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in chemistry. When Wohler, in 1825, analysed his cyanic acid, and Liebig his quite different fulminic acid in 1824, the composition of both compounds proved to be absolutely the same, containing each in round numbers 28% of carbon, 33% of nitrogen, 37% of oxygen and 2% of hydrogen. This fact, inconsistent with the then dominating conception that difference in qualities was due to difference in chemical composition, was soon corroborated by others of analogous nature, and so Berzelius introduced the term isomerism (Gr. iaoµepits, composed of equal parts) to denominate the existence of the property of substances having different qualities, in chemical behaviour as well as physical, notwithstanding identity in chemical composition. These phenomena were quite in accordance with the atomic conception of matter, since a compound containing the same number of atoms of carbon, nitrogen, oxygen and hydrogen as another in the same weight might differ in internal structure by different arrangements of those atoms. Even in the time of Berzelius the newly introduced conception proved to include two different groups of facts. The one group included those isomers where the identity in composition was accompanied by identity in molecular weight, i.e. the vapour densities of the isomers were the same, as in butylene and isobutylene, to take the most simple case; here the molecular conception admits that the isolated groups in which the atoms are united, i.e. the molecules, are identical, and so the molecule of both butylene and isobutylene is indicated by the same chemical symbol C4118, expressing that each molecule contains, in both cases, four atoms of carbon (C) and eight of hydrogen (H). This group of isomers was denominated metamers by Berzelius, and now often "isomers" (in the restricted sense), whereas the term polymerism (Gr. iroXb, many) was chosen for compounds like butylene, C 4 H 8, and ethylene, C 2 H 4, corresponding to the same composition in weight but differing in molecular formula, and having different densities in gas or vapour, a litre of butylene and isobutylene weighing, for instance, under ordinary temperature and pressure, about 2.5 gr., ethylene only one-half as much, since density is proportional to molecular weight.

A further distinction is necessary to a survey of the subdivisions of isomerism regarded in its widest sense. There are subtle and more subtle differences causing isomerism. In the case of metamerism we can imagine that the atoms are differently linked, say in the case of butylene that the atoms of carbon are joined together as a continuous chain, expressed by CC C C, normally as it is called, whereas in isobutylene the fourth atom of carbon is not attached to the third but to the second carbon atom, i.e. -C-C<ci. Now there are cases in which analogy of internal structure goes so far as to exclude even that difference in linking, the only remaining possibility then being the difference in relative position. This kind of isomerism has been denominated stereoisomerism (q.v.) often stereomerism. But there is a last group belonging here in which identity of structure goes farthest. There are substances such as sulphur, showing difference of modification in crystalline state - the ordinary rhombic form in which sulphur occurs as a mineral, while, after melting and cooling, long needles appear which belong to the monosymmetric system. These differences, which go S hand in hand with those] in other properties, e.g. specific heat and specific gravity, are absolutely confined to the crystalline state, disappearing with it when both modifications of sulphur are melted, or dissolved in carbon disulphide or evaporated. So it is natural to admit that here we have to deal with identical molecules, but that only the internal arrangement differs from case to case as identical balls may be grouped in different ways. This case of difference in properties combined with identical composition is therefore called polymorphism. To summarize, we have to deal with polymerism, metamerism, stereoisomerism, polymorphism; whereas phenomena denominated tautomerism, pseudomerism and desmotropism form different particular features of metamerism, as well as the phenomena of allotropy, which is merely the difference of properties which an element may show, and can be due to polymerism, as in oxygen, where by the side of the ordinary form with molecules 02, we have the more active ozone with 03. Polymorphism in the case of an element is illustrated in the case of sulphur, whereas metamerism in the case of elements has so far as yet not been observed; and is hardly probable, as most elements are built up, like the metals, from molecules containing only one atom per molecule; here metamerism is absolutely excluded, and a considerable number of the rest, having diatomic molecules, are about in the same condition. It is only in cases like sulphur with octatomic molecules, where a difference of internal structure might play a part.

Before entering into detail it may be useful to consider the nature of isomerism from a general standpoint. It is probable that the whole phenomenon of isomerism is due to the possibility that compounds or systems which in reality are unstable yet persist, or so slowly change that practically one can speak of their stability; for instance, such systems as explosives and a mixture of hydrogen and oxygen, where the stable form is water, and in which, according to some, a slow but until now undetected change takes place even at ordinary temperatures. Consequently, of each pair of isomers we may establish beforehand which is the more stable; either in particular circumstances, a direct change taking place, as, for instance, with maleic acid, which when exposed to sunlight in presence of a trace of bromine, yields the isomeric fumaric acid almost at once, or, indirectly, one may conclude that the isomer which forms under greater heat-development is the more stable, at least at lower temperatures. Now, whether a real, though undetected, change occurs is a question to be determined from case to case; it is certain, however, that a substance like aragonite (a mineral form of calcium carbonate) has sensibly persisted in geological periods, though the polymorphous calcite is the more stable form. Nevertheless, the theoretical possibility, and its realization in many cases, has brought considerations to the front which have recently become of predominant interest; consequently the possible transformations of isomers and polymers will be considered later under the denomination of reversible or dynamical isomerisms.

Especially prominent is the fact that polymerism and metamerism are mainly reserved to the domain of organic chemistry, or the chemistry of carbon, both being discovered there; and, more especially, the phenomenon of metamerism in organic chemistry has largely developed our notions concerning the structure of matter. That this particular feature belongs to carbon compounds is due to a property of carbon which characterizes the whole of organic chemistry, i.e. that atoms attached to carbon, to express it in the atomic style, cling more intensely to it than, for instance, when combined with oxygen. This explains a good deal of the possible instability; and, from a practical point of view, it coincides with the fact that such a large amount of energy can be stored in our most intense explosives such as dynamite, the explanation being that hydrogen is attached to carbon distant from oxygen in the same molecule, and that only the characteristic resistance of the carbon linkage prevents the hydrogen from burning, which is the main occurrence in the explosion of dynamite. The possession of this peculiar property by carbon seems to be related to its high valency, amounting to four; and, generally, when we consider the most primitive expression of isomerism, viz. the allotropy of elements, we meet this increasing resistance with increasing valency. The monovalent iodine, for instance, is transformed by heating into an allotropic form, corresponding to the formula I, whereas ordinary iodine answers to I 2. Now these modifications show hardly any tendency to persist, the one stable at high temperatures being formed at elevated temperatures, but changing in the reverse sense on cooling. In the divalent oxygen we meet with the modification called ozone, which, although unstable, changes but slowly into oxygen. Similarly the trivalent phosphorus in the ordinary white form shows such resistance as if it were practically stable; on the other hand the red modification is in reality also stable, being formed, for instance, under the influence of light. In the case of the quadrivalent carbon, diamond seems to be the stable form at ordinary temperatures, but one may wait long before it is formed from graphite.

This connexion of isomerism with resistant linking, and of this with high valency, explains, in considerable measure, why inorganic compounds afforded, as a rule, no phenomena of this kind until the systematic investigation of metallic compounds by Werner brought to light many instances of isomerism in inorganic compounds. Whereas carbon renders isomerism possible in organic compounds, cobalt and platinum are the determining elements in inorganic chemistry, the phenomena being exhibited especially by complex ammoniacal derivatives. The constitution of these inorganic isomers is still somewhat questionable; and in addition it seems that polymerism, metamerism and stereoisomerism play a part here, but the general feature is that cobalt and platinum act in them with high valency, probably exceeding four. The most simple case is presented by the two platinum compounds PtC12(NH3)2, the platosemidiammine chloride of Peyrone, and the platosammine chloride of Jules Reiset, the first formed according to the equation PtC1 4 K 2 + 2NH 3 = PtCl 2 (NH 3) 2 + 2KC1, the second according to Pt(NH 3) 4 C1 2 =PtC1 2 (NH 3) 2 +2NH 3, these compounds differing in solubility, the one dissolving in 33, the other in 160 parts of boiling water. With cobalt the most simple case was discovered in 1892 by S. Jorgensen in the second dinitrotetramminecobalt chloride, [Co(NO 2) 2 (NH 3) 4 ]Cl, designated as flavo - whereas the older isomer of Gibbs was distinguished as croceo-salt. An interesting lecture on the subject was delivered by A. Werner before the German chemical society (Ber., 1907, 40, p. 15). (See Cobalt; Platinum.) Dealing with organic compounds; it is metamerism that deserves chief attention, as it has largely developed our notions as to molecular structure. Polymerism required no particular explanation, since this was given by the difference in molecular magnitude. One general remark, however, may be made here. There are polymers which have hardly any inter-relations other than identity in composition; on the other hand, there are others which are related by the possibility of mutual transformation; examples of this kind are cyanic acid (Cnoh) and cyanuric acid (Cnoh) 3, the latter being a solid which readily transforms into the former on heating as an easily condensable vapour; the reverse transformation may also be realized; and the polymers methylene oxide (CH 2 O) and trioxymethylene (CH20)3. In the first group we may mention the homologous series of hydrocarbons derived from ethylene, given by the general formula C 7 ,H 2 ,,,, and the two compounds methylene-oxide and honey-sugar C6H1206. The cases of mutual transformation are generally characterized by the fact that in the compound of higher molecular weight no new links of carbon with carbon are introduced, the trioxymethylene being O CH2-0 CH 2 whereas honey-sugar correg probably C C H 2 -0% sponds to CH 2 0H[[ChohChohChohChohCho]], each point representing a linking of the carbon atom to the next. This observation is closely related to the above-mentioned resistivity of the carbon-link, and corroborates it in a special case. As carbon tends to hold the atom attached to it, one may presume that this property expresses itself in a predominant way where the other element is carbon also, and so the linkage represented by -C-C-is one of the most difficult to loosen.

The conception of metamerism, or isomerism in restricted sense, has been of the highest value for the development of our notions concerning molecular structure, i.e. the conception as to the order in which the atoms composing a molecule are linked together. In this article we shall confine ourselves to the fatty compounds, from which the fundamental notions were first obtained; reference may be made to the article Chemistry: Organic, for the general structural relations of organic compounds, both fatty and aromatic.

A general philosophical interest is attached to the phenomena of isomerism. By Wilhelm Ostwald especially, attempts have been made to substitute the notion of atoms and molecular structure by less hypothetical conceptions; these ideas may some day receive thorough confirmation, and when this occurs science will receive a striking impetus. The phenomenon of isomerism will probably supply the crucial test, at least for the chemist, and the question will be whether the Ostwaldian conception, while substituting the Daltonian hypothesis, will also explain isomerism. An early step accomplished by Ostwald in this direction is to define ozone in its relation to oxygen, considering the former as differing from the latter by an excess of energy, measurable as heat of transformation, instead of defining the difference as diatomic molecules in oxygen, and triatomic in ozone. Now, in this case, the first definition expresses much better the whole chemical behaviour of ozone, which is that of "energetic" oxygen, while the second only includes the fact of higher vapour-density; but in applying the first definition to organic compounds and calling isobutylene "butylene with somewhat more energy" hardly anything is indicated, and all the advantages of the atomic conception - the possibility of exactly predicting how many isomers a given formula includes and how you may get them - are lost.

To Kekule is due the credit of taking the decisive step in introducing the notion of tetravalent carbon in a clear way, i.e. in the property of carbon to combine with four different monatomic elements at once, whereas nitrogen can only hold three (or in some cases five), oxygen two (in some cases four), hydrogen one. This conception has rendered possible a clear idea of the linking or internal structure of the molecule, for example, in the most simple case, methane, CH 4, is expressed by H H-C-H H It is by this conception that possible and impossible compounds are at once fixed. Considering the hydrocarbons given by the general formula C x H y, the internal linkages of the carbon atoms need at least xi bonds, using up 2(xI) valencies of the 4x to be accounted for, and thus leaving no more than 2(x-11) for binding hydrogen: a compound C 3 H 9 is therefore impossible, and indeed has never been met. The second prediction is the possibility of metamerism, and the number of metamers, in a given case among compounds, which are realizable. Considering the predicted series of compounds C7,H2,,+2, which is the well-known homologous series of methane, the first member, the possible of isomerism lies in that of a different linking of the carbon atoms. This first presents itself when four are present, i.e. in the difference between C - C - C - C C-C-C and With this compound C 4 H 10, named butane, C isomerism is actually observed, being limited to a pair, whereas the former members ethane, C 2 H 6, and propane, C 3 H 8, showed no isomerism. Similarly, pentane, C 5 H 12, and hexane, C6H14, may exist in three and five theoretically isomeric forms respectively; confirmation of this theory is supplied by the fact that all these compounds have been obtained, but no more. The third most valuable indication which molecular structure gives about these isomers is how to prepare them, for instance, that normal hexane, represented by CH 3 CH 2 CH 2 CH 2 CH 2 CH3, may be obtained by action of sodium on propyl iodide, CH 3 CH 2 CH 2 I, the atoms of iodine being removed from two molecules of propyl iodide, with the resulting fusion. of the two systems of three carbon atoms into a chain of six carbon atoms. But it is not only the formation of different isomers which is included in their constitution, but also the different ways in which they will decompose or give other products. As an example another series of organic compounds may be taken, viz. that of the alcohols, which only differ from the hydrocarbons by having a group OH, called hydroxyl, instead of H, hydrogen; these compounds, when derived from the above methane series of hydrocarbons, are expressed by the general formula C7,H27,+10H. In this case it is readily seen that isomerism introduces itself in the three carbon atom derivative: the propyl alcohols, expressed by the formulae CH 3 CH2CH 2 0HandCH 3 CHOHCH3, are known as propyl and isopropyl alcohol respectively. Now in oxidizing, or introducing more oxygen, for instance, by means of a mixture of sulphuric acid and potassium bichromate, and admitting that oxygen acts on both compounds in analogous ways, the two alcohols may give (as they lose two atoms of hydrogen) CH 3 CH 2 COH and CH 3 C0CH 3. The first compound, containing a group COH, or more explicitly 0 = CH, is an aldehyde, having a pronounced reducing power, producing silver from the oxide, and is therefore called propylaldehyde; the second compound containing the group - CCOC - behaves differently but just as characteristically, and is a ketone, it is therefore denominated propylketone (also acetone or dimethyl ketone). And so, as a rule, from isomeric alcohols, those containing a group - CH 2.0H, yield by oxidation aldehydes and are distinguished by the name primary; whereas those containing CHOH, called secondary, produce ketones. (Compare Chemistry: Organic.) The above examples may illustrate how, in a general way, chemical properties of isomers, their formation as well as transformation, may be read in the structure formula. It is different, however, with physical properties, density, &c.; at present we have no fixed rules which enable us to predict quantitatively the differences in physical properties corresponding to a given difference in structure, the only general rule being that those differences are not large.

Perhaps a satisfactory point of view may be here obtained by applying the van der Waals' equation A(P-{-a/V2)(V-b)=2T, which connects volume V, pressure P and temperature T (see Condensation Of Gases). In this equation a relates to molecular attraction; and it is not improbable that in isomeric molecules, containing in sum the same amount of the same atoms, those mutual attractions are approximately the same, whereas the chief difference lies in the value of b, that is, the volume occupied by the molecule itself. For what reason this volume may differ from case to case lies close at hand; in connexion with the notion of negative and positive atoms, like chlorine and hydrogen, experience tends to show that the former, as well as the latter, have a mutual repulsive power, but the former acts on the latter in the opposite sense; the necessary consequence is that, when those negative and positive groups are distributed in the molecule, its volume will be smaller than if the negative elements are heaped together. An example may prove this, but before quoting it, the question of determining b must be decided; this results immediately from the above quotation, b being the volume Vat the absolute zero (T =0); so the volume of isomers ought to be compared at the absolute zero. Since this has not been done we must adopt the approximate rule that the volume at absolute zero is proportional to that at the boiling-point. Now taking the isomers H 3 CCC1 3 (M„ = 108) and C1H 2 CCHC1 2 (M„ = we see the negative chlorine atoms heaped up in the left hand formula, but distributed in the second; the former therefore may be presumed to occupy a larger space, the molecular volume, that is, the volume in cubic centimetres occupied by the molecular weight in grams, actually being 108 in the former, and 103 in the latter case (compare Chemistry: Physical). An analogous remark applies to the boiling-point of isomers. According to the above formula the critical temperature is given by 8aA/54b, and as the critical temperature is approximately proportional to the boiling-point, both being estimated on the absolute scale of temperature, we may conclude that the larger value of b corresponds to the lower boilingpoint, and indeed the isomer corresponding to the left-hand formula boils at 74°, the other at 114°. Other physical properties might be considered; as a general rule they depend upon the distribution of negative and positive elements in the molecule.