When there are more luminous points than one, we have only to draw separately the geometrical shadows due to each of the sources, and then **superpose** them.

It is easily shown that after a time we shall have to **superpose** on the original displacement a displacement proportional to the square of the particle velocity, and this will introduce just the same set of combination tones.

To obtain the complete solution of (II) we must of course **superpose** the free vibration (6) with its arbitrary constants in order to obtain a complete representation of the most general motion consequent on arbitrary initial conditions.

For a complete solution of (34) we must of course **superpose** the free vibration (30); but owing to the factor ehlt the influence of the initial conditions gradually disappears.