Chapter XV: Front Matter (15)

Schemes of cryptography are endless in their variety. Bacon lays down the following as the "virtues" to be looked for in them:--"that they be not laborious to write and read; that they be impossible to decipher; and, in some cases, that they be without suspicion." These principles are more or less disregarded by all the modes that have been advanced, including that of Bacon himself, which has been unduly extolled by his admirers as "one of the most ingenious methods of writing in cypher, and the most difficult to be decyphered, of any yet contrived" (Thicknesse, p. 13).

The simplest and commonest of all the ciphers is that in which the writer selects in place of the proper letters certain other letters in regular advance. This method of transposition was used by Julius Caesar. He, "per quartam elementorum literam," wrote _d_ for _a_, _e_ for _b_, and so on. There are instances of this arrangement in the Jewish rabbis, and even in the sacred writers. An illustration of it occurs in Jeremiah (xxv. 26), where the prophet, to conceal the meaning of his prediction from all but the initiated, writes _Sheshak_ instead of Babel (Babylon), the place meant; i.e. in place of using the second and twelfth letters of the Hebrew alphabet (_b_, _b_, _l_) from the beginning, he wrote the second and twelfth (_sh_, _sh_, _k_) from the end. To this kind of cipher-writing Buxtorf gives the name Athbash (from _a_ the first letter of the Hebrew alphabet, and _th_ the last; _b_ the second from the beginning, and _h_ the second from the end). Another Jewish cabalism of like nature was called Albam; of which an example is in Isaiah vii. 6, where Tabeal is written for Remaliah. In its adaptation to English this method of transposition, of which there are many modifications, is comparatively easy to decipher. A rough key may be derived from an examination of the respective quantities of letters in a type-founder's bill, or a printer's "case." The decipherer's first business is to classify the letters of the secret message in the order of their frequency. The letter that occurs oftenest is _e_; and the next in order of frequency is _t_. The following groups come after these, separated from each other by degrees of decreasing recurrence:--_a_, _o_, _n_, _i_; _r_, _s_, _h_; _d_, _l_; _c_, _w_, _u_, _m_; _f_, _y_, _g_, _p_, _b_; _v_, _k_; _x_, _q_, _j_, _z_. All the single letters must be _a_, _I_ or _O_. Letters occurring together are _ee_, _oo_, _ff_, _ll_, _ss_, &c. The commonest words of two letters are (roughly arranged in the order of their frequency) _of_, _to_, _in_, _it_, _is_, _be_, _he_, _by_, _or_, _as_, _at_, _an_, _so_, &c. The commonest words of three letters are _the_ and _and_ (in great excess), _for_, _are_, _but_, _all_, _not_, &c.; and of four letters--_that_, _with_, _from_, _have_, _this_, _they_, &c. Familiarity with the composition of the language will suggest numerous other points that are of value to the decipherer. He may obtain other hints from Poe's tale called _The Gold Bug_. As to messages in the continental languages constructed upon this system of transposition, rules for deciphering may be derived from Breithaupt's _Ars decifratoria_ (1737), and other treatises.

Bacon remarks that though ciphers were commonly in letters and alphabets yet they might be in words. Upon this basis codes have been constructed, classified words taken from dictionaries being made to represent complete ideas. In recent years such codes have been adapted by merchants and others to communications by telegraph, and have served the purpose not only of keeping business affairs private, but also of reducing the excessive cost of telegraphic messages to distant markets. Obviously this class of ciphers presents greater difficulties to the skill of the decipherer.

Figures and other characters have been also used as letters; and with them ranges of numerals have been combined as the representatives of syllables, parts of words, words themselves, and complete phrases. Under this head must be placed the despatches of Giovanni Michael, the Venetian ambassador to England in the reign of Queen Mary, documents which have only of late years been deciphered. Many of the private letters and papers from the pen of Charles I. and his queen, who were adepts in the use of ciphers, are of the same description. One of that monarch's letters, a document of considerable interest, consisting entirely of numerals purposely complicated, was in 1858 deciphered by Professor Wheatstone, the inventor of the ingenious crypto-machine, and printed by the Philobiblon Society. Other letters of the like character have been published in the _First Report of the Royal Commission on Historical Manuscripts_ (1870). In the second and subsequent reports of the same commission several keys to ciphers have been catalogued, which seem to refer themselves to the methods of cryptography under notice. In this connexion also should be mentioned the "characters," which the diarist Pepys drew up when clerk to Sir George Downing and secretary to the earl of Sandwich and to the admiralty, and which are frequently mentioned in his journal. Pepys describes one of them as "a great large character," over which he spent much time, but which was at length finished, 25th April 1660; "it being," says he, "very handsomely done and a very good one in itself, but that not truly alphabetical."

Shorthand marks and other arbitrary characters have also been largely imported into cryptographic systems to represent both letters and words, but more commonly the latter. This plan is said to have been first put into use by the old Roman poet Ennius. It formed the basis of the method of Cicero's freedman, Tiro, who seems to have systematized the labours of his predecessors. A large quantity of these characters have been engraved in Gruter's _Inscriptiones_. The correspondence of Charlemagne was in part made up of marks of this nature. In Rees's _Cyclopaedia_ specimens were engraved of the cipher used by Cardinal Wolsey at the court of Vienna in 1524, of that used by Sir Thomas Smith at Paris in 1563, and of that of Sir Edward Stafford in 1586; in all of which arbitrary marks are introduced. The first English system of shorthand--Bright's _Characterie_, 1588--almost belongs to the same category of ciphers. A favourite system of Charles I., used by him during the year 1646, was one made up of an alphabet of twenty-four letters, which were represented by four simple strokes varied in length, slope and position. This alphabet is engraved in Clive's _Linear System of Shorthand_ (1830), having been found amongst the royal manuscripts in the British Museum. An interest attaches to this cipher from the fact that it was employed in the well-known letter addressed by the king to the earl of Glamorgan, in which the former made concessions to the Roman Catholics of Ireland.

Complications have been introduced into ciphers by the employment of "dummy" letters,--"nulls and insignificants," as Bacon terms them. Other devices have been introduced to perplex the decipherer, such as spelling words backwards, making false divisions between words, &c. The greatest security against the decipherer has been found in the use of elaborate tables of letters, arranged in the form of the multiplication table, the message being constructed by the aid of preconcerted key-words. Details of the working of these ciphers may be found in the treatises named in this article. The deciphering of them is one of the most difficult of tasks. A method of this kind is explained in the Latin and English lives of Dr John Barwick, whose correspondence with Hyde, afterwards earl of Clarendon, was carried on in cryptography. In a letter dated 20th February 1659/60, Hyde, alluding to the skill of his political opponents in deciphering, says that "nobody needs to fear them, if they write carefully in good cyphers." In his next he allays his correspondent's apprehensiveness as to the deciphering of their letters.

"I confess to you, as I am sure no copy could be gotten of any of my
cyphers from hence, so I did not think it probable that they could be
got on your side the water. But I was as confident, till you tell me
you believe it, that the devil himself cannot decypher a letter that
is well written, or find that 100 stands for Sir H. Vane. I have heard
of many of the pretenders to that skill, and have spoken with some of
them, but have found them all to be mountebanks; nor did I ever hear
that more of the King's letters that were found at Naseby, than those
which they found decyphered, or found the cyphers in which they were
writ, were decyphered. And I very well remember that in the volume
they published there was much left in cypher which could not be
understood, and which I believe they would have explained if it had
been in their power."

An excellent modification of the key-word principle was constructed by Admiral Sir Francis Beaufort.

Ciphers have been constructed on the principle of altering the places of the letters without changing their powers. The message is first written Chinese-wise, upward and downward, and the letters are then combined in given rows from left to right. In the celebrated cipher used by the earl of Argyll when plotting against James II., he altered the positions of the words. Sentences of an indifferent nature were constructed, but the real meaning of the message was to be gathered from words, placed at certain intervals. This method, which is connected with the name of Cardan, is sometimes called the trellis or cardboard cipher.

The wheel-cipher, which is an Italian invention, the string-cipher, the circle-cipher and many others are fully explained, with the necessary diagrams, in the authorities named above--more particularly by Kluber in his _Kryptographik_. (J. E. B.)

CRYPTOMERIA, or JAPANESE CEDAR, a genus of conifers, containing a single species, _C. japonica_, native of China and Japan, which was introduced into Great Britain by the Royal Horticultural Society in 1844. It is described as one of the finest trees in Japan, reaching a height of 100 or more feet, usually divested of branches along the lower part of the trunk and crowned with a conical head. The narrow, pointed leaves are spirally arranged and persist for four or five years; the cones are small, globose and borne at the ends of the branchlets, the scales are thickened at the extremity and divided into sharply pointed lobes, three to five seeds are borne on each scale. _Cryptomeria_ is extensively used in Japan for reafforesting denuded lands, as it is a valuable timber tree; it is also planted to form avenues along the public roads. In Veitch's _Manual of Coniferae_ (ed. 2, 1900, p. 265) reference is made to "an avenue of Cryptomerias 7 m. in extent near Lake Hakone" in which "the trees are more than 100 ft. high, with perfectly straight trunks crowned with conical heads of foliage." Professor C. S. Sargent, in his _Forest Flora of Japan_, says, "Japan owes much of the beauty of its groves and gardens to the _Cryptomeria_. Nowhere is there a more solemn and impressive group of trees than that which surrounds the temples and tombs at Nikko where they rise to a height of 100 to 125 ft.; it is a stately tree with no rival except in the sequoias of California." Many curious varieties have been obtained by Japanese horticulturists, including some dwarf shrubby forms not exceeding a few feet in height. When grown in Great Britain _Cryptomeria_ requires a deep, well-drained soil with plenty of moisture, and protection from cold winds.

CRYPTO-PORTICUS (Gr. [Greek: kryptos], concealed, and Lat. _porticus_), an architectural term for a concealed or covered passage, generally underground, though lighted and ventilated from the open air. One of the best-known examples is the crypto-porticus under the palaces of the Caesars in Rome. In Hadrian's villa in Rome they formed the principal private intercommunication between the several buildings.

CRYSTAL-GAZING, or SCRYING, the term commonly applied to the induction of visual hallucinations by concentrating the gaze on any clear deep, such as a crystal or a ball of polished rock crystal. Some persons do not even find a clear deep necessary, and are content to gaze at the palm of the hand, for example, when hallucinatory pictures, as they declare, emerge. Among objects used are a pool of ink in the hand (Egypt), the liver of an animal (tribes of the North-West Indian frontier), a hole filled with water (Polynesia), quartz crystals (the Apaches and the Euahlayi tribe of New South Wales), a smooth slab of polished black stone (the Huille-che of South America), water in a vessel (Zulus and Siberians), a crystal (the Incas), a mirror (classical Greece and the middle ages), the finger-nail, a sword-blade, a ring-stone, a glass of sherry, in fact almost anything. Much depends on what the "seer" is accustomed to use, and some persons who can "scry" in a glass ball or a glass water-bottle cannot "scry" in ink.

The practice of inducing pictorial hallucinations by such methods as these has been traced among the natives of North and South America, Asia, Australia, Africa, among the Maoris, who sometimes use a drop of blood, and in Polynesia, and is thus practically of world-wide diffusion. This fact was not observed (that is, the collections of examples were not made) till recently, when experiments in private non-spiritualist circles drew attention to crystal-gazing, a practice always popular among peasants, and known historically to have survived through classical and medieval times, and, as in the famous case of Dr Dee, after the Reformation.

The early church condemned _specularii_ (mirror-gazers), and Aubrey and the _Memoirs_ of Saint-Simon contain "scrying" anecdotes of the 17th and 18th centuries, while Sir Walter Scott's story, _My Aunt Margaret's Mirror_, is based on a tradition of about 1750 in a noble Scottish family. The practice, in all times and countries, was used for purposes of divination. The gazer detected unknown criminals, or described remote events, or even professed to foretell things future. Sometimes the supposed magician or medicine man himself did the scrying; occasionally he enabled his client to see for himself; often a child was selected as the scryer. The process was usually explained as the result of the action of a spirit, angel or devil, and many unessential formulae, invocations, "calls," written charms with cabbalistic signs, and fumigations, were employed. These things may have had some effect by way of suggestion; the scryer may have been brought by them into an appropriate frame of mind; but, as a whole, they are tedious and superfluous.

A person can either induce the pictorial hallucinations (he may discover his capacity by accident, like George Sand, as she tells in her _Memoirs_--and other cases are known), or he cannot induce them, though he stare till his eyes water. It is almost universally found, in cases of successful experiment, that the glass ball, for example, takes a milky or misty aspect, that it then grows black, reflections disappearing, and that then the pictures emerge. Some people arrive at seeing the glass ball milky or misty, and can go no further. Others see pictures of persons or landscapes, only in black and white, and motionless. Others see in the glass coloured figures of men, women and animals in motion; while in rarer cases the ball disappears from view, and the scryer finds himself apparently looking at an actual scene. In a few attested cases two persons have shared the same vision. In experiments with magnifying glasses, and through spars, the ordinary effects of magnifying and of alteration of view are sometimes produced; sometimes they are not. The evidence, of course, is necessarily only that of the scryers themselves, but repeated experiments by persons of probity, and unfamiliar with the topic, combined with the world-wide existence of the practice, prove that hallucinatory pictures are really induced.

It has not been found possible to determine, before experiment, whether any given man or woman will prove capable of the hallucinatory experiences. Many subjects with strong powers of "visualization," or seeing things "in the mind's eye," cannot scry; others are successful in various degrees. We might expect persons who have experienced spontaneous visual hallucinations, of the kind vulgarly styled "ghosts" or "wraiths," to succeed in inducing pictures in a glass ball. As a matter of fact such persons sometimes can and sometimes cannot see pictures in the way of crystal-gazing; while many who can see in the crystal have had no spontaneous hallucinations. It is useless to make experiments with hysterical and visionary people, "whose word no man relies on"; they may have the hallucinatory experiences, but they would say that they had in any case.

The nearest analogy to crystal visions, as described, is the common experience of "hypnagogic illusions" (cf. Alfred Maury. _Les Reves et le sommeil_). With closed eyes, between sleeping and waking, many people see faces, landscapes and other things flash upon their view, pictures often brilliant, but of very brief duration and rapid mutation. Sometimes the subject opens his eyes to get rid of an unpleasant vision of this kind. People who cannot scry may have these hypnagogic illusions, and, so far, may partly understand the experience of the scryer who is wide awake. But the visions of the scryer often endure for a considerable time. He or she may put the glass down and converse, and may find the picture still there when the ball is taken up again. New figures may join the figure first seen, as when one enters a room. In these respects, and in the awakeness of the scryer, crystal pictures differ from hypnagogic illusions. In other ways the experiences coincide, the pictures are either fanciful, like illustrations of some unread history or romance, or are revivals of remembered places and faces.

Occasionally, in hypnagogic illusions, the observer can see the picture develop rapidly out of a blot of light or colour, beheld by the closed eyes. One or two scryers think that they, too, can trace the picture as it develops on the suggestion of some passage of light, colour or shadow in the glass or crystal. But, as a rule, the scryer cannot detect any process of development from such _points de mire_; though this may be the actual process.

On the whole there seems little doubt that successful crystal-gazing is the exertion of a not uncommon though far from universal faculty, like those of "chromatic audition"--the vivid association of certain sounds with certain colours--and the mental seeing of figures arranged in coloured diagrams (Galton, _Inquiry into Human Faculty_, pp. 114-154). The experience of hypnagogic illusions also seems far more rare than ordinary dreaming in sleep. Unfortunately, while these phenomena have been carefully studied by officially scientific characters, in England orthodox _savants_ have disdained to observe crystal-gazing, while in France psychologists have too commonly experimented with subjects professionally hysterical and quite untrustworthy. Our remarks are therefore based mainly on considerable personal study of "scrying" among normal British subjects of both sexes, to whom the topic was previously unknown.

The superstitious associations of crystal-gazing, as of hypnotism, appear to bar the way to official scientific investigation, and the fluctuating proficiency of the seers, who cannot command success, or determine the causes and conditions of success and failure, tends in the same direction. The existence, too, of paid professionals who lead astray silly women, encourages the natural scientific contempt for the study of the faculty.

The seeing of the pictures, as far as we have spoken of it, appears to be a thing unusual, but in no way abnormal, any more than dreams or hypnagogic illusions are abnormal. Crystal pictures, however, are commonly dismissed as mere results of "imagination," a theory which, of course, is of no real assistance to psychology. Persons of recognized "imaginativeness," such as novelists and artists, do not seem more or less capable of the hallucinatory experiences than their sober neighbours; while persons not otherwise recognizably "imaginative" (we could quote a singularly accurate historian) are capable of the experiences. It is unfortunate, as it awakens prejudice, but in the present writer's opinion it is true, that crystal-gazing sometimes is rewarded with results which may be styled "supra-normal." In addition to the presentation of revived memories, and of "objectivation of ideas or images consciously or unconsciously in the mind of the percipient," there occur "visions, possibly telepathic or clairvoyant, implying acquirement of knowledge by supra-normal means."[1]

A number of examples occurring during experiments made by the present writer and by his acquaintances in 1897 were carefully recorded and attested by the signatures of all concerned The cases, or rather a selection of the cases, are printed in A. Lang's book, _The Making of Religion_ (2nd ed., London, 1902, pp. 87-104). Others are chronicled in A. Lang's Introduction to Mr N. W. Thomas's work, _Crystal Gazing_ (1905). The experiments took this form: any person might ask the scryer (a lady who had never previously heard of crystal-gazing) "to see what he was thinking of." The scryer, who was a stranger in a place which she had not visited before, gave, in a long series of cases, a description of the person or place on which the inquirer's thoughts were fixed. The descriptions, though three or four entire failures occurred, were of remarkable accuracy as a rule, and contained facts and incidents unknown to the inquirers, but confirmed as accurate. In fact, some Oriental scenes and descriptions of incidents were corroborated by a letter from India which arrived just after the experiment; and the same thing happened when the events described were occurring in places less remote. On one occasion a curious set of incidents were described, which happened to be vividly present to the mind of a sceptical stranger who chanced to be in the room during the experiment; events unknown to the inquirer in this instance. As an example of the minuteness of description, an inquirer, thinking of a brother in India, an officer in the army, whose hair had suffered in an encounter with a tiger, had described to her an officer in undress uniform, with bald scars through the hair on his temples, such as he really bore. The number and proportion of successes was too high to admit of explanation by chance coincidence, but success was not invariable. On one occasion the scryer could see nothing, "the crystal preserved its natural diaphaneity," as Dr Dee says; and there were failures with two or three inquirers. On the other hand no record was kept in several cases of success.

Whoever can believe that the successes were numerous and that descriptions were given correctly--not only of facts present to the minds of inquirers, and of other persons present who were not consciously taking a share in the experiments, but also of facts necessarily unknown to all concerned--must of course be most impressed by the latter kind of success. If the process commonly styled "telepathy" exists (see TELEPATHY), that may account for the scryer's power of seeing facts which are in the mind of the inquirer. But when the scryers see details of various sorts, which are unknown to the inquirer, but are verified on inquiry, then telepathy perhaps fails to provide an explanation. We seem to be confronted with actual clairvoyance (q.v.), or _vue a distance_. It would be vain to form hypotheses as to the conditions or faculties which make _vue a distance_ possible. This way lie metaphysics, with Hegel's theory of the Sensitive Soul, or Myers' theory of the Subliminal Self. "The intuitive soul," says Hegel, "oversteps the conditions of time and space; it beholds things remote, things long past, and things to come."[2]

What we need, if any progress is to be made in knowledge of the subject, is not a metaphysical hypothesis, but a large, carefully tested, and well-recorded collection of examples, made by _savants_ of recognized standing. At present we are where we were in electrical science, when Newton produced curious sparks while rubbing glass with paper. By way of facts, we have only a large body of unattested anecdotes of supra-normal successes in crystal-gazing, in many lands and ages; and the scanty records of modern amateur investigators, like the present writer. Even from these, if the honesty of all concerned be granted (and even clever dishonesty could not have produced many of the results), it would appear that we are investigating a strange and important human faculty. The writer is acquainted with no experiments in which it was attempted to discern the future (except in trivial cases as to events on the turf, when chance coincidence might explain the successes), and only with two or three cases in which there was an attempt to help historical science and discern the past by aid of psychical methods. The results were interesting and difficult to explain, but the experiments were few. Ordinary scryers of fancy pictures are common enough, but scryers capable of apparently supra-normal successes are apparently rare. Perhaps something depends on the inquirer as well as the scryer.

The method of scrying, as generally practised, is simple. It is usual to place a glass ball on a dark ground, to sit with the back to the light, to focus the gaze on the ball (disregarding reflections, if these cannot be excluded), and to await results. Perhaps from five to ten minutes is a long enough time for the experiment. The scryer may let his consciousness play freely, but should not be disturbed by lookers-on. As a rule, if a person has the faculty he "sees" at the first attempt; if he fails in the first three or four efforts he need not persevere. Solitude is advisable at first, but few people can find time amounting to ten minutes for solitary studies of this sort, so busy and so gregarious is mankind. The writer has no experience of trance, sleep or auto-hypnotization produced in such experiments; scryers have always seemed to retain their full normal consciousness. As regards scepticism concerning the faculty we may quote what Mr Galton says about the faculty of visualization: "Scientific men as a class have feeble power of visual reproduction.... They had a mental deficiency of which they were unconscious, and, naturally enough, supposed that those who affirmed _they_ were possessed of it were romancing."

AUTHORITIES.--A useful essay is that of "Miss X" (Miss Goodrich Freer)
in the _Proceedings of the Society for Psychical Research_, v. The
history of crystal-gazing is here traced, and many examples of the
author's own experiments are recorded. A. Lang's _The Making of
Religion_, ch. v., contains anthropological examples and a series of
experiments. In N. W. Thomas's _Crystal Gazing_ the history and
anthropology of the subject are investigated, with modern instances.
For Egypt, see Lane's _Modern Egyptians_, and the _Journal_ of Sir
Walter Scott, xi. 419-421, with _Quarterly Review_, No. 117, pp.
196-208. These Egyptian experiments of 1830 were vitiated by their
method, the scryer being asked to see and describe a given person,
named. He ought not, of course, to be told more than that he is to
descry the inquirer's thoughts, and there ought never to be physical
contact, as in holding hands, between the inquirer and the scryer
during the experiment. There is a chapter on crystal-gazing in _Les
Nevroses et les idees fixes_ of Dr Janet (1898). His statements are
sometimes demonstrably inaccurate (see _Making of Religion_, Appendix
C). A curious passage on the subject, by Ibn Khaldun, an Arabian
medieval _savant_, is quoted by Mr Thomas from the printed Extracts of
MSS. in the Bibliotheque Nationale. There is also a chapter on
crystal-gazing in Myers' _Human Personality_. (A. L.)

FOOTNOTES:

[1] _Proceedings of the Society for Psychical Research_, v. 486.

[2] "Philosophie der Geistes," Hegel's _Werke_, vii. 179, 406, 408
(Berlin, 1845). Cf. Wallace's translation (Oxford, 1894).

CRYSTALLITE. In media which, on account of their viscosity, offer considerable resistance to those molecular movements which are necessary for the building and growth of crystals, rudimentary or imperfect forms of crystallization very frequently occur. Such media are the volcanic rocks when they are rapidly cooled, producing various kinds of pitchstone, obsidian, &c. When examined under the microscope these rocks consist largely of a perfectly amorphous or glassy base, through which are scattered great numbers of very minute crystals (microliths), and other bodies, termed crystallites, which seem to be stages in the formation of crystals. Crystallites may also be produced by allowing a solution of sulphur in carbon disulphide mixed with Canada balsam to evaporate slowly, and their development may be watched on a microscopic slide. Small globules appear (globulites), spherical and non-crystalline (so far as can be ascertained). They may coalesce or may arrange themselves into rows like strings of beads--margarites--(Gr. [Greek: margarites], a pearl) or into groups with a somewhat radiate arrangement--globospherites. Occasionally they take elongated shapes--longulites and baculites (Lat. _baculus_, a staff). The largest may become crystalline, changing suddenly into polyhedral bodies with evident double refraction and the optical properties belonging to crystals. Others become long and thread-like--trichites (Gr. [Greek: thrix, trichos], hair)--and these are often curved, and a group of them may be implanted on the surface of a small crystal. All these forms are found in vitreous igneous rocks. H. P. J. Vogelsang, who was the first to direct much attention to them, believes that the globulites are preliminary stages in the formation of crystals.

Microliths, as distinguished from crystallites, have crystalline properties, and evidently belong to definite minerals or salts. When sufficiently large they are often recognizable, but usually they are so small, so opaque, or so densely crowded together that this is impossible. In igneous rocks they are usually felspar, augite, enstatite, and iron oxides, and are found in abundance only where there is much uncrystallized glassy base; in contact-altered sediments, slags, &c., microlithic forms of garnet, spinel, sillimanite, cordierite, various lime silicates, and many other substances have been observed. Their form varies greatly, e.g. thin fibres (sillimanite, augite), short prisms or rods (felspar, enstatite, cordierite), or equidimensional grains (augite, spinel, magnetite). Occasionally they are perfectly shaped though minute crystals; more frequently they appear rounded (magnetite, &c.), or have brush-like terminations (augite, felspar, &c.). The larger microliths may contain enclosures of glass, and it is very common to find that the prisms have hollow, funnel-shaped ends, which are filled with vitreous material. These microliths, under the influence of crystalline forces, may rank themselves side by side to make up skeleton crystals and networks, or feathery and arborescent forms, which obey more or less closely the laws of crystallization of the substance to which they belong. They bear a very close resemblance to the arborescent frost flowers seen on window panes in winter, and to the stellate snow crystals. In magnetite the growths follow three axes at right angles to one another; in augite this is nearly, though not exactly, the case; in hornblende an angle of 57 deg. may frequently be observed, corresponding to the prism angle of the fully-developed crystal. The interstices of the network may be partly filled up by a later growth. In other cases the crystalline arrangement of the microliths is less perfect, and branching, arborescent or feathery groupings are produced (e.g. felspar, augite, hornblende). Spherulites may be regarded as radiate aggregates of such microliths (mostly felspar mixed with quartz or tridymite). If larger porphyritic crystals occur in the rock, the microliths of the vitreous base frequently grow outwards from their faces; in some cases a definite parallelism exists between the two, but more frequently the early crystal has served merely as a centre, or nucleus, from which the microliths and spherulites have spread in all directions. (J. S. F.)

CRYSTALLIZATION, the art of obtaining a substance in the form of crystals; it is an important process in chemistry since it permits the purification of a substance, or the separation of the constituents of a mixture. Generally a substance is more soluble in a solvent at a high temperature than at a low, and consequently, if a boiling concentrated solution be allowed to cool, the substance will separate in virtue of the diminished solubility, and the slower the cooling the larger and more perfect will be the crystals formed. If, as sometimes appears, such a solution refuses to crystallize, the expedient of inoculating the solution with a minute crystal of the same substance, or with a similar substance, may be adopted; shaking the solution, or the addition of a drop of another solvent, may also occasion the desired result. "Fractional crystallization" consists in repeatedly crystallizing a salt so as to separate the substances of different solubilities. Examples are especially presented in the study of the rare-earths. Other conditions under which crystals are formed are given in the article CRYSTALLOGRAPHY.

CRYSTALLOGRAPHY (from the Gr. [Greek: krystallos], ice, and [Greek: graphein], to write), the science of the forms, properties and structure of crystals. Homogeneous solid matter, the physical and chemical properties of which are the same about every point, may be either amorphous or crystalline. In amorphous matter all the properties are the same in every direction in the mass; but in crystalline matter certain of the physical properties vary with the direction. The essential properties of crystalline matter are of two kinds, viz. the general properties, such as density, specific heat, melting-point and chemical composition, which do not vary with the direction; and the directional properties, such as cohesion and elasticity, various optical, thermal and electrical properties, as well as external form. By reason of the homogeneity of crystalline matter the directional properties are the same in all parallel directions in the mass, and there may be a certain symmetrical repetition of the directions along which the properties are the same.

When the crystallization of matter takes place under conditions free from outside influences the peculiarities of internal structure are expressed in the external form of the mass, and there results a solid body bounded by plane surfaces intersecting in straight edges, the directions of which bear an intimate relation to the internal structure. Such a polyhedron ([Greek: polys], many, [Greek: hedra], base or face) is known as a crystal. An example of this is sugar-candy, of which a single isolated crystal may have grown freely in a solution of sugar. Matter presenting well-defined and regular crystal forms, either as a single crystal or as a group of individual crystals, is said to be crystallized. If, on the other hand, crystallization has taken place about several centres in a confined space, the development of plane surfaces may be prevented, and a crystalline aggregate of differently orientated crystal-individuals results. Examples of this are afforded by loaf sugar and statuary marble.

After a brief historical sketch, the more salient principles of the subject will be discussed under the following sections:--

I. CRYSTALLINE FORM.
(a) Symmetry of Crystals.
(b) Simple Forms and Combinations of Forms.
(c) Law of Rational Indices.
(d) Zones.
(e) Projection and Drawing of Crystals.
(f) Crystal Systems and Classes.
1. Cubic System.
2. Tetragonal System.
3. Orthorhombic System.
4. Monoclinic System.
5. Anorthic System.
6. Hexagonal System
(g) Regular Grouping of Crystals (Twinning, &c.).
(h) Irregularities of Growth of Crystals: Characters of Faces.
(i) Theories of Crystal Structure.

II. PHYSICAL PROPERTIES OF CRYSTALS.
(a) Elasticity and Cohesion (Cleavage, Etching, &c.).
(b) Optical Properties (Interference figures, Pleochroism,
&c.).
(c) Thermal Properties.
(d) Magnetic and Electrical Properties.