COOH——C——H COOH——C——H ║ ║ COOH——C——H H——C——COOH Maleic acid. Fumaric acid. 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.