixing a minimum molecular weight is furnished by Williamson's famous researches on ethers! The formulæ generally adopted for common alcohol and ether, previous to Williamson's work, were C,H,O, and C,H,O respectively (C = 6; O=8). Williamson allowed ethylic iodide to react on potassium alcoholate, expecting that ethylated alcohol would be produced,—thus C,H,KO, +CH I should give C,H,(C,H,O, +KI,—but the product was ordinary ether. If the generally accepted formula for ether were doubled the reaction would be explained, and ether would be regarded as an oxide of ethyl (CH),O, Again, Williamson found that when sulphuric acid acts on ethylic alcohol, and methylic alcohol is added to the mixture, a single substance having the properties of an ether, and the formula C,H,O or a whole multiple of this, distills over : if the formula of ether is C,H,O, then that of methylic ether is C,H,O, and a mixture of these ought to be obtained in the reaction just mentioned; but if ether is (CH),0, then the single ether obtained is probably methyl-ethyl oxide, i.e. CH,(C,H,O, (= 2C,H,O)". Thus was shewn, on purely

HOO. chemical grounds, the necessity of doubling the generally accepted molecular formula for ether.

No purely chemical method has been found for determining molecular weights which is capable of general application; each compound must be considered as a separate

1 See C. S. Journal, 4. 106 and 229.

• Translated into modern notation, these formulæ become (C,H3),0 and C,H,(CHO respectively.

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problem. The more important methods may however be roughly classified.

There is the method of analogies, which is well illustrated by the example of ether already considered. The smallest amount of sulphuretted hydrogen which takes part in chemical changes is represented by the formula H,S (assuming S=32) the hydrogen in this compound is replaceable in two parts—with production of KHS and KKS-hence the molecular formula is not less than H,S. But compounds of selenion and tellurium with hydrogen, analogous in general properties to sulphuretted hydrogen, are known; from the marked similarity between these two elements and sulphur it is very probable that the molecular formulæ of the two compounds in question are H, Se and H, Te respectively: as these formulæ satisfy the analytical numbers, they may be adopted. But if similar reasoning is applied to the cases of aluminum and indium-metals which are closely related it leads to a false conclusion : aluminum chloride is represented by the formula Al,Cla, hence the minimum molecular formula of indium chloride is probably In Clo; but this body has been recently gasified and shewn to have the molecular formula InClz.

The formula for water was once written HO. If potassium is thrown on to water, the solid product of the reaction is a white salt whose formula may be written HO.KO (0=8). But this substance is undecomposed by heat, and it exhibits none of the reactions which a compound of water with a metallic oxide might be expected to possess, nevertheless it contains hydrogen, oxygen and potassium; when it is fused with potassium, hydrogen is evolved and potassium oxide remains. The oxygen in this substance cannot be removed in parts. If the molecular formula of water is written H,0 (0=16) these facts are explained; the white solid then becomes KHO, and this formula--as the minimum molecular formula of the compound-is confirmed by the close analogies which exist between the properties of this body and those of alcohol, the molecular formula of which has been determined to be (C,H,OH. If water is acted on by chlorine or bromine, the simplest formula for the compound produced is HCl (or HBr);

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