## Binary Sentence Examples

- Gordan has also shown that the vanishing of the Hessian of the
**binary**n ic is the necessary and sufficient condition to ensure the form being a perfect n th power. - The
**binary**products e i e j, however, are expressible as linear functions of the units e i by means of a " multiplication table " which defines the special characteristics of the algebra in question. **BINARY**SYSTEM, in astronomy, a system composed of two stars revolving around each other under the influence of their mutual attraction.- The nomenclature of acids follows the same general lines as that for
**binary**compounds. - So the theory of the forms appertaining to a
**binary**form of unrestricted order was first worked out by Cayley and P. A. - THE Theory Of
**Binary**Forms A**binary**form of order n is a homogeneous polynomial of the nth degree in two variables. - THE Theory Of
**Binary**Forms A**binary**form of order n is a homogeneous polynomial of the nth degree in two variables. - 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? - In the Lavoisierian nomenclature acids were regarded as
**binary**oxygenated compounds, the associated water being relegated to the position of a mere solvent. - Thus, the affinity of hydrogen and oxygen for each other is extremely powerful, much heat being developed by the combination of these two elements; when
**binary**compounds of oxygen are decomposed by the electric current, the oxygen invariably appears at the positive pole, being negative to all other elements, but the hydrogen of hydrogen compounds is always disengaged at the negative pole. - If a compound contains two atoms it is termed a
**binary**compound, if three a ternary, if four a quaternary, and so on. - This view was accepted in 1817 by Leopold Gmelin, who, in his Handbuch der Chemie, regarded inorganic compounds as being of
**binary**composition (the simplest being oxides, both acid and basic, which by combination form salts also of**binary**form), and organic compounds as ternary, i.e. - Symbolic Form.-Restricting consideration, for the present, to
**binary**forms in a single pair of variables, we must introduce the symbolic form of Aronhold, Clebsch and Gordan; they write the form Iln n n-1 n-1 n n n aixi+a2x2) = 44+(1) a l a 2 x 1 x2+...+a2.x2=az wherein al, a2 are umbrae, such that n-1 n-1 n a 1, a 1 a 2, ...a 1 a 2, a2 are symbolical respreentations of the real coefficients ï¿½o, ai,... - -When the
**binary**form a y = (alxl +a2x2)n is transformed to A;. - And we may suppose such identities between the symbols that on the whole only two, three, or more of the sets of umbrae are not equivalent; we will then obtain invariants of two, three, or more sets of
**binary**forms. The symbolic expression of a covariant is equally simple, because we see at once that since AE, B, Ce,... - A
**binary**form of order n contains n independent constants, three of which by linear transformation can be given determinate values; the remaining n-3 coefficients, together with the determinant of transformation, give us n -2 parameters, and in consequence one relation must exist between any n - I invariants of the form, and fixing upon n-2 invariants every other invariant is a rational function of its members. - We can so determine these n covariants that every other covariant is expressed in terms of them by a fraction whose denominator is a power of the
**binary**form. - As regards simultaneous
**binary**forms, the system of two quadratics, and of any number of quadratics, is alluded to above and has long been known. - The
**Binary**Sextic.-The complete system consists of 26 forms, of which the simplest are x2y2z2 + (1 +8 m3) 2 (y3z3 +z3x3 +x3y3). - One advantage we have obtained is that, if we now write ao =o, and substitute a 8 _ 1 for a,, when s>o, we obtain d d aO da l +al da 2 +a2 da ï¿½....+an_2dan_1 which is the form of SZ for a
**binary**(n- Henceby merely diminishing each suffix in a seminvariant by unity, we obtain another seminvariant of the same degree, and of weight w-8, appertaining to the (n-I) ic. Also, if we increase each suffix in a seminvariant, we obtain terms, free from a 0, of some seminvariant of degree 8 and weight w+8. - 1 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second
**Binary**Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2. - Ursae majoris is a beautiful
**binary**star, its components having magnitudes 4 and 5; this star was one of the first to be recognized as a**binary**- i.e. - These facilities, coupled with the wide and fascinating field of research opened up by Sir William Herschel's discovery of the
**binary**character of double stars, gave an impulse to micrometric research which has continued unabated to the present time. - A distinction was formerly made between double stars of which the components were in revolution around each other, and those in which no relative motion was observed; but it is now considered that all double stars must really be
**binary**systems. - Interesting objects in this constellation are: a Geminorum or Castor, a very fine double star of magnitudes 2.0 and 2.8, the fainter component is a spectroscopic
**binary**; i Geminorum, a long period (231 days) variable, the extreme range in magnitude being 3.2 to 4; Geminorum, a short period variable, 10.15 days, the extreme range in magnitude being 3.7 to 4.5; Nova Geminorum, a "new" star discovered in 1903 by H. - Previous to Chevreul's researches on the fats (1811-1823) it was believed that soap consisted simply of a
**binary**compound of fat and alkali. - But the same relation does not hold of a satellite the mass of whose primary is not regarded as an absolutely known quantity, or of a
**binary**star. - When
**binary**compounds, or compounds of two elements, are decomposed by an electric current, the two elements make their appearance at opposite poles. - Salts formed from hydracids terminate in -ide, following the rule for
**binary**compounds. - The
**binary**conception of compounds held by Berzelius received apparent support from the observations of Gay Lussac, in 1815, on the vapour densities of alcohol and ether, which pointed to the conclusion that these substances consisted of one molecule of water and one and two of ethylene respectively; and from Pierre Jean Robiquet and Jean Jacques Colin, showing, in 1816, that ethyl chloride (hydrochloric ether) could be regarded as a compound of ethylene and hydrochloric acid. - 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.