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Rh . Alongside, however, of this persistent interchange there was a desire to distinguish between the terms, and to confine  to the Divine persons. This tendency arose in Alexandria, and its progress may be seen in comparing the early and later writings of Athanasius. That writer, in view of the Arian trouble, felt that it was better to speak of  as “the common undifferentiated substance of Deity,” and  as “Deity existing in a personal mode, the substance of Deity with certain special properties” ( ). At the council of Alexandria in 362 the phrase  was permitted, and the work of this council was supplemented by Basil, Gregory of Nazianzus and Gregory of Nyssa in the formula  or .

The results arrived at by these Cappadocian fathers were stated in a later age by John of Damascus (De orth. fid. iii. 6), quoted in R. L. Ottley, The Doctrine of the Incarnation, ii. 257.

HYPOSTYLE, in architecture, the term applied to a hall, the flat ceiling of which is supported by columns, as in the Hall of Columns at Karnak. In this case the columns flanking the central avenue are of greater height than those of the side aisles, and this admits of openings in the wall above the smaller columns, through which light is admitted over the aisle roof, through clerestory windows.

HYPOSULPHITE OF SODA, the name originally given to the substance known in chemistry as sodium thiosulphate, Na2S2O3; the earlier name is still commonly used, especially by photographers, who employ this chemical as a fixer. In systematic chemistry, sodium hyposulphite is a salt of hyposulphurous acid, to which Schutzenberger gave the formula H2SO2, but which Bernthsen showed to be H2S2O4. (See .)

 HYPOTHEC (Lat. hypotheca, Gr.  ), in Roman law, the most advanced form of the contract of pledge. A specific thing may be given absolutely to a creditor on the understanding that it is to be given back when the creditor’s debt is paid; or the property in the thing may be assigned to the creditor while the debtor is allowed to remain in possession, the creditor as owner being able to take possession if his debt is not discharged. Here we have the kind of security known as pledge and mortgage respectively. In the hypotheca, the property does not pass to the creditor, nor does he get possession, but he acquires a preferential right to have his debt paid out of the hypothecated property; that is, he can sell it and pay himself out of the proceeds, or in default of a purchaser he can become the owner himself. The name and the principle have passed into the law of Scotland, which distinguishes between conventional hypothecs, as bottomry and respondentia, and tacit hypothecs established by law. Of the latter the most important is the landlord’s hypothec for rent (corresponding to distress in the law of England), which extends over the produce of the land and the cattle and sheep fed on it, and over stock and horses used in husbandry. The law of agricultural hypothec long caused much discontent in Scotland; its operation was restricted by the Hypothec Amendment (Scotland) Act 1867, and finally by the Hypothec Abolition (Scotland) Act 1880 it was enacted that the “landlord’s right of hypothec for the rent of land, including the rent of any buildings thereon, exceeding two acres in extent, let for agriculture or pasture, shall cease and determine.” By the same act and by the Agricultural Holdings (Scotland) Act 1883 other rights and remedies for rent, where the right of hypothec had ceased, were given to the landlord.

 HYPOTHESIS (from Gr. , to put under; cf. Lat. suppositio, from sub-ponere), in ordinary language, an explanation, supposition or assumption, which is put forward in the absence of ascertained facts or causes. Both in ordinary life and in the acquisition of scientific knowledge hypothesis is all-important. A detective’s work consists largely in forming and testing hypothesis. If an astronomer is confronted by some phenomenon which has no obvious explanation he may postulate some set of conditions which from his general knowledge of the subject would or might give rise to the phenomenon in question; he then tests his hypothesis until he discovers whether it does or does not conflict with the facts. An example of this process is that of the discovery of the planet Neptune: certain perturbations of the orbit of Uranus had been observed, and it was seen that these could be explained on the hypothesis of the existence of a then unknown planet, and this hypothesis was verified by actual observation. The progress of inductive knowledge is by the formation of successive hypotheses, and it frequently happens that the demolition of one or even many hypotheses is the direct road to a new and accurate hypothesis, i.e. to fresh knowledge. A hypothesis may, therefore, turn out to be entirely wrong, yet it may be of the greatest practical use.

The recognition of the importance of hypotheses has led to various attempts at drawing up exact rules for their formation, but logicians are generally agreed that only very elementary principles can be laid down. Thus a hypothesis must contain nothing which is at variance with known facts or principles: it should not postulate conditions which cannot be verified empirically. J. S. Mill (Logic III. xiv. 4) laid down the principle that a hypothesis is not “genuinely scientific” if it is “destined always to remain a hypothesis”: it must “be of such a nature as to be either proved or disproved by comparison with observed facts”: in the same spirit Bacon said that in searching for causes in nature “Deum semper excipimus.” Mill’s principle, though sound in the abstract, has, except in a few cases, little practical value in determining the admissibility of hypotheses, and in practice any rule which tends to discourage hypothesis is in general undesirable. The most satisfactory check on hypothesis is expert knowledge in the particular field of research by which rigorous tests may be applied. This test is roughly of two kinds, first by the ultimate principles or presuppositions on which a particular branch of knowledge rests, and second by the comparison of correlative facts. Useful light is shed on this distinction by Lotze, who contrasts (Logic, § 273) postulates (“absolutely necessary assumptions without which the content of the observation with which we are dealing would contradict the laws of our thought”) with hypotheses, which he defines as conjectures, which seek “to fill up the postulate thus abstractly stated by specifying the concrete causes, forces or processes, out of which the given phenomenon really arose in this particular case, while in other cases maybe the same postulate is to be satisfied by utterly different though equivalent combinations of forces or active elements.” Thus a hypothesis may be ruled out by principles or postulates without any reference to the concrete facts which belong to that division of the subject to explain which the hypothesis is formulated. A true hypothesis, therefore, seeks not merely to connect or colligate two separate facts, but to do this in the light of and subject to certain fundamental principles. Various attempts have been made to classify hypotheses and to distinguish “hypothesis” from a “theory” or a mere “conjecture”: none of these have any great practical importance, the differences being only in degree, not in kind.

The adjective “hypothetical” is used, in the same sense, both loosely in contradistinction to “real” or “actual,” and technically in the phrases “hypothetical judgment” and “hypothetical syllogism.” (See and .)

See Naville, La Logique de l’hypothèse (1880), and textbooks of logic, e.g. those of Jevons, Bosanquet, Joseph; Liebmann, Der Klimax d. Theorien.

HYPOTRACHELIUM (Gr. , the lower part of the neck, <span title="tráchēlos"> ), in classical architecture, the space between the annulet of the echinus and the upper bed of the shafts, including, according to C. R. Cockerell, the three grooves or sinkings found in some of the older examples, as in the temple of Neptune at Paestum and the temple of Aphaea at Aegina; there being only one groove in the Parthenon, the Theseum and later examples. In the temple of Ceres and the so-called Basilica at Paestum the hypotrachelium consists of a concave sinking carved with vertical lines suggestive of leaves, the tops of which project forward. A similar decoration is found in the capital of the columns flanking the tomb of Agamemnon at Mycenae, but here the hypotrachelium projects forward with a cavetto moulding, and is carved with triple leaves like the buds of a