Originally it seems to have denoted the coast district between the Oder and the Vistula, a territory which was at first more or less dependent on Poland, but which, towards the end of the 12th century, was ruled by two native princes, who took the title of duke about 1170 and admitted the authority of the German king in 1181.
The essence of the tax denoted by these names was that the amount was fixed en bloc for a whole group of persons, and afterwards divided among them in various ways.
The intensity (at any point) of the field due to the magnetization may be denoted by H i, that of the external field by Ho, and that of the resultant field by H.
It is quite possible that shabattum and nubattum are from the same root and originally denoted much the same thing - a pause, abstention, from whatever cause or for ceremonial purposes.
Nevertheless, though the conceptions originally denoted by " evolution " and " development " were shown to be untenable, the words retained their application to the process by which the embryos of living beings gradually make their appearance; and the terms" development," " Entwickelung,"and " evolutio " are now indiscriminately used for the series of genetic changes exhibited by living beings, by writers who would emphatically deny that " development " or " Entwickelung " or " evolutio," in the sense in which these words were usually employed by Bonnet or Haller, ever occurs.
The Greek form of Gallia was FaXaria, but Galatia in Latin denoted another Celtic region in central Asia Minor, sometimes styled Gallograecia.
He constructed a map of as many as 576 of these lines, the principal of which he denoted by the letters of the alphabet from A to G; and by ascertaining their refractive indices he determined that their relative positions are constant, whether in spectra produced by the direct rays of the sun, or by the reflected light of the moon and planets.
As really denoted any integer or whole; whence the English word "ace."
The words " Asiatic " and " Oriental " are often used as if they denoted a definite and homogeneous type, but Russians resemble Asiatics in many ways, and Turks, Hindus, Chinese, &c., differ in so many important points that the common substratum is small.
Castor and Pollux), in astronomy, the third sign in the zodiac, denoted by the symbol II.
In Zeumer's edition of the Leges Wisigothorum the versions of Recceswinth and Erwig, where they differ from each other, are shown in parallel columns, and the laws later than Erwig are denoted by the sign "nov."
The hypothetical radicals of acids, were denoted by squares enclosing the initial letter of the base; an alkali was denoted by a triangle, and the particular alkali by inserting the initial letter.
Compounds were denoted by joining the symbols of the components, and by varying the manner of joining compounds of the same elements were distinguished The symbol V was used to denote a liquid, and a vertical line to denote a gas.
If two compounds combined, the + signs of the free compounds were discarded, and the number of atoms denoted by an Arabic index placed after the elements, and from these modified symbols the symbol of the new compound was derived in the same manner as simple compounds were built up from their elements.
At a later date Berzelius denoted an oxide by dots, equal in number to the number of oxygen atoms present, placed over the element; this notation survived longest in mineralogy.
The ringed structure of benzene, C 6 H 61 was first suggested in 1865 by August Kekule, who represented the molecule by six CH groups placed at the six angles of a regular hexagon, the sides of which denoted the valencies saturated by adjacent carbon atoms, the fourth valencies of each carbon atom being represented as saturated along alternate sides.
A doubly linked pair of atoms is denoted by the sign A with the index corresponding to the side; if there are two pairs of double links, then indices corresponding to both sides are employed.
If twelve grammes of amorphous carbon be burnt to carbon dioxide under constant volume, the heat evolved (96.96 cal.) does not measure the entire thermal effect, but the difference between this and the heat required to break down the carbon molecule into atoms. If the number of atoms in the carbon molecule be denoted by n, and the heat required to split off each atom from the molecule by d, then the total heat required to break down a carbon molecule completely into atoms is nd.
The chief of these ministers is denoted 6 E7rl r&o' 7r pay µarwv, and he corresponds to the vizier of the later East.
1 In the early decades of the Christian era the text was current in two forms, which are denoted by H a and H R in this article and in the edition of the text published by the Oxford University Press.
Such marks had often a religious significance, and denoted that the bearer was a follower of a particular deity.
But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.
The function Zap 1 a 2 P2 ...an n being as above denoted by a partition of the weight, viz.
The elementary functions are denoted by (1), (12), (13), ...
The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric function of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!
It should be noticed that the real function denoted by (ab) 2 is not the square of a real function denoted by (ab).
L ax 2 2 ax i l This is called the kth transvectant of f over 4); it may be conveniently denoted by (f, (15)k.
Every symmetric function denoted by partitions, not involving the figure unity (say a non-unitary symmetric function), which remains unchanged by any increase of n, is also a seminvariant, and we may take if we please another fundamental system, viz.
Let this number be denoted by (w; 0, n).
The extraordinary advantage of the transformation of S2 to association with non-unitary symmetric functions is now apparent; for we may take, as representative forms, the symmetric functions which are symbolically denoted by the partitions referred to.
If 0=2, every form is obviously a ground form or perpetuant, and the series of forms is denoted by (2), (22), (23),...(2K+1)....
R is denoted by I?'
- The numbers denoted by n (r) in ï¿½ 41 are the binomial coefficients shown in the table in ï¿½ 40; n (r) being the (r+ i) th number in the (n+ i) th row.
(n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of ï¿½41, be denoted by n [r 7.
A point A in space may be associated with a (real, positive, or negative) numerical quantity a, called its weight, and denoted by the symbol aA.
The equations q'+x = q and y+q' = q are satisfied by the same quaternion, which is denoted by q - q'.
It is the value of y which is generally denoted by q= q'; a special symbol for x is desirable, but has not been established.
This unit is called the supplement of E, and denoted by IE.
Any linear quantity may be denoted by a symbol (a 1, a2, ...
When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as j,, 3?
The intensity of magnetization, or, more shortly, the magnetization of a uniformly magnetized body is defined as the magnetic moment per unit of volume, and is denoted by I, I, or „a.
An angle e with the normal, the normal component of the magnetization, I cos e, is called the surface density of the magnetism, and is generally denoted by a.