74 PHYSICS. 
body ; and when the body possesses very little elasticity, the reflection may 
be total. In this latter case, the law that the angle of reflection is equal to 
the angle of incidence prevails; in the former, while one part is reflected 
according to the same law, the remainder is transmitted. 
Upon this law of reflection depends the phenomenon called the pr 
When sound strikes the reflecting surface at a right angle, it is thrown back 
again, and the quickness of the return depends on the distance from this 
surface. If this amount to 1125 feet, then the sound will complete its 
advance and return in two seconds: the tone will then be again heard after 
this time. As many syllables will be reflected by the echo as can be spoken in 
this time : the number may amount to seven or eight. The number of syllables 
repeated by an echo does not depend, then, so much upon rapidity of 
utterance, as upon the distance of the reflecting surface. At sea it has been 
found that even clouds have served as reflecting surfaces, so that it would 
seem as if the surface struck need not necessarily be a solid body. 
An echo often repeats the same syllable several times, this being produced 
by successive reflections of the same tone from different surfaces, or from 
two surfaces parallel to each other. Thus, from the top of the Rosstrappe 
in the Harz, the discharge of a pistol gives a manifold echo resembling 
rolling thunder. 
Here belongs the echo which returns a tone to a given spot, so as to be 
inaudible at a very short distance from it. Suppose an elliptical dome 
( pl. 19, fig. 93), aba’, whose foci are f and f’. A word spoken at one focus 
will be reflected to the other, and will be inaudible in the space between f 
and f’; a light whisper will be understood even if the distance between 
these points amounts to 80 or more feet. This phenomenon depends upon 
the fact that if lines be drawn from f and f’ to 7 and 7’, and any other 
points of the curve, these lines drawn to any one point will always make 
the same angle with the perpendicular at this point. Another phenomenon, 
such as occurs in the Rathskeller in Bremen, where the ticking of a clock in 
one corner of the arch is heard in the other, depends upon the fact that the 
flutings used to ornament the arches supply the place of tubes, which propa- 
gate sound better than the open air. 
The construction of rooms for public speaking or music, involves to a 
great extent the principles of the reflection of sound ; into all such construc- 
tions the parabola enters, or should enter, very largely, as a sound produced 
in the focus of a parabola is reflected in every direction with the greatest 
possible uniformity. 
d. Formation of Musical Tones. 
If we have a tube closed at one end, at the open end of which a sound 
wave enters, this latter will be transmitted to the other extremity and there 
be reflected. Standing vibrations may then be formed in the tube itself by 
the opposite action of the reflected and re-entering wave, as all the single 
strata in the tube begin their motion at the same time, attain at the same 
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