Chemical change which merely involves simple decomposition is thus seen to be influenced by the masses of the reacting substances and the presence of the products of decomposition; in other words the system of reacting substances and **resultants** form a mixture in which chemical action has apparently ceased, or the system is in equilibrium.

**Resultants**.-When we are given k homogeneous equations in k variables or k non-homogeneous equations in k - i variables, the equations being independent, it is always possible to derive from them a single equation R = o, where in R the variables do not appear.

Case of Three Variables.-In the next place we consider the **resultants** of three homogeneous polynomials in three variables.

48), at distances x and x+a from the left abutment, be their **resultants** on either side of C. Then the reaction at B is WIx/1+W2(x+a)/l.

Let all the **resultants** acting at the several centres of resistance be produced until they cut one another in a series of points so as to form an unclosed polygon.

The effect of this process is to give a series of points in the horizontal planes at which the **resultants** of all forces above those planes respectively cut FIG.

- These functions were originally known as " **resultants**," a name applied to them by Pierre Simon Laplace, but now replaced by the title " determinants," a name first applied to certain forms of them by Carl Friedrich Gauss.