_When two Undulations, from different Origins, coincide either
perfectly or very nearly in Direction, their joint effect is a
Combination of the Motions belonging to each._
Since every particle of the medium is affected by each undulation,
wherever the directions coincide, the undulations can proceed no
otherwise than by uniting their motions, so that the joint motion
may be the sum or difference of the separate motions, accordingly as
similar or dissimilar parts of the undulations are coincident.
I have, on a former occasion, insisted at large on the application of
this principle to harmonics; (Phil. Trans. for 1800. p. 130.) and it
will appear to be of still more extensive utility in explaining the
phenomena of colours. The undulations which are now to be compared
are those of equal frequency. When the two series coincide exactly in
point of time, it is obvious that the united velocity of the particular
motions must be greatest, and, in effect at least, double the separate
velocities; and also, that it must be smallest, and if the undulations
are of equal strength, totally destroyed, when the time of the greatest
direct motion belonging to one undulation coincides with that of the
greatest retrograde motion of the other. In intermediate states, the
joint undulation will be of intermediate strength; but by what laws
this intermediate strength must vary, cannot be determined without
further data. It is well known that a similar cause produces in sound,
that effect which is called a beat; two series of undulations of nearly
equal magnitude cooperating and destroying each other alternately, as
they coincide more or less perfectly in the times of performing their
respective motions.