Its function could determine the meaning of the symbols, since the most ancient Immortal writing is based on a complex system of symbolic context.
There are several symbolic acts descriptive of the siege.
The waratah or native tulip, the magnificent flowering head of which, with the kangaroo, is symbolic of the country, is one of the Proteaceae.
Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed a general symbolic method of logical inference.
That the name also prevailed as that of a god among other Semitic races (or even These sacred arks were carried in procession accompanied by symbolic figures.
Constitutional formulae like these, in fact, are nothing more than symbolic expressions of the character of the compounds which they represent, the arrangement of symbols in a certain definite manner being understood to convey certain information with regard to the compounds represented.
The loculi were intact and the epitaphs still in their places, so that " they form a kind of museum, in which the development, the formulae, and the symbolic figures of Christian epigraphy, from its origin to the end of the 3rd or 4th century, can be notified and contemplated, not in artificial specimens as in the Lateran, but in the genuine and living reality of their original condition."
It is clear from what has been said above that the liturgical vestments possessed originally no mystic symbolic meaning whatever; it was equally certain that, as their origins were forgotten, they would develop such a symbolic meaning.
We cannot even outline here the process of selection by which the symbolic meanings now stereotyped in the Roman Pontifical were arrived at.
With the amice, "Place on my head the helmet of salvation," &c. For the symbolic meanings of the various vestments see the separate articles devoted to them.
Two methods of treatment have been carried on in parallel lines, the unsymbolic and the symbolic; both of these originated with Cayley, but he with Sylvester and the English school have in the main confined themselves to the former, whilst Aronhold, Clebsch, Gordan, and the continental schools have principally restricted themselves to the latter.
Stroh, from a knowledge of the results, was able to verify and extend the results by the symbolic method.
A separation is the symbolic representation of a product of monomial symmetric functions.
(1 + a i x) (1+ = s i z we have the symbolic identity +02712+0.3x3+...
Where the multiplications on the leftand right-hand sides of the equation are symbolic and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation exp (M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities.
To express the function aoa2 - _ which is the discriminant of the binary quadratic aoxi -+-2a1x2x2-+a2x2 = ai =1, 1, in a symbolic form we have 2(aoa 2 -ai) =aoa2 +aGa2 -2 a1 ï¿½ al = a;b4 -}-alb?
To find the effect of linear transformation on the symbolic form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, Iï¿½1, A2, ï¿½2.
May be the same or different, it is necessary that every product of umbrae which arises in the expansion of the symbolic product be of degree n, in a l, a 2; in the case of b,, b 2 of degree n 2; in the case of c 1, c 2 of degree n3; and so on.
It will be shown later that all invariants, single or simultaneous, are expressible in terms of symbolic products.
Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.
-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.
The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.
Of the symbolic factors of the form are replaced by IA others in which new variables y1, y2 replace the old variables x1, x 2 .
We have seen that transvection is equivalent to the performance of partial differential operations upon the two forms, but, practically, we may regard the process as merely substituting (ab) k, (OW for azbx, 4x t ' respectively in the symbolic product subjected to transvection.
And that thence every symbolic product is equal to a rational function of covariants in the form of a fraction whose denominator is a power of f x.
Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...