312 P L P L administration is steadily going on, Polish employes being either I limited in number (to a fourth, for instance, for the examining magistrates), or else totally excluded from certain administrations (such as that of certain railways). The vexatious measures of Russian rule keep up a continuous feeling of discontent ; and, though it was allowed in 1864 that the agrarian measures would conciliate the mass of the peasantry with the Russian Government, it now appears that the peasants, while gaining in those feel ings of self-respect and independence which were formerly impossible to them, are not accommodating themselves to Russian rule ; the national feeling is rising into activity with them as formerly with the szlacfda, and it grows every day. There arc 27 towns the population of which exceeded 10,000 in habitants in 1880-82, and 66 towns having a population of more than 5000. The list of the former is as follows : Warsaw (1882), 406,260 ; Augustow, 11,100 ; Biata, 19,450 ; Czstochowo, 15,520 ; Garwolin, 14,620; Kalisz, 16,400; Kalwarya, 10,610; Kielce, 10,050 ; Konska "Wola, 14,300 ; Kutno, 13,210 ; task, 10,810; todz 49 590 ; tomza, 15,000 ; Lublin, 34,980 ; tukow, 11,030 ; Mtawa, 10,010; Piotrkow, 23,050; Ptock (1883), 19,640; Radom (1883), 19,870 ; Se.domierz, 14,080 ; Siedlce, 12,320 ; Sieradz, 15,040; Suwaiki, 18,640; Turek, 11,500; Wloctawek, 20,660; Wtodawa, 17,980; Zgerz, 13,360. (P. A. K.) POLARITY AND EXANTIOMORPHISM. 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 cases 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 enantiomorph 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 of barley or a cat s tail, in which we recognize the distinc tion between the two poles or ends, which we may call A 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 enantiomorphism. In the examples of polarity just given the condition occurs because the parts of the body are arranged in the direction of the axis in a particular order which is different when read backwards. The simplest expression for such a state of matters will be found in the case of a substance composed of equal numbers of three different kinds of particles, these particles being arranged along the axis in the order A | abcabc abc B, where A and B are poles and a, b, c particles of three different kinds. Of course the same may occur with a more complicated constitution, the condition being that the cyclical order read from A to B is different from that read from B to A. Even with particles all of the same kind we can imagine this sort of polarity produced by such an arrangement as A aa a a a an a a a aa a a a 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 B 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 about it. As we took a cat s tail as an example of the one, so we may take a sable muff as an example of the other. Aa we stroke the tail in one direction along the axis, so 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 muff. 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. We 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, b, and c, arranged a 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 rotating 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 passing has polarity of the first kind ; and a magnet, in which 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 oar left and right hands respectively, 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 some cases of crystalline polarity. Both kinds of polarity occur in crystals. We have no direct means of ascertaining how the ultimate particles of a crystal are arranged, but it seems reasonable to suppose that there is a relation between the form of the crystal 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, we naturally suspect that this is the external indication of such an arrangement 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 tourmaline 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 crystals are not similarly terminated at the two ends. It is this kind of crystalline polarity (often called " hemimorphism ") which (as was
first observed by Haiiy and more fully investigated by