# Ternary sentence example

The idea_can be generalized so as to have regard to

**ternary**and higher forms each of the same order and of the same number of variables.Thus the

**ternary**quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester.For instance, those of a

**ternary**form involve two classes which may be geometrically interpreted as point and line co-ordinates in a plane; those of a quaternary form involve three classes which may be geometrically interpreted as point, line and plane coordinates in space.This paper will discuss methods for making

**ternary**sequence diffusers.It was verified very exactly by Stas's experiments, in which he removed the oxygen from the

**ternary**compound silver iodate and found that the whole of the silver and the iodine remained in combination with each other as silver iodide; his results prove, to one part in ten millions, that the combining ratio of the silver and the iodine is unaltered by the removal of the oxygen.AdvertisementWith mercury it forms amalgams. Bismuth is a component of many

**ternary**alloys characterized by their low fusibility and expansion in solidification; many of them are used in the arts (see Fusible Metal).The

**ternary**graph includes an optional legend that shows the data input.The amount of γ ' depends on the chemical composition and temperature, as illustrated in the

**ternary**phase diagrams below.Can handle a distorted page,

**ternary**plots, polar plots.So be sure to ponder your reasons when choosing the

**ternary**operator.Advertisement**Ternary**and Higher Forms.-The**ternary**form of order n is represented symbolically by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,...For example, take the

**ternary**quadratic (aixl+a2x2+a3x3) 2 =a2x, or in real form axi +bx2+cx3+2fx 2 x 3+ 2gx 3 x 1 +2hx i x 2.The

**ternary**cubic has been investigated by Cayley, Aronhold, Hermite, Brioschi and Gordan.Hesse showed independently that the general

**ternary**cubic can be reduced, by linear transformation, to the form x3+y3+z3+ 6mxyz, a form which involves 9 independent constants, as should be the case; it must, however, be remarked that the counting of constants is not a sure guide to the existence of a conjectured canonical form.This is of degree 8 in the coefficients, and degree 6 in the variables, and, for the canonical form, has the expression -9m 6 (x 3 +y 3 +z 3) 2 - (2m +5m 4 +20m 7) (x3 +y3+z3)xyz - (15m 2 +78m 5 -12m 8) Passing on to the

**ternary**quartic we find that the number of ground forms is apparently very great.AdvertisementFor the unipartite

**ternary**quantic of order n he finds that the fundamental system contains a (n+4) (n -1) individuals.He successfully considers the systems of two and three simultaneous

**ternary**quadratics.The alloy of the point e is the

**ternary**eutectic; it deposits the three metals simultaneously during the whole period of its solidfication and solidifies at a constant temperature.It is evident that any other property can be represented by similar diagrams. For example, we can construct the curve of conductivity of alloys of two metals or the surface of conductivity of

**ternary**alloys, and so on for any measurable property.This subject is far from being exhausted, and it is not improbable that the alloy-producing capacity of aluminium may eventually prove its most valuable characteristic. In the meantime,

**ternary**light alloys appear the most satisfactory, and tungsten and copper, or tungsten and nickel, seem to be the best substances to add.AdvertisementWe have in the Hessian the first instance of a covariant of a

**ternary**form.The theory of the invariants and covariants of a

**ternary**cubic function u has been studied in detail, and brought into connexion with the cubic curve u = o; but the theory of the invariants and covariants for the next succeeding case, the**ternary**quartic function, is still very incomplete.