When chemical change is expressed with the aid of molecular formulae not only is the distribution of weight represented, but by the mere inspection of the symbols it is possible to deduce from the law of gaseous combination mentioned above, the relative volumes which the agents and **resultants** occupy in the state of gas if measured at the same temperature and under the same pressure.

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.