influence of Vibratory Motions. 433 
number of vibrations made by the body in the same time; hence 
the interval between two successive impulses, would be equal to 
the duration of two of these vibrations: thérefore, under the 
above supposition, the interval between two impulses will sur- 
pass by a little the duration of two vibrations, and if the reac- 
tion of these vibrations upon the nascent contractions and expan- 
sions is not sufficiently powerful to modify their length, and thus 
occasion unison, the small excess in the duration of the intervals 
in question will maintain itself. This being the case, let us set 
out from the first impulse. This will cause the body to perform 
a descending vibration, which will be followed by an ascending 
one; the second impulse will take place shortly after the com- 
mencement of a new descending vibration; the third will act 
during the third descending vibration, but at a more ad- 
vanced phase of the same; the fourth impulse will arrive at a 
still somewhat more advanced phase of the fourth descending 
vibration ; and so on until at length an impulse virtually coin- 
cides with the end of such a vibration. Under the influence of 
these repeated impulses, the amplitude of the vibrations of the 
body will necessarily increase until the arrival of the impulse last 
considered. But again, in consequence of the small excess in 
the interval between two impulses, the latter will next take place 
during ascending vibrations, and at more and more advanced 
phases of the same; so that after a number of impulses equal to 
that of the preceding, the body will again receive a shock at the 
termination of a vibration. Now this second group of impulses 
will evidently destroy whatever the first has produced ; in other 
words, it will gradually diminish the amplitude of the vibrations, 
and conclude by annulling the same. A third group of impulses 
will revive these vibrations, a fourth will annul them again, and 
so on indefinitely. The note of the body which receives the shock 
ought therefore to be alternately more and less intense; on the 
other hand, on account of the relative velocities of the body and 
the detached masses, the note of the jet will be less intense when 
the masses reach the body during its descending, than when they 
strike it during its ascending vibrations; hence it is seen that 
the note of the jet is least when that of the body is most 
intense, and vice versd. This granted, if the vibrations of the 
body acquire in their greatest amplitudes sufficient energy, 
and if at the same time the relative velocity of the impulses 
bscomes sufficiently small, the note of the jet may be entirely 
disguised during the moments when that of the body is most 
intense, and in its turn may reappear and again predominate 
during the intermediate periods; consequently both notes will 
be heard periodically. 
But if the body is only capable of performing vibrations of 
Phil, Mag. 8. 4. Vol. 14, No. 95, Dec. 1857. 2F 
