Considerations of this nature have led to the conclusion that if optical isomerism is to be ex plained, it is necessary to assume that the four atoms or groups held by an asymmetric carbon atom are situated at equal distances from the carbon atom and at equal distances from one an other—which is equivalent to assuming that the asymmetric carbon atom is situated at the cen tre of a regular tetrahedron, and the four differ ent atoms or groups held by it arc situated at the four corners of the tetrahedron. This, then, is the fundamental hypothesis of stereo-chemistry. Its application to the study of isomerism is very difficult to explain or to grasp without the use of models. A crude but sufficient form of model may be readily made in a few minutes from pasteboard, by cutting out four equal equi lateral triangles and fastening them together to form a regular tetrahedron, by means of strips of gummed paper. Small slips of paper of differ ent colors may be used to represent the four dif ferent atoms or groups and may be fastened to the corners by means of pins. With the aid of two such models it is easy to demonstrate the following cases: (1) With three slips of paper of one color and one of another color, only one ar is possible, which corresponds, for to the fact that only one nitro-methane, can be obtained. (2) With two slips of paper of one color and two of another color, again only one arrangement is possible, which corresponds, for instance, to the fact that only one methylene chloride, CH,C1, can be obtained. (3) With two slips of paper of one color, one slip of another color, and one of a third color, again only one arrangement is possible. which corresponds, for instance, to the fact that only one propionie acid. CH,(CH,) can be obtained. (4) With four slips of different colors two different arrangements are possible. which corresponds to the fact that only molecules con taining an asymmetric carbon atom, i.e. one linked to four different atoms or groups, can he different in spite of being made up of the same atoms linked together in the same manner. The two models will, in this ease, be like an object and its image in a mirror, or like the right hand and the left hand: turn both hands palm down ward and it is impossible to superpose them so that the corresponding fingers touch—the thumb of the right hand will touch, not the thumb, but the little finger of the left hand, etc. Thus the models will ilinstrate the difference between the two optically active lactic acids, malic acids, or mandelic acids (see above) ; or, in general, any pair of optical isomers whose molecules contain one asymmetric carbon atom. As an instructive example it may be demonstrated, by means of the models, why only one acetic acid, is possible; why only one monu-chlor-acetic acid, (C1) is possible; why only one di ehlor-aectie acid. is possible; why only one tri-chlor-acetic acid, is possible; why two optically isomeric chloro bromo-acetie acids, C(H) (Cl) (Br) (COOH), are possible; and why two optically isomeric chloro bromo-lluor-acetie acids, C(Cl) (Br) (F) (C0011), are possible.
As already pointed out above, optical isomers are invariably found to possess precisely the same chemical and physical properties and to differ only with regard to the direction in which they rotate the plane of polarized light. The question now suggests itself, How can such iso mers be separated from each other when mixed? This problem is so much the more important, be cause all reactions by which compounds with asymmetric carbon atoms may be produced from compounds containing no such atoms cause the simultaneous production of both bptical isomers in precisely equal quantities; so that a separa tion is required whenever optically active com pounds are to be prepared artificially (in nature either one or the other of a pair of optical isomers is often found isolated). Three methods have thus far been found for effecting the sepa ration. First, it is possible, in many cases, and under certain conditions of temperature, to sepa rate the isomers meehanieally—in these namely. in which the two crystallize from their solutions separately, In all such eases the two isomers are found to form enantiomorphous crys tals. Below, or sometimes above. the point or interval of temperature at which this takes place, the two isomers usually crystallize together, forming a double compound, the so-called `ra cemic' modification of the given compound. The racemic modification is optically inactive be cause its two components tend to rotate the plane of polarized light to the same extent in opposite directions. The second method of separating optical isomers is applicable only to acids and bases. If a mixture of two optically isomeric acids is treated with an optically active base, two salts result differing more or less con siderably in solubility, and therefore capable of being separated by fractional crystallization. The result is similar when a mixture of two optically active isomeric bases is treated with an optically active acid. Finally, the third method is based on the fact that certain processes of fermentation often destroy one of the optical isomers and leave the other intact. Thus, /evo-glucose may be prepared by subjecting to fermentation its mix ture with **rim-glucose. the latter alone being affected by the fermentation. The reason of such facts is not yet understood. It has been assumed by some that the living organisms (e.g. Penicil lium &ileum) causing fermentation are capable of discriminating, by a sort of instinct, between the isomers, and, while feeding on one, reject the other. But the lifeless enzymes (q.v.) ob tained from ferments have been shown to exercise the same action as the ferments themselves: and hence the peculiar action of the latter may he as sumed to be due to the purely chemical proper ties of their enzymes.
Passing now to the consideration of compounds whose molecules contain more than one asym metric carbon atom, the most important ease to be mentioned is that of tartaric acid, (COOH)