ca maniac «1p 2S pesticide adi 
ao oe 
— 
Propagation of Pulses in Elastic Media. 375 
" x h ? ms wet 
_ But we have before found Ha. Substituting H for its 
value in the preceding equation, we have S=H+h. If then we 
put H+A for the velocity of the pulse, the space through which 
a H+ 
a body must fall to acquire that velocity will be i 
In this expresgion h is to be regarded as the intensity of the 
pulse : it being the length of that column of particles which must be 
superadded to the height of a homogeneous atmosphere, in order 
to produce in the air that degree of increased condensation which 
- the pulse effects in the particles through which it passes. 
If in the expression last found we make h=0, the expres- 
H, 
sion becomes 3 This is the result arrived at by Newton and 
which, as we have already remarked, was regarded by him and 
48 how generally received as the theoretical formula for the space 
through which a body must fall to acquire the velocity of sound. 
But it is evident from our demonstration that the velocity due to 
that space, instead of being the velocity of any assignable pulse, 
18 simply a limit below which no pulse can be propagated in an 
elastic fluid whose subtangent is H.* 3 | 
A pulse which produces the sensation of sound must produce 
teal motion in the particles through which it passes. In such a 
pulse A must have some finite magnitude. Nor can that magni- 
tude be by any: means the smallest that is competent to produce 
Motion in the air; for if such were the fact, then the slightest 
impulse given to the air by a vibratory movement, even waving 
the hand in it, should produce the sensation of sound, The in- 
tensity of a pulse which is competent to produce that sensation, 
will of course vary with the sensibility of the ear which is to 
receive it ; and consequently the nature of the case does not allow 
Us to assign any definite magnitude to the minimum intensity of 
Sonorous pulses; but we know by experience that the velocity of 
a 
_* Newton’s demonstration of this problem has been regarded by several distin- 
Prished mathematicians as obscure and inconclusive, omm« wit 
pothesis that a particle put in motion by a pulse is accelerated und retarded ac- 
rding to the law of the oscillating pendulum. Gabriel Cramer (sce Glasgow 
edition of Newton's Princi ia, Book I, prop. 48, notes) objects to the result ar- 
Tived at by Newton, that it flows from his hypothesis and not from the nature of 
gs. ; 
serene go e Iv e ert 
Fagrion.se Cramer rege the space through which the eer vibrates as an 
‘Anitesimal gpaait .. In such cas vides uy it can ma) ek ifference what i 
