Polymorphism. It has been shown in Chapter VII. that Mitscherlich had in several instances proved the possibility of the occurrence of the same substance in two different forms, notably sodium dihydrogen phosphate NaH₂PO₄.H₂O, calcium carbonate CaCO₃ (as calcite and aragonite), the metallic sulphates known as vitriols, and the chemical element sulphur, and that he gave to the phenomenon the name “dimorphism.” Since that time large numbers of dimorphous substances have been discovered, and several which occur in three forms and even a few in no less than four totally distinct forms. Until the establishment of the geometrical theory of crystal structure, as expounded in Chapter IX., this phenomenon of polymorphism gave rise to endless fruitless discussion. It was most generally attributed to the different nature of the so-called “physical molecule,” which was supposed to be an aggregate of chemical molecules and the unit of the space-lattice determining the crystal system; the different polymorphous varieties were supposed to be built up of structural units or physical molecules consisting of an aggregation of a different number of chemical molecules. Several attempts were made by various investigators, notably by Muthmann and by Fock, to determine the number of chemical molecules constituting the physical molecule.

All these efforts, however, ended unsatisfactorily, and in the year 1896 the author showed, in a memoir^[11] on “The Nature of the Structural Unit,” that in general the physical molecule is a myth, and that the chemical molecule is the only structural unit possessing the full chemical composition of the substance in question; and that its centre of gravity, or better, any representative point within it, such as a particular atom, is the unit point of the Bravais space-lattice of the crystal structure, while the atoms of which the chemical molecule are composed, arranged stereometrically identically similarly in all the molecules, are the points of the individual point-systems which make up the combined point-system. This does not imply a necessarily parallel and identically orientated arrangement of all the molecules, as at first postulated by Sohncke and which is a fact for his sixty-five point-systems; for in accordance with the conclusions of Schönflies, von Fedorow, and Barlow discussed in Chapter IX., cases are possible in which alternate molecules may be arranged as each other’s mirror images. Such are the cases of external molecular compensation or molecular combination, two oppositely enantiomorphous sets of molecules balancing each other within the structure, but by exterior compensation as regards the molecule itself. Moreover, the principle of mirror-image symmetry enters, as stated in Chapter IX, altogether into the constitution of no less than 165 of the 230 types of homogeneous structure possible to crystals.

Hence the conception of a physical molecule is totally unnecessary and, moreover, erroneous. The alkali sulphates and selenates exhibit dimorphism, one member of the series, ammonium selenate, having only hitherto been observed in the pure state in the second, monoclinic, form, and never in the ordinary rhombic form; and the author has conclusively proved for these salts, and also for the double salts which they form with the sulphates and selenates of magnesium, zinc, iron, nickel, cobalt, manganese, copper, and cadmium, that the chemical molecule is the only kind of molecule present, and that its representative points are, as just stated, the nodes of the Bravais space-lattice of the crystal structure, determining both the system of the crystal and its obedience to the law of rational indices.

The explanation of polymorphism thus proves, in the light of the results which have now been laid before the reader, to be a remarkably simple one. Special pains were taken in explaining those results to show that the temperature had a great deal to do with the conditions of equilibrium of the crystal structure, for it determines the intermolecular distances, that is, the amount of separation of the molecules, and thus controls their possibility of movement with respect to one another. Now the behaviour of the chemical molecules on the advent of crystallisation is undoubtedly largely influenced by the stereometric arrangement of the atoms composing them, and it is possible for the latter to be such that the molecules may take up several different parallel or enantiomorphously related positions; or as we have just seen, a regular alternation within the crystal structure of such mirror-image positions may be taken up. These different arrangements, whether parallel or enantiomorphously opposite, may be, and probably will be, of different degrees of stability, each of these different forms finding its maximum stability of equilibrium at some particular temperature, which is different for the different varieties. Hence, at a series of ascending or descending temperatures, assuming the pressure to remain the ordinary atmospheric, these different types of homogeneous crystal structures will be most liable to be produced, each at its own particular temperature, for which stable equilibrium of that crystal structure occurs.

These different assemblages are as a rule quite dissimilar, certainly in the crystal elements, often in class and not infrequently in system. Generally two such different crystalline forms are all that are possible within the life-range of temperature of the substance. But occasionally three or even as many as four such different forms are found to be capable of existence within the temperature life-limits of the substance.

Polymorphism is thus completely and simply explained as a direct result of the establishment of the geometrical theory of crystal structure as laid down in Chapter IX. The equilibrium of the homogeneous structure is a function of the temperature, and the stereometric arrangement of the atoms in the chemical molecule of a substance may be such as permits of two or more homogeneous arrangements of the molecules in assemblages of varying degrees of stability, but each of which has a maximum stability at a particular temperature. Hence, within any given range of temperature such a substance will assume that type of homogeneous arrangement of its molecules in a crystal which corresponds to the stablest equilibrium within these temperature limits, assuming the pressure constant within the bounds of the usual atmospheric variations. Employing the language of physical chemistry, such a substance will thus present two or more different solid “phases,” each characterised by its specific crystalline form, the elementary parallelepipedon of which is quite a distinct one. Each phase possesses also its own specific optical and other physical properties, such as melting point, solubility, thermal expansion, and elasticity.

It would appear as if the element sulphur is also polymorphous in this sense, for the monoclinic prismatic form (Fig. 2, Plate I.)—the best known and most easily prepared, from the state of fusion, of all the forms other than the common rhombic form, in which sulphur is found in the neighbourhood of volcanoes and in which it is also deposited from solution in carbon bisulphide—is of distinctly lower stability, the crystals passing in a few days into powder composed of minute crystals of the stable rhombic variety. But in the case of carbon, with its totally different and apparently at ordinary temperatures equally stable varieties of octahedral-cubic diamond (Fig. 82, Plate XVI.) and hexagonal graphite, there is some doubt; for although the diamond is converted into graphite at a red heat in the electric arc, it is doubtful whether we are not in the presence of a case of chemical polymerism or allotropy, like the case of ozone, where three atoms of oxygen compose the molecule, instead of the two atoms in the molecule of ordinary oxygen. The fact that the negatively electrified electronic corpuscles of the Crookes tube cause the same conversion of diamond into graphite, producing according to Parsons and Swinton a temperature of 4,890° C. in the act, is evidence in favour of allotropy, as the charged corpuscles are a very likely agent for breaking down such atomic combinations. Moreover, diamond is volatilised out of contact with air at 3,600° C. without liquefaction, and the vapour when cold condenses as graphite. But there is reason to believe, from experiments by Sir Andrew Noble and Sir William Crookes, that under great pressure carbon does liquefy at 3,600° C., and that the liquid drops on cooling crystallise as diamond.

The yellow and red varieties of phosphorus may also be due to a similar cause, the yellow variety, which forms excellent crystals, corresponding to P₄, while the red variety may correspond to a molecule composed of a different number of atoms than four.

Another view of the nature of polymorphism has lately been brought forward by Lehmann, as the result of his remarkable experimental discovery of “liquid crystals,” to which fuller reference will be made in Chapter XVI. This new view is, however, but an amplification of the foregoing explanation of polymorphism, indicating the possible mode in which the stereometric position of the atoms in the molecule does actually influence and even determine the particular homogeneous structure which shall be erected, and explains why the temperature plays such an important rôle. Lehmann’s theory is that any one definitely stereometrically constituted chemical molecule can only display one particular homogeneous structure and form of crystal, and that when at a particular temperature the system or class of symmetry is altered, this occurs because the stereometric arrangement of the atoms within the molecule is altered, that is, a new form of molecule is produced, which naturally gives rise to a new form of crystal. As far as the author understands it, this does not mean an isomeric change from the chemical point of view, the chemical compound remaining the same, but that the stereometric positions of the atoms have been changed, without altering their chemical attachments, but sufficiently to change the nature of the point-system which they produce. A significant fact in support of this view is that the molecules of the substances forming liquid crystals are usually very complicated and extended ones, comprising a large number of atoms, the molecules, in fact, corresponding in length with the long names of the organic substances of which they are generally composed.

Lehmann’s work has certainly proved that the molecule is endowed with more individuality than has hitherto been ascribed to it, and he even shows that there is some ground for believing that his liquid crystals are such because this directive orientative force resident in the molecules themselves maintains them in their mutually crystallographically orientated positions even in the liquid state, which may be and sometimes is as mobile as water. It thus appears that any general acceptance of Lehmann’s ideas will only tend to amplify and further explain the nature of polymorphism on the lines here laid down, the temperature of conversion of one form into another being merely that at which either a different homogeneous packing is possible, or that at which the stereometric relations of the atoms in the molecule are so altered as to produce a new form of point-system without forming a new chemical compound.

Enantiomorphism of Crystalline Form and Optical Activity. It has already been stated that two supplementary forms which are similar but not identical, the one being the inverse or mirror-image reflection of the other, as a right-hand glove is to a left-hand one, are termed “enantiomorphous.” Also it has been shown that all those crystal forms which have no plane of symmetry, either of simple symmetry or alternating symmetry (which is equivalent to saying that no centre of symmetry is present in addition to no plane of symmetry), are enantiomorphous, and that such forms belong to eleven specific classes. It has further been shown that the introduction of this principle of mirror-image symmetry or enantiomorphism into the conditions already laid down by Bravais and Sohncke for a homogeneous structure, by von Fedorow, Schönflies, and Barlow, enabled those investigators to derive the remaining 165 of the 230 possible types of homogeneous structures compatible with crystal structure, over and above the 65 already established by Bravais and Sohncke, and thus to complete the geometry of crystal structure, when the units of such structure are represented by points. Sohncke subsequently accepted the new principle, and modified his own theory so as to bring it into line with it. He exhibited some disinclination, however, at first, to accept the idea—which is a part of the assumption of the other three authors just referred to, and which appears to be absolutely necessary to explain one or two of the most complicated of the crystal classes—of the possibility of two enantiomorphous kinds of molecule being present in the crystal of the same single substance, the balancing of the two sets having the effect of producing mirror-image symmetry of the whole crystal, that is, the development of a plane of symmetry.

Now the whole subject is of deep interest, both physical and chemical as well as crystallographical, inasmuch as it is precisely such substances as show enantiomorphism,—and can thus exist in two forms, one of which is the mirror-image of the other and not its identical counterpart, the two being like a pair of gloves,—which are found to possess the property of rotating the plane of polarised light and which are therefore said to be “optically active.” Moreover, the property may be displayed by both the crystals and their respective solutions, or by the crystals only. If, therefore, two optical antipodes of the same substance are known, one rotating the plane of polarisation to the right and the other rotating it to the same extent to the left, their crystals invariably exhibit mirror-image symmetry with respect to each other. The converse does not necessarily hold good, however, that a crystal possessing the symmetry of one of these eleven classes will always exhibit optical activity.

Pasteur^[12] was the first to recognise this important relation between enantiomorphous crystalline form and optical activity, in the case of tartaric acid, which has the empirical formula C₄H₆O₆ and the constitution:

Tartaric acid was isolated by Scheele in 1769, and its discovery was described in the very first memoir of that distinguished chemist. Another very similar acid, as regards some of its more apparent properties, was afterwards, in 1819, described by John of Berlin, and investigated by Gay-Lussac in 1826; the latter obtained it from the grape juice deposits of the wine manufactory of Kestner at Thann in the Vosges. It was still more fully investigated by Gmelin in 1829, who called it racemic acid (Traubensäure). But it needed the genius of Berzelius to prove that it really had the same composition as tartaric acid, although so different to that acid in some of its properties.

We have here as a matter of fact, the first instance brought to light involving the principle of isomerism, the existence of two or more distinct compounds having the same chemical composition as regards the numbers of atoms of the same elements present, but differing in chemical or physical properties, or both, owing to the different arrangement of those atoms within the molecule. The “isomers” may be chemical or purely physical; the latter involves no alteration of the linking of the atoms, but merely of their disposition in space, and is the kind met with in the case of the tartaric acids.

Biot, so noted for his optical researches, showed afterwards that tartaric and racemic acids behave optically differently in solution, an aqueous solution of the former rotating the plane of polarisation to the right whilst that of racemic acid is optically inactive, not rotating the plane of polarisation at all. That is, if the dark field be produced in the polariscope, by crossing the polarising and analysing Nicol prisms at right angles, tartaric acid solution will restore the light again, and the analyser will have to be rotated to the right in order to reproduce darkness. In the case of tartaric acid, the crystals themselves also rotate the plane of polarisation, the amount being as much as 11°.4 in sodium fight for a plate of the crystal one millimetre thick. On the other hand, neither the solution nor the crystals of racemic acid rotate the plane of polarisation at all.

Pasteur’s discovery, made in the year 1848, consisted in finding that racemic acid is really a molecular compound of two physical “isomers,” namely, of ordinary tartaric acid, which, as we have seen, rotates the plane of polarisation to the right, and of another variety of tartaric acid which rotates the beam of polarised fight to the same extent to the left. The latter and ordinary tartaric acid he therefore distinguished as lævo tartaric acid and dextro-tartaric acid respectively. Pasteur went even further than this, in discovering yet a fourth variety of tartaric acid, which is optically inactive like racemic acid, but which cannot be split up into two optically active antipodes.

Indeed, it has since been shown that there are three varieties of this truly inactive tartaric acid; they are cases of isomerism of the chemical molecule itself, that is, the stereometric arrangement of the atoms in the molecule is different in the three cases. For the molecule of tartaric acid—in common with the molecules of all carbon compounds the solutions of which, or which themselves in the liquid state, rotate the plane of polarisation—possesses an asymmetric carbon atom, an atom of carbon which is linked by its four valency attachments to four different kinds of atoms or radicle groups; indeed, the molecule of tartaric acid contains two such asymmetric carbon atoms, namely, the two in the pair of CHOH groups. For each of these carbon atoms is linked by one attachment to the carbon atom of the outer COOH group, by another to an atom of hydrogen, by a third to the oxygen of the group OH, and by its fourth attachment to the carbon atom of the other group CHOH, which carries the rest of the molecule, that is, this attachment is to the other half-molecule CHOH.COOH. Hence, it is quite obvious that there can be two different dispositions of the atoms in space, one of which would be the mirror-image of the other, while leaving the arrangement of the atoms about the two asymmetric carbon atoms dissimilar and not symmetrical in mirror-image fashion. That is, the two dispositions would render the molecules in the two cases enantiomorphous with respect to each other, and these two would be the arrangements respectively in the two optically active varieties. That this is the correct explanation of the ordinary dextro variety and the lævo variety of tartaric acid can now admit of no doubt.

But if the groups round the two asymmetric carbon atoms are symmetrical in mirror-image fashion, there will be compensation within the molecule itself, and the substance will be optically inactive from internal reasons. This is the explanation of the optically inactive variety which is unresolvable into any components. The different varieties of this inactive form are doubtless due to the different possibilities of arrangement of the atoms in each half, while leaving the two halves round each asymmetric carbon atom symmetrical to each other.

We now know that the decomposable inactive variety, racemic acid, may be readily obtained by· dissolving equal weights of the ordinary dextro and lævo varieties in water and crystallising the solution by slow evaporation at the ordinary temperature. For further investigation has fully borne out the conclusion of Pasteur, that racemic acid simply consists of a molecular compound of the two active varieties. It is thus itself inactive because it is externally compensated, the two kinds of enantiomorphous molecules being alternately regularly distributed throughout the whole crystal structure, the very case which von Fedorow, Schönflies, and Barlow assumed to be possible, and which Sohncke only tardily admitted. The crystalline form of racemic acid is, as was to be expected, quite different from the monoclinic form of the active tartaric acids, being triclinic; and indeed it is not crystallographically comparable with the active form, inasmuch as the crystals of racemic acid contain a molecule of water of crystallisation, whereas the active varieties crystallise anhydrous.

Ordinary dextro and lævo tartaric acids crystallise in identical forms of the sphenoidal or monoclinic-hemimorphic class of the monoclinic system, the class which is only symmetrical about a digonal axis, the unique symmetry plane of the monoclinic system, which also operates when full monoclinic symmetry is developed, being absent in this class. Hence the interfacial crystal angles, the monoclinic axial angle, and the axial ratios are identical for the two varieties. But the crystals are hemimorphic, owing to the absence of the symmetry plane, and complementarily so, the dextro variety being distinguished by the presence of only the right clino-prism {011}, while the lævo variety is characterised by the presence only of the left-clino-prism {0̄11}, these two complementary forms, each composed of only two faces and which on a holohedral crystal exhibiting the full symmetry of the monoclinic system would both be present as a single form of four faces, being never both developed on the same optically active crystal.

This hemimorphism of the two kinds of crystals will be rendered clear by Figs. 63 and 64, representing typical crystals of dextro and lævo tartaric acids which are obviously the mirror images of each other.

A remarkable discovery was made by Pasteur in connection with one of the salts of racemic acid, sodium ammonium racemate, Na(NH₄)C₄H₄O₆, or

which is obtained by adding ammonia to the readily procurable salt hydrogen sodium racemate. Sodium ammonium racemate was found by Pasteur to be decomposable into the salts of dextro and lævo tartaric acids, on crystallisation of a solution saturated at 28° C. by inoculation with a crystal of either of those active salts. The solution on cooling being in the state of slight supersaturation, which we now know from the work of Ostwald and of Miers as the metastable condition, corresponding to the interval between the solubility and supersolubility curves (see Fig. 98), if a crystal say of sodium ammonium lævo-tartrate be introduced, this variety crystallises out first and can be separated from the residual dextro-salt, which can then be subsequently crystallised. Moreover, in certain direct crystallisations of sodium ammonium racemate without such specialised inoculation, Pasteur found all the crystals hemimorphic, some right-handed and some left-handed, and he was actually able to isolate from each other crystals of the two varieties. On separate recrystallisation of these two sets of crystals, he found them to retain permanently their right or left-handed character, indicating that the molecules themselves composing these crystals were enantiomorphous. Their solutions correspondingly rotated the plane of polarisation of light in opposite directions. Pasteur afterwards obtained from the dextro-salt pure ordinary (dextro) tartaric acid, and from the lævo-salt the lævo-acid, by converting them first into the lead salts and then precipitating the lead as sulphide by sulphuretted hydrogen.

In the case of lævo tartaric acid, this was its first isolation, as it had hitherto been unknown. Gernez afterwards independently found that a saturated solution of sodium ammonium racemate affords crystals of the lævo-salt just as readily as of the dextro-salt; if a crystal of either salt be introduced, crystals corresponding to that variety are produced.

Another most fruitful observation of Pasteur, the principle of which has since been the means of isolating one of the two constituents of many racemic compounds, was that when the spores of Penicillium glaucum are added to a solution of racemic acid containing traces of phosphates the ordinary dextro component is destroyed by the organism, while the lævo component is unattacked so long as any dextro remains; hence, if the fermentation operation be stopped in time the lævo-acid may be isolated and crystallised. Why a living organism thus eats up by preference one variety only, possessing a particular right or left-handed screw structure, of a compound containing the same elementary constituents chemically united in the same manner, remains a most interesting biological mystery.

The crystals of both dextro and lævo tartaric acids prove to be pyro-electric, that is, develop electric excitation when slightly heated. The end which exhibits the development of the clinodome develops positive electricity in each case, when the crystal is allowed to cool after warming, so that the two varieties are oppositely pyro-electric, just as they are oppositely optically active. The most convenient method of demonstrating the fact is to dust a little of Kundt’s powder, a mixture of finely powdered red lead and sulphur, through a fine muslin sieve on to the crystal as it cools. The sulphur becomes negatively electrified and the red lead positively by mutual friction of the particles in the sifting, and the sulphur thus attaches itself to the positively electrified part of the crystal and the red lead to the negatively electrified end. This phenomenon of the development by the two varieties of an optically active substance of opposite electrical polarity has since been shown to be a general one.

Finally, on mixing concentrated solutions containing equivalent weights of dextro and lævo tartaric acid Pasteur observed that heat was evolved, a sign of chemical combination, and the solution afterwards deposited on cooling crystals of racemic acid. Hence, the only conclusion possible is that racemic acid must be a molecular compound of the two oppositely optically active tartaric acids. It thus partakes of the character of a double salt, analogous to potassium magnesium sulphate for instance. Consequently the crystal structure is one in which alternating molecules of the two acids are uniformly distributed, and the case is actually presented of two oppositely enantiomorphous sets of molecules producing a homogeneous structure.

This interesting pioneer case of tartaric acid has been the cause of the term “racemic” being applied to the inactive form of a substance when it is decomposable into two oppositely optically active enantiomorphous varieties of the substance. No well authenticated exception has been found, in all the many instances which have been observed of the phenomenon since Pasteur’s time, to the fact that optically active substances exhibit what was formerly termed hemihedrism; that is, expressing the case in accordance with our later more accurate ideas of crystal structure as elucidated in previous chapters, such substances invariably belong to classes of symmetry possessing less than the full number of elements of symmetry possible to the system to which the class belongs. These classes are eleven in number, those possessing no plane of symmetry; they are, namely, the asymmetric class of the triclinic system, the sphenoidal class of the monoclinic system (to which the two tartaric acids, dextro and lævo, belong), the bisphenoidal class of the rhombic system, the pyramidal and trapezohedral classes of the trigonal, tetragonal, and hexagonal systems, and the tetrahedral-pentagonal-dodecahedral and pentagonal-icositetrahedral classes of the cubic system.

The optical activity has been proved by Le Bel and Van t’Hoff to be due in most cases to enantiomorphism of the chemical molecules, that is, to the enantiomorphous stereometric arrangement of the atoms in the molecules, and therefore also,—as we have just seen, in accordance with the geometrical theory of crystal structure,—of the combined point-system in the case of each of the two varieties.

The point-systems are probably of a spiral screw-like character, either right-handed or left-handed, as has been shown by Sohncke to be the case for the two varieties of quartz, which crystallises in the trapezohedral class of the trigonal system, one of the eleven classes just enumerated. The example afforded by quartz will be developed fully in the next two chapters, as this beautifully crystallised mineral enables us to study and to demonstrate the phenomena of optical activity in a unique manner and on the large scale.

The solutions as well as the crystals are usually optically active in the cases where, as in the instance of the tartaric acids, the substances are soluble in water or other solvent. Occasionally, however, the optical activity is lost by dissolving in a solvent, and in such cases it is the point-system only, and not the molecules themselves, which is enantiomorphous. Sodium chlorate, NaClO₃, is an instance of this kind. Moreover, a crystal can belong, as already mentioned, to one of the eleven above enumerated classes of symmetry without displaying optical activity, as all the point-systems possessing the symmetry of these eleven classes do not exhibit screw-coincidence movements. Barium nitrate, Ba(NO₃)₂, is such a case.

The two “optical antipodes,” as the dextro and lævo varieties are conveniently termed, of an optically active substance thus possess an enantiomorphous crystal structure; but they are alike in their physical properties such as density, melting point, optical refraction and optic axial angle, cleavage, and elasticity. The crystal angles are identical for the forms which are developed in common by them, and which are usually those which the particular low class of symmetry possesses in common with the holohedral class of the system. The crystallographic difference between the two varieties comes in with respect to the specific forms characteristic of the particular class of lower than full systematic symmetry, and these forms are never displayed in common by the two varieties, this being the essence of the enantiomorphism. When the crystals are not rich in faces, however, it frequently happens that only the common forms of higher symmetry just referred to are developed on the crystals, and the two varieties are then indistinguishable in exterior configuration; it is only on testing their rotatory power, either by means of a section-plate of the crystal or by means of a solution, or their pyro-electric properties, or, lastly, their etch-figures afforded by a trace of a solvent (which etchings on the crystal faces are enantiomorphous and an excellent indication of the true symmetry), that their real character can be ascertained. Many mistakes have been made in the past, and crystals assigned to a higher than their true class of symmetry, owing to the investigation of only a single crop of crystals fortuitously poor in the number of forms displayed.

In the racemic form, if one should be deposited from the mixed solutions of the two optical antipodes as a molecular compound of the latter, we have an occurrence akin to polymerism, that is, the combination into a single whole entity of a number of molecules, essentially two in the case of racemism. Just as polymeric varieties of organic substances are always found to have quite different crystalline forms, so an optically inactive racemic form of a substance is generally quite different crystallographically to the dextro and lævo varieties. But there is usually some similarity along specific zones of the crystals, a kind of isogonism or morphotropy being developed, such as has been shown to occur, for instance, by Armstrong and Pope in the case of the substance sobrerol.^[13]

Besides the true racemic form it is often observed that under certain conditions crystals are obtained which appear to combine the characters of both the dextro and lævo varieties, exhibiting both series of distinguishing hemimorphic or hemihedral forms on the same crystal; that is, they show the full, holohedral, symmetry of the system. This has been shown by Kipping and Pope^[14] to be due to repeated twinning, thin layers of the right and left-handed varieties being alternated, just, in fact, as in the interesting form of quartz known as amethyst, to which reference with experimental demonstration will be made in Chapter XIV.; the whole structure assumes in consequence the simulated higher symmetry which usually accompanies laminated twinning. Such forms have been termed “pseudo-racemic.” In their memoir (loc. cit., p. 993) Kipping and Pope summarise a large amount of highly interesting work on this chemico-crystallographic subject which has been carried out by them, and it may be useful to quote their precise definition of the relationship between racemic and pseudo-racemic substances. They say:

“We define a pseudo-racemic substance as an intercalation of an equal, or approximately equal, proportion of two enantiomorphously related components, each of which preserves its characteristic type of crystalline structure, but is so intercalated with the other as to form a crystalline individual of non-homogeneous structure. A solid racemic compound, on the other hand, may be defined as a crystalline substance of homogeneous structure which contains an equal proportion of two enantiomorphously related isomerides.

“The relations holding between a mere mixture of optical antipodes, a pseudo-racemic substance, and a racemic compound, are closely parallel to those existing between a crystalline mixture, an isomorphous mixture, and a double salt. The crystallographic methods, by which a double salt can be distinguished from an isomorphous mixture, may be directly applied to distinguish between racemic and pseudo-racemic substances. Thus, according as the crystalline substance obtained from a mixture of two salts resembles or differs from either of its components crystallographically, it is regarded either as an isomorphous mixture or a double salt; similarly, an inactive externally compensated substance, which closely resembles its active isomerides crystallographically, is to be considered as pseudo-racemic, whereas when the contrary is true, it is to be regarded as racemic.”

The work of Kipping and Pope may be regarded as having finally vindicated and substantiated the law of Pasteur, that substances of enantiomorphous molecular configuration develop enantiomorphous crystalline structures, and that the crystal structures assumed by enantiomorphously related molecular configurations are themselves enantiomorphously related.

This subject, the main results and principles of which have now been elucidated, may well be closed with a reference to an interesting case of enantiomorphism and optical activity which the author has himself investigated,^[15] and which is very similar to the case of the tartaric acids. It had been previously shown^[16] by P. F. Frankland and W. Frew, that when calcium glycerate was submitted to the fermenting action of the Bacillus ethaceticus one-half only of the glyceric acid was destroyed, and that the remaining half was optically active, rotating the plane of polarisation to the right.

Now glyceric acid,

has manifestly one so-called asymmetric carbon atom (that is, a carbon atom the four valencies of which are satisfied by attachment to four different monad elements or groups), that belonging to the CHOH group. There are consequently two possible arrangements of the molecule in space, probably corresponding to the two optically active varieties, namely, those represented, as far as is possible in one plane, as below, the asymmetric carbon atom (not shown in the graphic representation) being supposed to be at the centre of the tetrahedron, which is usually taken to represent a carbon atom with its four valencies.

Dextro-glyceric acid itself proved to be an uncrystallisable syrup, but the calcium salt, Ca(C₃H₅O₄)₂.2H₂O, was obtained in crystals sufficiently well-formed to permit of a complete crystallographic investigation, which the author undertook by friendly arrangement with Prof. Frankland. Although the acid itself is dextro-rotatory, aqueous solutions of the calcium salt are lævo-rotatory to the extent of –12.09 units of “specific rotation” for sodium light.

The crystals were colourless well-formed prisms which proved to be of monoclinic symmetry, the best individuals being formed by very slow evaporation of the aqueous solution. They were terminated at both ends by pyramid and dome faces, and sometimes grew to the length of a centimetre. The actual crystal elements found after a full series of measurements were as under:—

Crystal system: monoclinic.

Class of Monoclinic System: sphenoidal or monoclinic-hemimorphic.

Habit: prismatic.

Monoclinic axial angle: β=69° 6′.

Ratio of axes: a : b : c = 1.4469 : 1 : 0.6694.

Forms observed:

It will thus be seen that the system and the class are precisely those of the two active tartaric acids, which renders the case the more interesting. The usual appearance of the crystals is shown in Fig. 65, and the stereographic projection is given in Fig. 66, which will elucidate the symmetry more clearly, the plane of projection being the plane of symmetry The latter, however, in this class is inoperative, the two ends of the digonal symmetry axis, which runs perpendicularly to the plane of the paper, being differently terminated, as in the tartaric acids. The faces of the forms o = {111} and m = {011} were never found developed on the left side of the symmetry plane, that is, on the left side of the crystal as drawn in Fig. 65, the symmetry plane running perpendicularly to the paper vertically from front to back; they were only present on the right. Conversely, the faces of s = {̄1̄11} and n = {̄2̄11} were never found developed on the right, but only on the left of the plane of possible symmetry.

Moreover, it was frequently observed that the right-hand faces (110) and (̄110) of the primary prismform p were much more brilliant and truly plane than those on the left hand, (1̄10) and (̄1̄10), which were usually dull and often curved, as were also frequently the faces of the left-hand forms s and n. The right-hand distinguishing forms m and o, on the contrary, were generally most brilliant and gave admirable reflections of the goniometer signal-slit.

The following table represents the results of the angular measurements, twelve different well-formed individual crystals having been employed. The angles marked with an asterisk were the important angles the mean observed values of which were accepted as correct, being the best measured angles, and which were therefore used as the basis of the calculations.

There is a moderately good cleavage parallel to the basal plane c = {001}.

The optical properties afford conclusive proof of the monoclinic nature of the symmetry. The plane of the optic axes is perpendicular to the possible symmetry plane, b = {010}, and the first median line makes an angle of 23° with the vertical axis c, emerging consequently nearly normal to the basal plane c = {001}, so that a section-plate parallel to the c-faces, or a tabular crystal or cleavage plate parallel to c, shows the optic axial rings and brushes well. The values of the apparent optic axial angle in air, 2E, and of the true optic axial angle within the crystal, 2V_a, the latter measured with the aid of a pair of accurately ground section-plates perpendicular to the first and second median lines and immersed in oil, are given in the next table.

The intermediate refractive index β was found to be as under—

The double refraction was also determined and found to be of positive sign.

The optical properties of calcium dextro-glycerate thus confirm absolutely the monoclinic nature of the symmetry, as regards the crystal system. And it was conclusively demonstrated by the goniometrical part of the investigation that the exterior symmetry was not such as agreed with holohedral monoclinic symmetry, but with that of the sphenoidal class, in which the only one of the two elements of monoclinic symmetry (the plane of symmetry and the digonal axis of symmetry) in operation is the digonal axis, thus leaving the two terminations of that axis, at opposite sides, right and left, of the possible symmetry plane, unsymmetrical. And this is precisely the symmetry which is characteristic of an enantiomorphous optically active substance.

Unfortunately, the corresponding lævo-salt has not yet been obtained in measurable crystals, but there can be no doubt that whenever such are forthcoming they will display enantiomorphism in the precisely opposite and complementary sense, the facial forms characteristic in this dextro-salt of the right termination of the digonal axis being absent on that side of the systematic symmetry plane but developed on the left side instead, and vice versa, and that the two enantiomorphous forms will together make up the whole of the faces required by the full symmetry of the monoclinic system.

A concrete instance like this, worked out practically in the laboratory, brings home the precise nature of this interesting relationship, between crystallographic and molecular enantiomorphism on the one hand and optical activity on the other hand, in a particularly clear and forcible manner. It is hoped that this brief account of it will also consequently have been of assistance to the reader, in more clearly appreciating the main points of this chapter.