All that can be recognized from the biblical records, however, is the period of internal prosperity which Israel and Judah enjoyed under Jeroboam and Uzziah (qq.v.) respectively.
4), like the remarkable vicissitudes in the traditions of Moses, Aaron and the Levites (qq.v.), represents changing situations of real significance, whose true place in the history can with difficulty be recovered.
The basis of this growth is partly the story-telling instinct innate in all men, which loves to heighten an effect, sharpen a point or increase a contrast - the instinct which breathes in Icelandic sagas like that of Burnt Njal; partly the instinct of idolization, if it may be so called, which leads to the perversion into impossible greatness of an approved character, and has created, in this instance, the legendary figures of Peter the Hermit and Godfrey of Bouillon (qq.v.); partly the religious impulse, which counted nothing wonderful in a holy war, and imported miraculous elements even into the sober pages of the Gesta.
In 493 the imminent prospect of a Persian invasion brought into power men like Themistocles and Miltiades (qq.v.), to whose firmness and insight the Athenians largely owed their triumph in the great campaign of 490 against Persia.
The Melchites therefore are those who accept the decrees of Ephesus and Chalcedon as distinguished from the Nestorians and Jacobite Church (qq.v.).
If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..
The chief lead ores are galena and cerussite; of minor importance are anglesite, pyromorphite and mimetesite (qq.v.).
Thus e 1 e 2 = - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.
The values of x and y are different, unless V (qq o) = o.
5) is QQ'- QS = BD sec 4:,(I - cos SQQ') = BD sec cI)(1 +cos 20) = 2BD cos 4); from which it follows that an error of given magnitude in the figure of a surface is less important in oblique than in perpendicular reflection.
The origin of this particular form of worship can scarcely be sought in Egypt; the Apis which was worshipped there was a live bull, and image-worship was common among the Canaanites in connexion with the cult of Baal and Astarte (qq.v.).
If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.
Riscus, rischium, and risicum are found, according to Du Cange (Gloss., qq.v.), as early as the 13th century.
In the articles on Apocalyptic Literature and Apocryphal Literature (qq.v.) we have shown the large lines of differentiation between apocalyptic and prophecy.
This is actually the case; the Carboniferous, Cretaceous and Jurassic systems (qq.v.) contain coal-bearing strata though in unequal degrees,- the first being known as the Coal Measures proper, while the others are of small economic value in Great Britain, though more productive in workable coals on the continent of Europe.
The recognition of this fact is expressed, at the present day, by the division of the Sporozoa into several well-defined orders, which are grouped in two main divisions, each containing more or less closely related forms. One of these groups consists of the Gregarines, Coccidia and Haer_aosporidia (qq.v.).
Recently, however, considerable doubt has been thrown upon the general occurrence of this latter condition in certain Myxosporidia (Microsporidia); and the present writer adopts as preferable, therefore, the terms Ectospora and Endospora (qq.v.), invented by E.
The male god Dagon has his partner Astarte (qq.v.), and Baal-zebub, a famous oracle of Ekron (2 Kings i.) finds a parallel in the local " baals " of Palestine.'
Calcium silicate is also present in the minerals: olivine, pyroxenes, amphiboles, epidote, felspars, zeolites, scapolites (qq.v.).
In the first place, we find in this group two distinct types of person or individual, the polyp and the medusa (qq.v.), each capable of a wide range of variations; and when both polyp and medusa occur in the life-cycle of the same species, as is frequently the case, the result is an alternation of generations of a type peculiarly characteristic of the class.
During this period De la Gardie was the ruling spirit of the government and represented the party of warlike adventure as opposed to the party of peace and economy led by Counts Bonde and Brahe (qq.v.).
There are some fundamental divergencies in the representations of the traditions of both David and Saul (qq.v.), and there is indirect and 1 Cf.
Sing.), which show that the Latin first spoken by the Vestini was not that of Rome, but that of their neighbours the Marsi and Aequi (qq.v.).
Of Eucken and Miinsterberg (qq.v.).
- The works mentioned below are for the most part those not included in the separate bibliographies to the articles on the individual popes (qq.v.).
These families are described and their affinities discussed in the articles Neuroptera and Hexapoda (qq.v.).
PAELIGNI, a people of ancient Italy, first mentioned as a member of a confederacy which included the Marsi, Marrucini and Vestini (qq.v.), with which the Romans came into conflict in the second Samnite War, 325 B.C. (Lw.
The flame issuing from the furnace by (o) is always further utilized for boiling down the liquors obtained in a later stage, either in a pan (p) fired from the top and supported on pillars (qq) as shown in the drawing, or in pans heated from below.
The earliest inhabitants of Messenia are said to have been Pelasgians and Leleges (qq.v.), of whom the latter had their capital at Andania.
(qq.v.) made an heroic and entirely disinterested attempt in the latter part of the 3rd century to improve the conditions by a redistribution of land, a widening of the citizen body, and a restoration of the old severe training and simple life.
Linnaeus applied the Latin term Vermes to the modern zoological divisions Mollusca, Coelentera, Protozoa, Tunicata, Echinoderma (qq.v.), as well as to those forms which more modern zoologists have recognized as worms. As a matter of convenience the term Vermes or Vermidea is still employed, for instance in the International Catalogue of Zoological Literature and the Zoological Record, to cover a number of wormlike animals.
Of the above, Reindeer and Elk are dealt with in separate articles (qq.v.).
Long from the source of the Swale or Ure) and the Trent (170 m.), qq.v.
Draw Pp and Qq touching both catenaries, Pp and Qq will intersect at T, a point in the directrix; for since any catenary with its directrix is a similar figure to any other catenary with its directrix, if the directrix of the one coincides with that of the other the centre of similitude must lie on the common directrix.
Similarly Qq must pass through the centre of similitude.
Hence T, the point of intersection of Pp and Qq, must be the centre of similitude and must be on the common directrix.
The principal market centres are Leeuwarden, the chief towns, Sneek, Bolsward, Franeker (qq.v.), Dokkum (40J3) and Heerenveen (5011).
A(pp) =X, B(qq) =u, C(rr) =v, ~
This has a reciprocal Q -1= p-r = qq-1 - wp1 rq1, and a conjugate KQ (such that K[QQ'] = KQ'KQ, K[KQ] = Q) given by KQ = Kq-}-rlKp+wKr; the product QQ' of Q and Q' is app'+nqq'+w(pr'+rq'); the quasi-vector RI - K) Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-scalar (in a different sense from the rest of this article) 2(1+K)Q is Combebiac's scalar (Sp+Sq)+Combebiac's plane.
If Q and Q' are commutative, that is, if QQ' = Q'Q, then Q and Q' have the same centre and the same radius.