At a later stage in the chapter experiments will be described
which are consistent with our conclusions, but cannot be taken
as a complete proof of the correctness of the assumptions.
This chapter must be regarded rather as a description of the
properties of transverse waves than as a logical deduction of
those properties from the laws of elasticity.
48. Waves arising fi-om the Harmonic Vibration
of a series of particles. Let us suppose we have a series
of particles placed at equal distances from each other along a
straight line, and each capable of vibrating harmonically in a
direction at right angles to that line, the lines of vibration all
lying in the same plane.
3—2



36



TRANSVERSE WAVES



[CH. Ill



Imagine the particles to be vibrating with equal periods
and amplitudes, and in such phases that each is some constant
fraction of its period behind the particle on its left. There
is then a constant difference of phase between any two con-
secutive particles, the retardation of phase increasing as we go
from left to right along the series. Suppose, for instance, that
each is one eighth of a period behind its left-hand neighbour,
and that at the moment we are considering particle 1 is pass-
ing downwards through its equilibrium position. Then since
2 is one eighth of a period behind 1, it will not have reached
its equilibrium position, but will be moving downwards
towards it. Its position can be found graphically from a
diagram similar to Fig. 7.
Describe a circle with radius* equal to the amplitude of
vibration of each of the particles, and draw a diameter P^Pj.
