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.
It is a fundamental result in dynamics that, if a body be projected vertically upwards in vacuo, with a velocity of v centimetres per second, it will rise to a height of v 2 /2g centimetres, where g represents the numerical value of the acceleration produced by gravity in centimetre-second units.
He is notorious for his wilful exaggeration, both in narrative and numerical statements.
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.
It is among the Invertebrata that epidemics of destruction are referred to, though we should bear in mind that it is only the difference in numerical proportion that prevents our speaking of an epidemic of elephants or of rabbits, though we use the term when speaking of blight insects; there is little consistency in the matter, as it is usual to speak of an invasion or scourge of locusts, caterpillars, &c. Insect injuries are very varied in degree and in kind.
The principles by means of which the magnitude and position of balance weights are worked out are given in the article Mechanics (Applied Mechanics), and the whole subject of locomotive balancing is exhaustively treated with numerous numerical examples in The Balancing of Engines by W.
The nature of this problem is illustrated by the numerical example in § g.
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.
1 Thus Canon V., according to which a word is reduced to its numerical value and interpreted by another word of the same value, is recognized in the New Testament (cf.
The numerical values are, it is to be noted, exceedingly small.
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.
When a homogeneous polynomial is transformed by general linear substitutions as hereafter explained, and is then expressed in the original form with new coefficients affecting the new variables, certain functions of the new coefficients and variables are numerical multiples of the same functions of the original coefficients and variables.
Other " Galois " groups were defined whose substitution coefficients have fixed numerical values, and are particularly associated with the theory of equations.
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.
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,,.
= ...+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.
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.
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.
Its symbolic expression, to a numerical factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.
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).
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:
But no one at the time foresaw (what now seems so evident) that this was the only way an army of eight hundred thousand men--the best in the world and led by the best general--could be destroyed in conflict with a raw army of half its numerical strength, and led by inexperienced commanders as the Russian army was.