may be drawn that this represents the structure of rock-salt. The two kinds of atoms, sodium and chlorine, may be placed alternately along the three directions, as shown in fig. 9. As so represented the structure may also be regarded as an interpenetration of two space- lattices of the face-centred cubic type (fig. 40), with the sodium atoms on one lattice and the chlorine atoms on the other. One lattice can be brought into the position occupied by the other by a parallel shift along a cube edge through the distance between two consecutive planes. The actual distance between the cube planes, and consequently also between the atomic centres, has been deter- mined to be 2-81 X lo- 8 cm., or rather more than a hundred-millionth of an inch. In the drawings, the scale of the lattice is enormously enlarged and only an infinitesimal portion of the crystal is repre- sented. Some idea of this may be conveyed by saying that if we took a cubic inch of rock-salt and represented the whole of the structure on the same scale as in fig. 9 the drawing would be rather more than a thousand miles across. The same structure is also shown by galena (lead sulphide, PbS), the crystals of which also possess a perfect cubic cleavage : the two kinds of atoms shown in fig. 9 here represent lead and sulphur. Other examples are potassium chloride, potassium bromide, etc.
Examples of crystals with the structure of the centred cubic lat- tice (fig. 4b) are those of the metals iron, sodium, tungsten, etc. The face-centred cubic lattice (fig. 4c) is represented by crystals of the metals copper, silver, gold, platinum, etc.
A special type of cubic lattice, known as the " diamond lattice," consists of another kind of interpenetration of two face-centred lattices. In fig. 10, to avoid confusion, only one such lattice is represented in detail the white particles clearly having positions shown in fig. 4c. Four black particles belonging to the other lattice are placed each at a centre of alternate sub-cubes in the first lattice. Through the whole structure there are, of course, equal numbers of the white and black particles. The positions of two more black par- ticles are indicated in the next storey above of the white-particle lattice. Now it will be seen that around each black particle there is a tetrahedral arrangement of four white particles; and around each white particle a tetrahedral arrangement of four black particles (but, conversely, it is only alternate tetrahedral groups of each kind that have a particle of the other kind at their centre). The front out- lines of two of these tetrahedra are indicated in the figure. The upper tetrahedron of four black particles has at its centre the white particle in the centre of the top cube face; and one of these same black particles is at the centre of the tetrahedron of white particles at alternate corners of the upper, front, right-hand sub-cube. The first tetrahedron can be brought into coincident position with the second by sliding it downwards and forwards along one-quarter of the diagonal of the cube, and then rotating it through 90 about a cube edge. The same is also true of the whole lattice; i.e. one lattice can be brought into exactly the position of the other by these two successive operations. The symmetry of the whole model is that of the tetrahedral class of the cubic system; but, in addition, the two sets of particles are directed towards different directions. Regarding the particles as spheres of equal size and in contact with one another, then each one is touched by only four others, the latter with a tetrahedral arrangement; much of the space is thus vacant, and more spheres of the same size could be dropped into the larger interspaces. Or again, if the particles (all of the same size) entirely fill X space, they will have the form of regular tetrahedra the four corners of which are each replaced by three faces of the rhombic- dodecahedron (much as in fig. 33, vol. 7, p. 575, but with the faces of the tetrahedron cut off to regular hexagons).
This type of structure is shown by diamond, silicon, grey tin, and zinc-blende, and also by copper-pyrites (a tetragonal mineral, but with very nearly cubic angles). In the first three, being chemical elements, the atoms on the two lattices are of the same kind. In diamond each carbon atom is surrounded tetrahedrally by four others at a distance, between the centres, of 1-53 Xio- 8 cm. In zinc-blende (ZnS) the, zinc atoms lie on one lattice, whilst the sulphur atoms lie on the other. Since the two lattices are identical and superposable, it is immaterial whether the black particles represent sulphur or zinc atoms. In copper-pyrites (CuFeS2) the sulphur atoms are said to lie on one lattice and the copper and iron on the other; the copper and iron atoms being in alternate horizontal layers perpendicular to the principal axis of the crystal. It is, however, to be remarked that these three minerals, to which the same type of structure is ascribed, exhibit marked differences in their cleavages. Diamond has a perfect octahedral cleavage, zinc- blende a perfect rhombic-dodecahedral cleavage, whilst copper- pyrites has none. Again, the high density and the extreme hardness of diamond would seem to suggest that there should be less un- occupied space in the structure.
A fuller account is given in Bragg's book quoted above. A series of excellent summaries of this and other matters relating to chemical crystallography are given by T. V. Barker in the Annual Reports of Progress of the Chemical Society (London, 1913 et seq.). In the latter will also be found the best available account of the extraor- dinary work of the Russian crystallographer, E. S. Fedorov, who perished in Petrograd in 1919.
REFERENCES. A comprehensive and general treatise is A. E. H. Tutton's Crystallography and Practical Crystal Measurement (London. 1911 ; 2nd ed. 1921). A popular work of the same author is Crystals (International Scientific Series, London 1911). Structure theories are discussed by P. Niggli, Geometrische Krystallographie des Diskon- tinuums (Berlin 1918); F. M. Jaeger, Lectures on the Principle oj Symmetry (Amsterdam 1917; 2nd ed. 1920); J. Beckenkamp, Statische und kinetische Kristalltheorien (Berlin 1915); see also Bragg and Barker quoted above. Elementary text-books are: T. L. Walker, Crystallography, an Outline of the Geometrical Proper- ties of Crystals (New York 1914) in which the subject is treated from the point of view of two-circle goniometry; Sir Wm. P. Beale, An Amateur's Introduction to Crystallography from Morphological Observations (London 1915); P. Groth, Elemenle der physikalischen und chemischen Krystallographie (Munich 1921); J. Beckenkamp, Leilfaden der Kristallographie (Berlin 1919). A collection of thou- sands of drawings of crystals with critical lists of forms is given by V. Goldschmidt, Atlas der Krystallformen (several 4to vols., in progress, Heidelberg 1913, etc.). New crystal-forms together with other crystallographic constants are listed in the international Tables annuelles de constantes et donnees numeriques (4 vols., Paris 1912, etc.). An historical sketch of the early development of crystallog- raphy is given by Helene Metzger, La genese de la science des cris- taux (Paris 1918). (L. J. S.)
CSAKY, ALBIN, COUNT (1841-1912), Hungarian statesman,
was born on April 18 1841 at Krompach, in the county of Szepes,
and studied law at Kassa (Kaschau) and Budapest. Deputy
in 1865, he was from 1868 to 1880 Obergespan (lord-lieutenant),
in which capacity he gained the reputation of an excellent administrator. In 1884 he pleaded eloquently in the House of
Magnates for the establishment of civil marriage, and in 1888
was Minister of Education in the Cabinet of Koloman Tisza.
Together with Szilagyi, the Minister of Justice, Csaky was one
of the most decided champions of obligatory civil marriage and
of the rights of the Jews. He resigned in 1894, and in 1900 was
appointed president of the House of Magnates, an office which he
resigned on the fall of the Liberal party in 1906. Under the
Khuen-Hedvary Government he became on June 18 1910 once
more president of the House of Magnates.
CUBA (see 7.594*). From 1909, when for the second time the
management of Cuban affairs was turned over by the United
States to the Cuban Government, until the end of 1920, there
was a steady growth in Cuba's prosperity. This growth was
greatly accelerated during the first half of the year last mentioned,
but suffered a serious reverse toward the end of the year.
The census of 1919 showed a pop. of 2,898,905 (1907, 2,048,980),
an average of 65-56 per sq. mile. The total immigration was in
1914, 24,420; in 1918, 37,320; and in 1919, 80,485. Of immigrants
in 1919, 39,573 were from Spain. The immigrants from Jamaica,
who numbered only 995 in 1914 and 9,184 in 1918, increased
to 24,187 in 1919. It is stated that probably 75% of the immigrants return to the country of origin within the course of a
year, coming to Cuba only for the high wages paid during the
cane cutting and grinding season.
The Sugar Industry. Sugar is the basis of Cuba's prosperity. The climate and fertile soil are admirably adapted to the growth of sugar cane, and the island has come to be recognized as the "sugar bowl of the world." The high prices that prevailed in 1919-20 enabled the sugar industry to put more of the soil under cane than ever before and to construct many of the most modern and efficient sugar mills in the world. The sugar crop, which in 1910-1 totalled I>379t6o9 long tons, steadily increased, except for a slight decline in 1914-5. In 1918-9 the production reached 3,720,000 tons or 61 % of the total cane sugar produced by the western hemisphere, 34% of the world's cane sugar production, and 25% of the world's total sugar production, as against an average of 1 1 % in the decade preceding the World War. Production increased more than 50% during the five years 1913-4.10 1918-9. During the period 1909-14, approximately 95% of Cuba's crop went to the United States (almost half of that country's supply), the remaining 5% being used for home consumption. In 1917-8 the entire crop, except that used for home consumption, was purchased by the United States and the Allies, two-thirds for the former, one-third for the latter. The 1918-9 crop was similarly contracted for, but part of the share of the United States was later diverted to other countries. The crop for 1919-20 was 3,730,077 tons. The price, which had been from two to three cents a pound before the war, advanced slowly but steadily during the war. The crop for 1917-8 was sold to the United States at 4-6 cents f. o. b. Cuban ports, and that for 1918-9 at 5^ cents. But the next year the world's shortage (nearly 2,000,000 tons compared with 1913-4), the increased consumption in the United States and the failure of the latter to purchase the 1919-20 crop, although it was offered and could probably have been obtained at about 6J cents a pound, caused a keen competition for the Cuban supplies,
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