70 PHYSICS. 
cuit, and begins a new one. The distance between two water particles in 
the same conditions of oscillation is called a wave length, and these particles 
have then precisely equal oscillations, while those lying on the half wave 
length are in precisely opposite conditions of oscillation. Other conditions 
occur where the motion is not perfectly regular, as then the paths cease te 
he circular, and frequently become elliptical, with the long diameter some- 
times horizontal, sometimes vertical. If the horizontal diameter = 0, the 
particles oscillate only at right angles to the direction of the waves, and it is 
motion of this kind that propagates waves in a stretched cord. A cord 
wave, when reaching a certain point, is thrown back again, ands may 
traverse the same route several times: two waves again may easily meet, 
and by their combination produce a standing wave. 
Let us now examine the character of the motion of a cord or string during 
a standing vibration. -A standing vibration of a string may be readily pro- 
duced by taking one not too tightly stretched, and, drawing it out of the 
position of equilibrium, letting it go again. All parts will be simultaneously 
on one or the other side of the position of equilibrium,—they will be simul- 
taneously at their maximum of distance from this position, the amplitude of 
oscillation only being different for each particle. The oscillations of a tense 
string when brought out of its equilibrium, or when disturbed by a bow 
drawn across its middle, are of precisely the same character; they are so 
rapid, however, as to be indistinguishable to the eye: they therefore give a 
tone. The standing vibrations in a string can also be shown by attaching 
one end, and with the other held in the hand, describing small circles, in 
which case the vibrations will form a great circle in the centre: accelerate 
the motion of the hand, and there will be in the middle of the string a point 
of rest, each half swinging as the whole did previously. Pd. 19, fig. 51, 
represents these vibrations: a is the point of rest ; the nodes, ab and ac, are 
the vibrations or bellying of the string. Two nodes and three bellyings 
even may by a still greater velocity be produced. There is a better mode 
of observing these nodes than the one just mentioned: take a stretched 
string, be ( fig. 52), and place a rest at a, so that ab = 4bc, and draw the 
bow of a fiddle across the smaller portion; the other portion will be set in 
vibration, and in such a manner that at the middle point there will be a 
second node, and consequently two bellies formed. The position of the 
node may be shown by its being the only point along the string where a 
small bit of paper laid across will not be thrown off by the vibrations of the 
string. Place the rest at one quarter of the length of the string, and there 
will be in the larger portion two nodes and three bellies. 
It is not strings alone that vibrate in this manner: plates, bells, and 
smaller bodies may also be set in vibration, and exhibit certain vibration 
nodes. To cause such bodies to vibrate, the apparatus, p/. 19, fig. 62, is 
employed, in which the plate of wood, glass, or metal, is laid upon the lower 
small cylinder, and then firmly fastened by means of the upper screw and a 
piece of cork. Set the plate into vibrations, which is best done by drawing 
across it a fiddle-bow, and the nodal lines and vibrating portions will ve 
rendered evident by strewing over the plate fine sand or lycopodium. The 
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