Propagation of Pulses in Elastic Media. 373 
pulses. This we shall do by solving the general problem of the 
velocity of pulses by a new process, whic comprehends the in- 
tensity of the pulse as an essential element. Having done this, 
we shall see the relation in which the case solved by Newton 
stands to the general law; and if we mistake not, it will then be 
apparent that the velocity found in that case is not the velocity 
of sound. 
A pulse, considered as propagated through a line of particles 
and considered with reference to its physical condition at any in- 
Stant of time, consists of a series of contiguous ‘particles in that 
line, greater or less in number, which are more dense than the 
particles before and behind them on the line, and which are in 
motion with some velocity, while the particles before and behind 
are at rest and in their natural state of density. This series of 
particles, as it advances, encounters successively the stationary 
Particles, compressing them to the same density, putting, them in 
Motion, and thus adds them to the series. In the mean time, an 
equal number of the posterior particles of the series expand, re- 
Stming their natural density, and come to rest. It is obvious that 
if the propelling force due to the reaction of the particles expand- 
ing from the posterior extremity of the series, is equal to the re- 
tarding force of the particles encountered by the anterior extrem- 
ily, (as must always be the case if the elasticity is perfect, and if 
€ action is confined to the particles in the line,) then the pulse 
will continue to advance indefinitely, and with a uniform veloci- 
ty; a velocity however which, as we shall see, is not independent 
of the degree of condensation to which the particles are brought. 
c 
D 
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ESR, 
as 3 
Particle behind it is greater than that of the particle before it, and 
Where the density is a maximum, it is likewise a point where the 
Let mn be the space which.a particle in its + : 
hatural state occupies on the line AB, and let sx ™ eee 
that P 7} . I a * 
