The numerical values are, it is to be noted, exceedingly small.
His treatise on numerical divisions, weights and measures (Distributio) is extant, with the exception of the concluding portion.
In 1905 the value of the wool export regained the £20,000,000 level, and with the rapid recovery of the numerical II.
Its symbolic expression, to a numerical factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.
Largesse was especially given on the field of victory, and was, moreover, liberally distributed to stifle sedition and mutiny among the troops, the numerical strength of which was continually increased as the empire enlarged its borders.
- the same influence, for instance, as the Italians, who had an imposing numerical force.
When, therefore, the latter, on the 22nd, marched southward to reopen his communications by the defeat of the enemy's army, always the surest means of solving this difficulty, he actually reached the neighbourhood of Eckmuhl with a sufficient numerical superiority had he only been prompt enough to seize his opportunity.
A V(I - a) This constant k gives a numerical value for the chemical affinity, and the equation should represent the effect of dilution on the molecular conductivity of binary electrolytes.
Other " Galois " groups were defined whose substitution coefficients have fixed numerical values, and are particularly associated with the theory of equations.
D x the first evectant; and thence 4cxdi the second evectant; in fact the two evectants are to numerical factors pres, the cubic covariant Q, and the square of the original cubic.
The discriminant of f is equal to the discriminant of 0, and is therefore (0, 0') 2 = R; if it vanishes both f and 0 have two roots equal, 0 is a rational factor of f and Q is a perfect cube; the cube root being equal, to a numerical factor pres, to the square root of A.
Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.
Of these thirteen sections, the first contains a simple description of the more prominent phenomena, without mathematical symbols or numerical data.
Inside a magnetized body, B is the force that would be exerted on a unit pole if placed in a narrow crevasse cut in the body, the walls of the crevasse being perpendicular to the direction of the magnetization (Maxwell, § § 399, 604); and its numerical value, being partly due to the free magnetism on the walls, is generally very different from that of H.
He attended lectures on the numerical solution of equations and on definite integrals by M.
When a character is said to be transmitted, or to be correlated with another character, the biometricist declares the statement valueless without numerical estimations of the inheritance or correlation.
The ultimate value of numerical inquiries must depend on the equivalence of the units on which they are based.
The nature of this problem is illustrated by the numerical example in § g.
Manchester in 1906, when the Labour party were returned for the first time in numerical force - over 50 in all.
The old B retained the numerical value of the Greek i as 2, and no numerical value was given to the new symbol.
In Greek, where I is the twentieth letter of the alphabet, or, if the merely numerical and p are excluded, the eighteenth, another form 1 or S according to the direction of the writing is also widespread.
(5) Every letter of a word is reduced to its numerical value, and the word is explained by another of the same quantity.
Where the induction is high the lines will be crowded together; where it is weak they will be widely separated, the number per square centimetre crossing a normal surface at any point being always equal to the numerical value of B.
The magnetic susceptibility expresses the numerical relation of the magnetization to the magnetizing force.
Equations (33) and (34) show that when, as is generally the case with ferromagnetic substances, the value of is considerable, the resultant magnetic force is only a small fraction of the external force, while the numerical value of the induction is approximately three times that of the external force, and nearly independent of the permeability.
Curves of magnetization (which express the relation of I to H) have a close resemblance to those of induction; and, indeed, since B = H+47r1, and 47rI (except in extreme fields) greatly exceeds H in numerical value, we may generally, without serious error, put I = B /47r, and transform curves of induction into curves of magnetization by merely altering the scale to which the ordinates are referred.
It seems that confusion and trouble will be best avoided by abstaining from the introduction of the non-evident somites, the ocular and the praegenital, into the numerical nomenclature of the component somites of the three great body regions.
The chamber has the right of initiative in the organization of the annual budget laws and those relative to the numerical strength of the army and navy.
And, their own predominance being assured by their numerical strength and influence, they accorded equal shares of power to the other monti.
The commission also called attention to the numerical insufficiency of magistrates and native commissioners in certain parts of Natal.
According to this reading, William sought to rectify his position by asserting, not the numerical identity of the universal in each individual, but rather its sameness in the sense of indistinguishable similarity.
In the case of division we get two kinds of arithmetical formula, which, however, may be regarded as requiring a single kind of numerical process in order to determine the final result.
We must count with something; and the successive somethings obtained by the addition of successive units are in fact numerical quantities, not numbers.
While mensuration is concerned with the representation of geometrical magnitudes by numbers, graphics is concerned with the representation of numerical quantities by geometrical figures, and particularly by lengths.
There are also cases in which graphics and mensuration are used jointly; a variable numerical quantity is represented by a graph, and the principles of mensuration are then applied to determine related numerical quantities.
Graphic representation thus rests on the principle that equal numerical quantities may be represented by equal lengths, and that a quantity mA may be represented by a length mL, where A and L are the respective units; and the science of graphics rests on the converse property that the quantity represented by pL is pA, i.e.
The numerical factor 6 is called the coefficient of a 5 bc 2 (ï¿½ 20); and, generally, the coefficient of any factor or of the product of any factors is the product of the remaining factors.
It must, of course, be remembered (ï¿½ 23) that this is a statement of arithmetical equality; we call the statement an " identity," but we do not mean that the expressions are the same, but that, whatever the numerical values of a, b and c may be, the expressions give the same numerical result.
Owing to the existence of a strong Mussulman minority among its inhabitants, the warlike character of the natives, and the mountainous configuration of the country, which enabled a portion of the Christian population to maintain itself in a state of partial independence, the island has constantly been the scene of prolonged and sanguinary struggles in which the numerical superiority of the Christians was counterbalanced by the aid rendered to the Moslems by the Ottoman troops.
This is rendered possible by the fact that we can use a single letter to represent a single number or numerical quantity, however many digits are contained in the number.
He is notorious for his wilful exaggeration, both in narrative and numerical statements.
In this mode of treating the question the order of the terms is numerical, and though the amount of labour is such as might well have deterred a younger man, yet the details were easy, and a great part of it might be entrusted to a mere computer.
The overwhelming numerical superiority of the Sla y s, and the very great differences in ethnical type, belief and mythology between the IndoEuropean and the Ural-Altaic races, may have contributed to the same end.
The principal orders, arranged according to their numerical importance, are as follows: - Leguminosae,Rubiaceae, Orchidaceae, Compositae, Gramineae, Euphorbiaceae, Acanthaceae, Cyperaceae and Labiatae.
Af Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 ï¿½; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.
The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.
The small magnet may be a sphere rigidly magnetized in the direction of Ho; if this is replaced by an isotropic sphere inductively magnetized by the field, then, for a displacement so small that the magnetization of the sphere may be regarded as unchanged, we shall have dW = - vIdHo = v I+-, whence W = - 2 I + H2 ° (37) The mechanical force acting on the sphere in the direction of displacement x is 1 Hopkinson specified the retentiveness by the numerical value of the " residual induction " (=47rI).
Races," in the article Austria), the census returns of 1880, 1890 and 1900, exhibiting the numerical strength of the different nationalities, are of great interest.
The Church of England claims as adherents 39% of the population, and the Roman Catholic Church 22%; next in numerical strength are the Wesleyans and other Methodists, numbering 12% i the various branches of the Presbyterians 11%, Congregationalists 2%, and Baptists 2%.
= ...+O(s i s 2 s 3 ...)xl1x12x13...+..., where 0 is a numerical coefficient, then also O ?2 0.3 P1 P2 P3 Al A2 A3 +.
Since, If F = An, 4) = By, 1 = I (Df A4) Of A?) Ab A"'^1Bz 1=, (F, Mn Ax I Ax 2 Axe Ax1) J The First Transvectant Differs But By A Numerical Factor From The Jacobian Or Functional Determinant, Of The Two Forms. We Can Find An Expression For The First Transvectant Of (F, ï¿½) 1 Over Another Form Cp. For (M N)(F,4)), =Nf.4Y Mfy.4), And F,4, F 5.4)= (Axby A Y B X) A X B X 1= (Xy)(F,4))1; (F,Ct)1=F5.D' 7,(Xy)(F4)1.
It is (f = (ab) 2 a n-2 r7 2 =Hx - =H; unsymbolically bolically it is a numerical multiple of the determinant a2 f a2f (32 f) 2ï¿½ It is also the first transvectant of the differxi ax axa x 2 ential coefficients of the form with regard to the variables, viz.
The French alphabet, written out with the same numerical values as the Hebrew, in which the first nine letters denote units and the others tens, will have the following significance:
Next in numerical importance to the Mongolians are the races which have been called by Professor Huxley Melanochroic and Xanthochroic. The former includes the dark-haired people of southern Europe, and extends over North Africa, Asia Minor, Syria to south-western Asia, and through Arabia and Persia to India.
Carpenter (1899, 1902-1904) has lately endeavoured to show an exact numerical correspondence in segmentation between the Hexapoda, the Crustacea, the Arachnida, and the most primitive of the Diplopoda.
And by elimination we obtain the resultant ao 0 bo 0 0 al ao b1 bo 0 a 2 a i b 2 b 1 bo a numerical factor being disregarded.