ANALCITE, a commonly occurring mineral of the zeolite group. It crystallizes in the cubic system, the common form being the icositetrahedron (211), either alone (fig. 1) or in combination with the cube (100); sometimes the faces of the cube predominate in size, and its corners are each replaced by three small triangular faces representing the icositetrahedron (fig. 2). Although cubic in form, analcite usually shows feeble double refraction, and is thus optically anomalous. This feature of analcite has been much studied, Sir David Brewster in 1826 being the earliest investigator. Crystals of analcite are often perfectly colourless and transparent with a brilliant glassy lustre, but some are opaque and white or pinkish-white. The hardness of the mineral is 5 to 512, and its specific gravity is 2·25. Chemically, analcite is a hydrated sodium and aluminium silicate, NaAlSi2O6+H2O; small amounts of the sodium being sometimes replaced by calcium or by potassium. The water of crystallization is readily expelled by heat, with modification of the optical characters of the crystals. Before the blowpipe the mineral readily fuses with intumescence to a colourless glass. It is decomposed by acids with separation of gelatinous silica.
Fig. 1.Fig. 2.
Analcite usually occurs, associated with other zeolitic minerals, lining amygdaloidal cavities in basic volcanic rocks such as basalt and melaphyre, and especially in such as have undergone alteration by weathering; the Tertiary basalts of the north of Ireland frequently contain cavities lined with small brilliant crystals of analcite. Larger crystals of the same kind are found in the basalt of the Cyclopean Islands (Scogli de’ Ciclopi or Faraglioni) N.E. of Catania, Sicily. Large opaque crystals of the pinkish-white colour are found in cavities in melaphyre at the Seisser Alpe near Schlern in southern Tirol. In all such cases the mineral is clearly of secondary origin, but of late years another mode of occurrence has been recognized, analcite having been found as a primary constituent of certain igneous rocks such as monchiquite and some basalts. The irregular grains, of which it has the form, had previously been mistaken for glass.
Owing to the fact that analcite often crystallizes in cubes, it was long known as cubic zeolite or as cuboite. The name now in use was proposed in 1797 in the form analcime, by R. J. Haüy, in allusion to the weak (ἄναλκις) electrification of the mineral produced by friction. Euthallite is a compact, greenish analcite, produced by the alteration of elaeolite at various localities in the Langesund-fjord in southern Norway. Eudnophite, from the same region, was originally described as an orthorhombic mineral dimorphous with analcite, but has since been found to be identical with it. Cluthalite, from the Clyde (Clutha) valley, is an altered form of the mineral. (L. J. S.)
ANALOGY (Gr. ἀναλογία, proportion), a term signifying, (1) in general, resemblance which falls short of absolute similarity or identity. Thus by analogy, the word “loud,” originally applied to sounds, is used of garments which obtrude themselves on the attention; all metaphor is thus a kind of analogy. (2) Euclid used the term for proportionate equality; but in mathematics it is now obsolete except in the phrase, “Napier’s Analogies” in spherical trigonometry (see Napier, John). (3) In grammar, it signifies similarity in the dominant characteristics of a language, derivation, orthography and so on. (4) In logic, it is used of arguments by inference from resemblances between known particulars to other particulars which are not observed. Under the name of “example” (παράδειγμα) the process is explained by Aristotle (Prior Anal. ii. 4) as an inference which differs from induction (q.v.) in having a particular, not a general, conclusion; i.e. if A is demonstrably like B in certain respects, it may be assumed to be like it in another, though the latter is not demonstrated. Kant and his followers state the distinction otherwise, i.e. induction argues from the possession of an attribute by many members of a class that all members of the class possess it, while analogy argues that, because A has some of B’s qualities, it must have them all (cf. Sir Wm. Hamilton, Lectures on Logic, ii. 165-174, for a slight modification of this view). J. S. Mill very properly rejects this artificial distinction, which is in practice no distinction at all; he regards induction and analogy as generically the same, though differing in the demonstrative validity of their evidence, i.e. induction proceeds on the basis of scientific, causal connexion, while analogy, in absence of proof, temporarily accepts a probable hypothesis. In this sense, analogy may obviously have a universal conclusion. This type of inference is of the greatest value in physical science, which has frequently and quite legitimately used such conclusions until a negative instance has disproved or further evidence confirmed them (for a list of typical cases see T. Fowler’s edition of Bacon’s Nov. Org. Aph. ii. 27 note). The value of such inferences depends on the nature of the resemblances on which they are based and on that of the differences which they disregard. If the resemblances are small and unimportant and the differences great and fundamental, the argument is known as “False Analogy.” The subject is dealt with in Francis Bacon’s Novum Organum, especially ii. 27 (see T. H. Fowler’s notes) under the head of Instantiae conformes sive proportionatae. Strictly the argument by analogy is based on similarity of relations between things, not on the similarity of things, though it is, in general, extended to cover the latter. See works on Logic, e.g. J. S. Mill, T. H. Fowler, W. S. Jevons. For Butler’s Analogy and its method see Butler, Joseph.
The term was used in a special sense by Kant in his phrase, “Analogies of Experience,” the third and most important group in his classification of the a priori elements of knowledge. By it he understood the fundamental laws of pure natural science under the three heads, substantiality, causality, reciprocity (see F. Paulsen, I. Kant, Eng. trans. 1902, pp. 188 ff.).
ANALYSIS (Gr. ἀνὰ and λύειν, to break up into parts), in general, the resolution of a whole into its component elements; opposed to synthesis, the combining of separate elements or minor wholes into an inclusive unity. It differs from mere “disintegration” in proceeding on a definite scientific plan. In grammar, analysis is the breaking up of a sentence into subject, predicate, object, &c. (an exercise introduced into English schools by J. D. Morell about 1852); so the analysis of a book or a lecture is a synopsis of the main points. The chief technical uses of the word, which retains practically the same meaning in all the sciences, are in (1) philosophy, (2) mathematics, (3) chemistry.
(1) Logical analysis is the process of examining into the connotation of a concept or idea, and separating the attributes from the whole and each other. It, therefore, does not increase knowledge, but merely clarifies and tests it. In this sense Kant distinguished an analytic from a synthetic judgment, as one in which the predicate is involved in the essence of the subject. Such judgments are also known as verbal, as opposed to real or ampliative judgments. The processes of synthesis and analysis though formally contradictory are practically supplementary; thus to analyse the connotation is to synthesize the denotation of a term, and vice versa; the process of knowledge involves the two methods, analysis being the corrective of synthetic empiricism. In a wider sense the whole of formal logic is precisely the analysis of the laws of thought. Analytical psychology is distinguished from genetic and empirical psychology inasmuch as it proceeds by the method of introspective investigation of mental phenomena instead of by physiological or psycho-physical experiment. For the relation between analysis and synthesis on the one hand, and deduction and induction on the other, see Induction.
(2) In mathematics, analysis has two distinct meanings, conveniently termed ancient and modern. Ancient analysis,
