which show no asymmetry, and hence no possibility of optical activity or enantiomorphous modifications.

In the case of maleic acid it will be seen that the same groups (COOH or H) are represented on the same side of the molecule—in other words, they are placed symmetrically in a plane—whereas in fumaric acid they are placed diagonally or are axially symmetrical. Isomers of the first case are classified as malenoid or cis-forms, while those of the latter are termed fumaroid or trans-forms.

Substances of the character referred to are, as a rule, mutually convertible with more or less ease; they are susceptible of what is called geometrical inversion. Thus fumaric acid may be readily converted into maleic acid by heating; maleic chloride is gradually transformed into fumaric chloride at ordinary temperatures. Sunlight, or a particular solvent, or the presence of some substance which acts as a catalyst, may effect the inversion. Cis and trans isomerism is also met with among cyclic compounds; it occurs among the terpenes; and certain alkaloids, as, for example, cocaïne, exhibit it.

Although the doctrine of stereo-chemistry was first enunciated in the case of carbon, and was, indeed, for a time solely confined to compounds in which carbon was the nucleal element, there is no a priori reason why the phenomenon should be so restricted. Van ’t Hoff, in fact, in 1878, discussed the question in relation to nitrogen compounds. Stereo-isomeric nitrogen derivatives were first obtained by Victor Meyer and his pupils, and the stereo-chemistry of nitrogen has since proved to be a very fruitful field of investigation, notably in the hands of Goldschmidt, Beckmann, Hantzsch and Werner, Le Bel, Ladenburg, Bamberger, Kipping, H. O. Jones, Pope, and others. The stereo-chemistry of nitrogen differs from that of carbon, inasmuch as variation of valency plays a far more important part in the case of nitrogen than it has hitherto been observed to do in that of carbon; the spatial representation of the trivalent nitrogen atom differs from that of the pentavalent atom. Le Bel, in 1891, succeeded in obtaining an optically active nitrogen enantiomorph by the application of Pasteur’s biochemical method. Optically active compounds have since been prepared by Pope and Peachey and H. O. Jones. Pope and Peachey have also prepared optically active compounds of sulphur, selenium, and tin; and Kipping has obtained an asymmetric compound of silicon.

In 1863 Geuther, and, independently, Frankland and Duppa, made known the existence of aceto-acetic ester. By Geuther this compound was termed ethyl-di-acetic acid

CH3.C(OH): CHCOOC2H5

by Frankland and Duppa it was considered to be acetone-carboxylic acid

CH3.CO.CH2.COOC2H5.

The essential difference in these formulæ, as the two names respectively indicate, is that the first implies that the ester has an acidic or hydroxylic character, proved by its forming characteristic salts; the other that it contains the group CO, proved by its yielding acetone and the usual reactions of the ketones. The attempt to settle the constitution of this substance gave rise to much controversy, and, as it was found to be very reactive, led to a great amount of conflicting experimental work. The ultimate result was to show that both formulæ are correct: at the time of reaction the ester is sometimes hydroxylic, at other times ketonic, or, adopting the terminology of Brühl, it sometimes shows the enol form, at other times the keto form. Other substances were subsequently found to behave in the same way. In 1885 the question was discussed by Laar, who suggested the term tautomerism (ταὐτό, the same; μέρος, a part) to denote the fact that one and the same substance could have structural formulæ varying with conditions of reaction and depending upon the migrations of certain of its atoms within the molecule. During the last twenty years a large number of examples of the kind have been discovered. They are found to occur, not only among aliphatic substances, but in cyclic and heterocyclic compounds. We now know that such intermolecular changes may occur by the migration of any of the elements or groups present in the molecule. Thus, to confine ourselves to simple and well-known examples, the transformation of sodium phenyl carbonate into sodium salicylate, discovered by Kolbe, is due to the wandering of an atom of hydrogen from the benzene residue to oxygen, thus: