John Le Conte—Sound-Shadows in Water. 85 
EXPLANATION OF THE PHENOMENA OBSERVED. 
15. Greater distinctness of Sound-shadows in Water—The 
much greater distinctness of acoustical shadows in water, as com- 
pared with those in air, appears to be pretty clearly established 
y the experiments of Colladon, and the fact seems to be abun- 
dantly confirmed by those which we have recorded in the 
preceding pages. This is an interesting and significant phenom- 
enon in relation to the theory of sound.’ At first sight, it might 
be supposed that the difference is due to the greater velocity of 
propagation of the sound-wave in water. This may have been 
ir John Herschel’s idea, when he explains Colladon’s results 
by reference to the greater elasticity of water.* 
ut, as already indicated (3), according to the mathematical 
theory of undulations the intensity of the effects, due to the 
secondary waves propagated into the geometrical shadow from 
the borders of the obstacle, is not directly dependent upon the 
velocity of propagation, but is properly a function of the wave- 
length: the diffractive divergence being less for short than for 
long waves. Hence it follows, that the distinctness of sound- 
shadows, like those of light, should depend upon the shortness 
of the wave-lengths. We have already seen (5) that the experi- 
ment verifies this prevision of theory in the case of sound- 
waves in air, by demonstrating that acute sounds cast more 
distinct shadows than grave sounds. Does this principle apply 
to sound-shadows in water? . 
me physicists have attempted to explain the phenomenon 
of the great distinctness of sound-shadows in water, as indicated 
by the observations of Colladon (8), by assuming that the 
lengths of the sonorous waves propagated through water are 
much shorter than those transmitted through air.t But no reason 
18 given for this fundamental assumption, other than that it is 
required by the demands of the theory of undulations, in order 
to account for the more perfect shadows in water. It evidently 
would be vastly more philosophical to establish as a matter of 
fact the greater shortness of the sound-waves in water, and thus 
to verify the deductions of theory. This we shall endeavor to 
accomplish. 
16. Measurement of Wave-lengths—W ith regard to continuous 
or musical sounds, we have the means of very readily determin- 
elocity of Sound — 
; Number of Vibrations. 
It is evident, therefore, that the number of vibrations or musica 
Pitch of the sonorous body remitting the same, the wave-length 
™M water, so far from being shorter, must be more than four times 
* “Treatise on ” bw 02. 
+ Vide W. H. e pordaire gtoprte eB Nek PAL,” “ Acoustics and Optics,” 
ing the wave-length; for it is equal to 
