Encyclopaedia Britannica, or, a Dictionary of arts, sciences, and miscellaneous literature : enlarged and improved. Illustrated with nearly six hundred engravings > Volume 1, A-AME

Chap. IT. ACOUSTICS.
propaga- ioW v’10i;n tlian when faftened to a plain board, &c. .
tion of jn the foun(i 0f a bell we cannot avoid obferving this
echo very diftinftly. The found appears to be made
^ up of diilina pulfes, or repetitions of the fame note
produced by the ftroke of the hammer. It can by no
means be allowed, that the note would be more acute
though thefe pulfes were to fucceed one another more
rapidly ; the found would indeed become more fimple,
but would ftill preferve the fame tone.—In mufical
firings the reverberations are vaftly more quick than
in bells j and therefore their found is more uniform or
fimple, and confequently more agreeable than that of
# See Har- bells. In mufical glaffes *, the vibrations, muft be in-
monica. conceivably quicker than in any bell or flringed inflila¬
ment : and hence they are of all others the mod: fimple
and the mod agreeable, though neither the mod acute
nor the louded.—As far as we can judge, quicknefs
of vibration contributes to the uniformity, or fimphci-
ty, but not to the acutenefs, nor to the loudnefs, ot
a mufical note.
It may here be objected, that each of the different
pulfes, of which we obferve the found of a bell to be
compofed, is of a very perceptible length, and far from
being indantaneous ; fo that it is not fair to infer that
the found of a bell is only a repetition of a fingle .in¬
dantaneous droke, feeing it is evidently the repetition
of a lengthened note.—To this it may be replied,, that
the inappretiable found which is produced by.diiking
a bell in a non-eladic date, is the very fame which, be¬
ing fird propagated round the bell, forms one of thele
diort pulfes that is afterwards re-echoed as long as the
vibratipns of the metal continue, and it is impodible
that tfye quicknefs of repetition , of any found can ei¬
ther increafe or diminidi its gravity.
Chap. II. Of the Propagation of Sound. Newton's
Dohrine explained and ’^indicated.
Propa- The writers on found have been betrayed into thefe
gation of difficulties and obfcurities, by rejeiting the 47th pro-
lound. p0fltion, B. II. of Newton, as inconclufive reafoning.
Of this propofition, however, the late ingenious Dr
Matthew Young biffiop of Clonfert, formerly of Tri¬
nity college, Dublin, has given a clear, explanatory,
and able defence. He candidly owns that the demon-
dration is obfcurely dated, and takes the liberty of
varying, in fome degree, from the method purfued by
Newton.
“ 1, The parts of all founding bodies (he obfervesj,
vibrate according to the law of a cycloidal pendulum .
for they may be confidered as compofed of an indefi¬
nite number of eladic fibres 5 but thefe fibres vibrate
according to that law. Vide Uelfhatn, p. 270.
“ 2. Sounding bodies propagate their motions on all
fides in diredlum, by fucceffive condenfations and rare-
fa&ions, and fucceffive goings forward and returnings
backward of the particles. Vide Prop. 43. B. II. New¬
ton Princip.
“ 3. The pulfes are thofe parts of the air which vi¬
brate backwards and forwards •, and which, by going
forward, drike (pu/fant) againd obdacles. The lati¬
tude of a pulfe is the reftilineal fpace through which
the motion of the air is propagated during one vibra¬
tion of the founding body.
4. All pulfes move equally fad. This is proved
VOL. LPartl.
153
by experiment} and it is feund that tiny deferibe 1070 rmps»-
Paris feet, or 1142 London feet in a fecond, whether
the found be loud or low, grave or acute. i >
“ c. Prob. To determine the latitude or a pulle.
Divide the fpace which the pulfe defcribes in a given
time (4) by the number of vibrations performed in the
fame time by the founding body, (Cor. I. Prop. 24.
Smith's Harmonics'), the quotient is the latitude. .
“ M. Sauveur, by fome experiments on organ pipes,
found that a body, which gives the graved harmonic
found, vibrates 12 times and a half in a fecond, .and
that the dirilled founding body vibrates 51.100 times
in a fecond. At a medium, let us take the body which
gives what Sauveur calls his fxed found: it periorms
100 vibrations in a fecond, and in the fame time the
pulfes deferibe 1070 Parifian feet ; therefore the fpace
deferibed by the pulfes whild the body vibrates once,
that is, the latitude, or interval of the pulfe, will be
10.7 feet. .
“ 6. Prob. To find the proportion which the great-
p(l fpace, through which the particles of the air vi¬
brate, bears to the radius of a circle, whole perimeter
is equal to the latitude of the pulfe.
“ During the fird half of the progrefs of the eladic
fibre, or founding body, it is continually getting near¬
er to the next particle 5 and during the^ latter half of
its progrefs, that particle is getting farther from the
fibre, and thefe portions of time are equal (Helfjam) :
therefore we may conclude, that at the end of the pro¬
grefs of the fibre, the fird particle of. air will be nearly
as far didant from the fibre as when it began to move,
and in the fame manner we may infer, that all the par¬
ticles vibrate through fpaces nearly equal to that run
over by the fibre.
“ Now M. Sauveur (Acad. Scienc. ann. 1700, p.
141.) has found by experiment, that the middle point
of a chord which produces Ws fixed found, and whofe
diameter is \ of a line, runs over in its fmalled.fen-
fible vibrations of a line, and in its greated vibra¬
tions 72 times that fpace ; that is, 72XtV a line, or
4 lines, that is, ^ of an inch.
“ The latitude of the pulfes of this fixed found is
10.7 feet (5) ; and fince the circumference of a circle
is to its radius as 710 is to 113, the greated fpace de-
feribed by the particles will be to the radius of a cir¬
cle, whofe periphery is equal to the latitude of the
pulfe as \d of an inch is to 1.7029 feet, or 20.4348
inches, that is, as 1 to 61.3044. , .
“ If the length of the didng be increafed or dimi-
nifhed in any proportion, cceteris paribus, the greated
fpace deferibed by its middle point will vary in thq
fame proportion. For the indexing force is to the
tending force as the didance of the dring from the
middle point of vibration to half the length of the
dring (fee Heljham and Martin); and therefore the
inflecting and tending forces being given,, the dring
will vibrate through fpaces proportioned to its length *,
but the latitude of the pulfe is inverfely as the number
of vibrations performed by the dring in a given time
(5), that is, direCtly as the time of one vibration, or
direCtly as the length of the dring (Prop. 24. Cor. 7.
Smith's Harmonics) ; therefore the greated . fpace
through which the middle point of the dring vibrates
will vary in the direCt ratio of the latitude of the pulfe,
or of the radius of a circle whofe circumference is equal
U to