POLARITY AND ENANTIOMORPIIISM. Any figure, such as a solid of revolution, which has one line in it in reference to which the figure is symmetrical may be said to have an axis, and the points at which the axis cuts the surface of the figure are poles. But the term polarity when applied to material figures or substances is usually confined to eases where there are not only a definite axis and poles, but where the two poles have distinct characters which enable us to recognize them and say which is which. It is in this sense that the word is used here.

Two figures or two portions of matter are said to be enantiomorple to each other when these forms are not superposable, i.e., the one will not fit into a mould which fits the other, but the one is identical in form with the mirror image of the other.

Polarity. - As examples of polarity we may take an awn and B by finding that it is easy to stroke from say A to B but not in the opposite direction. As an example of enantiomorphism we may take our two hands, which will not fit the same mould or glove, but the one of which resembles in figure the mirror image of the other.

It will be seen by and by, that there is a close relation between polarity- and enantiomorphisrn.

In the examples of polarity just given the condition composed of equal numbers of three different kinds of particles, these particles being arranged along the axis in the order A abcabc abc B, read from 13 to A. Even with particles all of the same kind Ive can imagine this sort of polarity produced by such an arrangement as A I aa a a a aa a a rt aa a a tt B, where the density varies periodically as we pass along the axis, but so that the order of variation is different in passing from A to II and from B to A. There is another sort of polarity produced also by' an arrangement such as that described above, but here not along the axis but we stroke the muff in one sense about the axis. This arrangement also produces polarity, for there is a real difference between the two ends of the mutt The one is that into which we put our right hand, the other that into which we put our left hand if the fur is to lie downwards in front. If we reverse the ends we find the fur sticking up in front, and we have thus as little difficulty in distin-guishing the two poles from one another in this as in the former sort of polarity.

Yce can easily imagine the particles of a compound sub-stance to be arranged so as to produce this polarity. To take a simple case, - the molecules of the substance may be formed of three atoms a, and c, arranged a b with the planes of the molecules all at right angles to the axis, so that on turning the substance about the axis in one sense the atoms in every molecule follow each other in the order abc, and of course in the opposite order when the rotation is reversed.

In these examples the polarity is due to an arrangement of the matter at rest, but both kinds of polarity may be produced by motion. Thus a rot,ating body has polarity of the second kind; the axis is the axis of rotation, and the two poles differ from each other as the two ends of a muff do. A wire along which a current of electricity is passim, has polarity of the first kind ; and a magnet, in whicFi currents of electricity may be supposed to circulate about the axis, has polarity of the second kind.

There is an important difference between these two kinds of polarity. We have seen that they depend on two different conditions--the one on an arrangement of matter or motion along the axis, the other on a similar arrange-ment about the axis. This gives rise to a difference in their relation to their mirror image.

If we hang up a cat's tail by one end, say the A end, in front of a mirror, we see in the mirror the image of a cat's tail hanging by its A end. But if we hang up a muff by one end, say the right-hand end, before a mirror, we see in the mirror the image of a muff hanging by its left-hand end. If we put our hands into the muff in the usual way and stand before the mirror we see a person with his hands in a, muff in the usual way. But his right and left hands correspond to our left and right hands respectii-ely, and the right and left ends of the muff in the mirror are the images of the left and right ends respectively of the real muff. Thus the mirror image of a body having polarity of the second kind has its polarity reversed.

But the muff and its image are not truly enantiomorph. They differ in position but in nothing else. Turn the one round and it will fit the other.

Magnetic and electric polarity having been already dis-cussed under ELECTRICITY and MAGNETISM, we shall here consider sonic cases of crystalline polarity'.

Both kinds of polarity occur in crystals.

We have no direct ineans of ascertaining how the ultimate particles of a crystal are arrano.ed, but it seems reasonable to suppose that there is a reration between the form of the cry-stal and the structure of its smallest parts ; and, when we find the crystals of particular substances always showing polarity of the one or the other kind, wo naturally suspect that this is the external indication of such an arrang,ement of the particles as has been shown above to be capable of producing structural polarity. Of crystalline polarity of the first kind the most striking instances are tourinaline and electric calamine (hydrated silicate of zinc), forms of which are shown in figs. 1 and 2, in which it will be seen that the cry-stals are not similarly terminated at the two ends. It is this kind of crystalline polarity (often called " heinimorphism ") which (as was first observed by- )fatly and more fully investigated by

As an instance of the same kind of crystalline polarity of a somewhat more complicated character, also associated with pyroelectricity, we may take boracite. The cry-stals of this mineral exhibit combinations of the cube, the rhombic dodecahedron, and the tetrahedron, as shown in fig. 3. If four lines are drawn corresponding to the four dia-gonals of the, cube, it will be observed that at the two ends of each of these axes the crystal is differently developed. (In the figure one of these axes is in-dicated by the dotted line.) These axes, therefore, resemble the single axis in tourmaline and electric calamine, and are also axes of pyroelectricity, the end at which the tetrahedral face is situated being the antilogous pole.' Scheelite, apatite, ilmenite, and fergusonite are examples are representations of forms of ilmenite, apatite, and fergusonite.

Crystalline polarity of both kinds no doubt depends on the arrangement of the molecules and on their structure; it manifests itself by the occurrence of hemihedral or hemiinorphic forms. A crystal may have a polar structure although the,se external marks of pol-arity are absent, just as the faces parallel to planes of cleavage do not appear on every crystal.

Another kind of contrast between the two complementary hemihedral Marbach observed that different specimens of iron pyrites (and also of cobalt glance) have very different thermoelectric characters, differing indeed from one another more than bismuth and antimony. Gustav Rose showed that these thermoelectrically- opposite kinds are also crystallographically opposite. There is indeed no geometrical difference between two opposite hemiliedral forms in the regular sy-stem, but Rose detected a differ-ence in the lustre and striation of the faces of the two kinds, and by examining the rare cases in which the two opposite pentagonal dodecahedra or tetragonal icositetrahedra occur on the same crystal proved that the one surface character belongs to the one, the other surface character to the other of the two complementary-hemihedra.

Enantiomorphism. - A figure having polarity of the first kind gives a mirror image resembling itself in form and in position ; a figure having polarity of the second kind gives a mirror image resembling itself in form but not in position - the poles being inverted. A figure the axis of which has both kinds of polarity will therefore give a mirror image not superposable to the figure itself, because the polarity' of the second kind is reversed while that of the first kind remains unchanged. The figure and its mirror image are enantiomorph, as well as polar. We can construct a figure which is enantiomorph to its mirror image but not polar. Imagine a muff so nia.de that in one half the fur lies the one way, and the opposite way in the other half (fig. 7, where the arrow-heads indicate the lie of the fur). In which-ever way we put our hands into this muff one end will be wrong ; the muff in the figure has, in fact, two right-hand ends. It has therefore no polarity ; the two ends are exactly alike. But there are two ways in which such a non-polar muff could be made - with two right-hand ends as in the figure, or with two left-hand ends, and these two forms are enantiomorph. A helix or screw has similar properties (compare fig. 8 with fig. 7); if uniform it is non-polar, but is either right- or left-handed. Hence the property which each of two enantiomorph bodies pos-sesses has been called by Sir William Thomson "helicoidal asymmetry."

As we have crystals exhibiting polarity of both kinds, so we have also enantiomorph crystals, indeed the word enantiornorph was first used by Naumann to express the relation between such crystals. The crystallographic theory of enantiomorph crystals has been very fully worked out. We may divide them into two groups - (1) those in which the helicoidal asymmetry depends on the presence of tetartohedral forms of the regular or of the hexagonal system, and (2) those in which it depends on the presence of hemiliedral forms of the rhombic systcni or hemimorphic forms of the monoclinic system.

In the first group the asymmetry seems to be produced by the manner in which the molecules, themselves sym-metrical, are arranged in the crystal. In the second group the molecules themselves appear to have helicoidal asym-metry. This is shown by the action of these substances on polarized light. We shall take examples from each group. If we allow a solution of sodium chlorate to crystallize we find that the crystals, which belong to the regular system, are of two kinds enantiomorph to each other. These are represented in fig. 9. The enantio-morphism depends on the combination_of_ the tetrahedron ally active, the amount of the rotation for the same strength of solution and the same length of path in it being the sa.me in both acids, but the sense of the rotation is right-handed in the one and left-handed in the other. It is clear that here we have to do with enantiomorph molecules. In ordinary physic,a1 properties such as den-sity, solubility, refracting power - in short, in everything not invoicing right- Or left-handedness - the acids are iden-tical. When mixed in equal proportions they unite and form racemic acid which is optically- inactive, and from racemic acid we can by various means recover unchanged the right and left-handed tartaric acids. We now know a considerable number of cases where, as in that of the two tartaric acids, both enantiomorphs have been discovered, and many where only one has as yet been found.

It is natural that we should ask. what peculiarity of constitution can give a molecule this helicoidal asymmetry? A very ingenious answer to this question was given simul-taneously and independently by the French chemist Le Bel and the Dutch chemist Van 't Hoff. Wc shall give a short statement of the essential points of this in-teresting theory.

All the known substances which are optically active in solution are compounds of carbon, and may be regarded as derived from marsh gas, a compound of one atom of carbon and four of hydrogen, by the replacement of hydro-gen by other elements or compound radicals. Now we do not know how the atoms of hydrogen are actually arranged relatively to each other and to the atom of carbon in the molecule of marsh gas, but, if we may make a sup-position on the subject, the most simple is to imagine the four hydrogen atoms at the apices of a regular tetrahedron in the centre of which is the carbon atom as in the diagrams (fig. 11), where C represents the posi-tion of the carbon atom and a, /3, 7, 8 that of the four atoms of hydrogen.

If these hydrogen atoms are replaced by atoms of other elements or by compound radicals we should expect a change of form of the tetrahedron. If two or more of the atoms or radicals united to the carbon atom are similar there is only one way of arranging them, but if they are all different there are two ways in which they 'nay be arranged, as indicated in the figures. It will be seen that these two arrangements are enantiornorph. in the figures the tetrahedron is represented as regular, but if the dis-tance from C depends on the nature of the atom the tetrahedron, when a, /3, y, and 8 are all different, will not be symmetrical, but its two forms will be enantiornorph. A carbon atom combined with four different atoms or com-pound radicals may therefore be called an asymmetric carbon atom.

Now all substances of ascertained constitution, the solutions of which are optically active, contain an asym-metric carbon atom, and their molecules should therefore, on the above hypothesis, have helicoidal asymmetry.

The converse is not generally true. Many- substances contain an asymmetric carbon atom but are optically inactive. It is easy to reconcile this with the theory; indeed, a little consideration will show that it is a necessary consequence of it.

Let us suppose that we have the symmetrical combina-tion of C with a, a, 13, 7 and that we treat the substance in such a way that one a is replaced by 8. The new arrangement is asymmetiical, and will be right or left as the one or the other a is replaced. But the chances for the two are equal, and therefore, as the number of mole-cules in any quantity we can deal with is very great, the ratio of the number of right-handed molecules in the new substance to the number of left-handed ones will be sensibly- that of unity-. It is therefore evident that by ordinary chemical processes we cannot expect to produce optically active from optically inactive substances ; all that we can get is an inactive mixture of equal quantities of the two oppositely active substances.

As these two substances have identical properties in every respect where right- or left-handedness is not in-volved, the problem of separating them is a difficult one. We may note three distinct ways in which the separation can be effected.

(1) By crystallization. For example, the right and left double tartrates of soda and ammonia crystallize in enan-tioniorph forms (fig. 12) and are less soluble in water than the double racetnate formed by their union. If therefore racemic acid (the optically inactive compound of equal I quantities of right and left tartaric acids) is half neutraland the pentagonal dodecahedron.1 Now when a ray of plane polarized light is passed through one of these crystals the plane of polarization is rotated, the amount of rotation being proportional to the length of the path in the crystal. The crystals having the form a rotate to the right, those having the form b to the left. They are therefore optically as well as crystallogmphically enantio-morph. But a solution of sodium chlorate is without action on the plane of polarization, even if the solution be made by dissolving only right-handed or only left-handed crystals, and if a crystal be fused the fused mass is optically inactive, so that it would seem that the optical activity depends on the arrangement of the niolecules in the crystal and not on any- enantiommphism in the mole-cules. The enantiornorphism of quartz crystals is indi-cated by the presence of faces of a tetartohedral form (vol. xvi. p. 389). The two kinds of crystals rotate the plane of polarization equally, but in opposite senses, when a plane polarized ray- is passed through a section cut at right angles to the axis of the crystal. Ltere also the optical activity ceases when crystalline structure is de-stroyed by fusion or solution.

Right-handed and left-handed tartaric acids crystallize in enantiomorph forms (fig. 10). Their solutions are opticized with soda and half with ammonia, we obtain an optically- inactive solution containing a mixture of the two double salts. If this solution is allowed to crystallize each salt crystallizes independently, and the crystals can be separated by picking them out. Further, a super-saturated solution of the one double salt is not made to crystallize by contact with a crystal of the other, so that if we make a supersaturated solution of the inactive mix-ture and drop into the vessel, at different places, two cry-stals one of the right the other of the left salt, crystal-lization occurs at each place, at the one of the one kind and at the other of the other.

By- the action of another optically- active substance. While the salts of the two opposite tartaric acids with an inactive base are precisely- alike in solubility, density, and other physical characters, and, if they crystallize, crystal-lize in the same form (or in enantimnorph forms), it is not at all so when the base is optically active; thus right tartaric acid forms a crystalline salt with left asparagine, while with the same base left tartaric acid gives an uncrystallizable compound.

By the action of living ferments. The minute fungi which act as ferments do not show any right- or left-hand-edness as far as their obvious anatomical structure is con-cerned, but Pasteur has shown that some of them are, if we may use the expression, physiologically asymmetrical. As an example we may give the very- interesting case of mandelic acid. This acid, which stands to benzoic alde-hyde (bitter almond oil) in the same relation as lactic acid does to common aldehyde, contains one a.symmetric carbon atom in its molecule. It is optically inactive, and there-fore, if Le Bel and Van 't Hoff's theory is true, it must be a mixture of two oppositely active acids. Now Lewko-witsch found that when Penicilium glaucum is cultivated in