ACOUSTICS. 
86 
nature. It Is further urged, that this flow vermicular 
motion but ill reprefents the velocity with which founds 
travel, as we know by experience that it is" almoft thirteen 
miles in a minute. In fhort, it is urged, that fuch undu¬ 
lations as have been defcribed, when coming from feveral 
ipnorous bodies at once, would crofs, obftruft, and con¬ 
found, each other; fo that, if they were conveyed to the 
ear by this means, we fnould hear nothing but a medley of 
difcord and broken articulations. Thefe objections have 
given rife to the following theory : 
Every found may be conlidered as driven off from the 
founding body in ftraight lines, and impreffed upon the air 
in one direction only: but whatever imprefTion is made 
upon the fluid in one direction, is dift'ufed upon its furface 
into all directions; fo that the found firft driven direCtly 
forward foon fills up a wide fphere, and is heard on eve¬ 
ry fide. Now, as to the pulfes, which a founding body is 
known to make, each pulfe (fay the fupporters of this 
theory) is itfelf a diftinCt and perfect found, and the inter¬ 
val between every two pulfes is profoundly filent. Conti¬ 
nuity of found from the fame body is only a deception of 
the hearing; for, as each diftinct found fucceeds at very 
fmall intervals, the organ has no time to tranfmit its ima¬ 
ges with equal fwiftnefs to the mind, and the interval is 
thus loft to fenfe: juft as when children run with their 
flicks along a rail, a continuing found is thus reprefented, 
though the flroke againft each is perfectly diftinCt. 
According to this theory, therefore, the pulfes are no¬ 
thing more than diftinCt founds repeated by the fame body, 
the firft flroke or vibration being ever the loudeft, and tra¬ 
velling farther than thofe that follow ; while each fucceed- 
ing vibration gives a new found, but with diminifhed force, 
till at laft the pulfes decay away totally, as the force decays 
that gives them exiftence. 
Some bodies, wanting elafticity, give back no repetition 
of found ; the noife is at once begotten and dies: while 
other, bodies, more elaftic and capable of vibration, give 
back a found, and repeat it feveral times fucceflively. 
Thefe laft are laid to have a tone. This tone of the elaftic 
firing, or bell, is notwithflanding nothing more than a limi- 
lar found of what the former bodies produced, but with 
the difference of being many times repeated. So that, if 
we would give the former bodies a tone, it will be necef- 
fary to make them repeat their found, by repeating our 
blows fwiftly upon them. 
Let us now fuppofe, that by fwift and continued flrokes 
we give a non-elaftic body its tone: it is very obvious, 
that no alterations will be made in this tone by the quick- 
nefs of the flrokes, though repeated ever fo fafl. Thefe 
will only render the tone more equal and continuous, but 
make no alteration in the tone it gives. On the contrary, 
if we make an alteration in the force of each blow, a dif¬ 
ferent tone will then undoubtedly be excited. The diffe¬ 
rence will be fmall, for the tones of inflexible bodies are 
capable but of fmall variation; however, there will cer¬ 
tainly be a difference. The table on which we write, for 
inflance, will return a different found when flruck with a 
club, from what it did when flruck only with a fwitch. 
Thus non-elaftic bodies return a difference of tone, not in 
proportion to the fwiftnefs with which their found is re¬ 
peated, but in proportion to the greatnefs of the blow 
wiiich produces it: for, in two equal non-elaftic bodies, 
that body produces the deepeft tone which is flruck by the 
greatefl blow. 
We now then come to a critical queftion : What is it that 
produces the difference of tone in two elaftic founding 
bells, or firings ? Or what makes one deep, and the other 
Thrill ? This queftion has been anfwered by faying, that 
the depth or height of the note proceeded from the flow- 
nefs or fwiftnefs of the times of the vibrations. The 
lioweft vibrations, it has been faid, are qualified for pro- 
ducingthe deepeft tones, while the fwifteft vibrations pro¬ 
duce the higheft tones. In this cafe an effeCt has been 
given for a caufe. It is in fa6t the force w-ith which the 
founding firing ftrikes the air when flruck upon, that 
makes the true diftindtien in the tones of founds. It 
is this force, with greater or lefs impreflions, refembling 
the greater or lefs force of the blows upon a non-elaftig 
body, which produces correfpondent affedtions of found. 
The greatefl forces produce the deepeft found: the high 
notes are the etfedt of fmall efforts. In the fame manner 
a bell, wide at the mouth, gives a grave found ; but, if it 
be very mafty withal, that will render it ftill graver; but 
if mafty, wide, and long or high, that will make the tone 
deepeft of all. 
Thus then will elaftic bodies give the deepeft found, in 
proportion to the force with which they ftrike the air; but, 
if we fhould attempt to increafe their force by giving them 
a ftronger blow, this will be in vain; they will ftill return 
the fame tone; for fuch is their formation, that they are 
fonorous only becaufe they are elaftic, and the force of 
this elafticity is not increafed by our flrength, as the great¬ 
nefs of a pendulum’s vibration will not be increafed by 
falling from a greater height. 
Thus far of the length of chords. Now, as to the fre¬ 
quency with which they vibrate tire deepeft tones, it has 
been found, from the nature of elaftic firings, that the 
longeft firings have the wideft vibrations, and confequent- 
ly go backward and forward flowed ; while, on the con¬ 
trary, the fhorteft firings vibrate the quickeft, or come and 
go in the fhorteft intervals. From hence thofe who have 
treated of founds, have afferted, as was faid before, that 
the tone of the firing depended upon the length or the 
ftiortnefs of the vibrations. This, however, is not the 
cafe. One and the fame firing, when flruck, muft always, 
like the fame pendulum, return precifely fimilar vibra¬ 
tions; but it is well known, that one and the fame firing, 
when flruck upon, does not always return precifely the 
fame tone : fo that in this cafe the vibrations follow one 
rule, and the tone another. The vibrations muft be in¬ 
variably the fame in the fame firing, which does not return 
the fame tone invariably, as is well known to performers 
on the violin, who can alter the tone of a firing an oCtave, 
by a fofter method of drawing the bow ; and thefe are call¬ 
ed flute-notes. The only reafon, it has been alleged, that 
can be afligned for this, muft certainly be the different force 
of the flrokes made upon the air. In one cafe, it has 
double the tone of the other; becaufe, upon the foft touch¬ 
es of the bow, only half of its elafticity is put into vibration. 
This being underftood (continue the authors of this 
theory), we fhall be able clearly to account for many things 
relating to found that have hitherto been inexplicable. 
Thus, for inflance, if it be afked, When two firings are 
ftretched together of equal lengths, tenfions, and thicknefs, 
how does it happen, that one of them being (truck, and 
made to vibrate throughout, the other fhall vibrate through¬ 
out alfo ? The anfwer is obvious: The force that the firing 
flruck receives is communicated to the air, and the aip 
communicates the fame to the fimilar firing ; which there¬ 
fore receives all the force of the former; and, the force 
being equal, the vibrations muft be fo too. Again, If 
one firing be but half the length of the other, and be 
flruck, how will the vibrations be ? The anfwer is, The 
longeft firing will receive all the force of the firing half 
as long as itfelf, and therefore it will vibrate in propor¬ 
tion, that is, through half its length. In the fame man¬ 
ner, if the longeft firing were three times as long as the 
other, it would only vibrate in a third of its length ; or, if 
four times, in a fourth of its length. In fhort, whatever 
force the fmaller firing imprefles upon the air, the air will 
imprefs a fimilar force upon the longer firing, and par¬ 
tially excite its vibrations. 
From hence alfo we may account for the caufe of thofe 
charming melancholy gradations of found in the Eolian 
lyre ; an inftrument eafily made, being nothing more than 
a long narrow box of thin deal, about 30 inches long, 5 
inches broad, and i| inches deep, with a circle in the 
middle of the upper fide or belly about i-£ inch diameter, 
pierced with fmall holes. On this fide are from feven to 
fifteen firings of very fine gut, ftretched over bridges at 
each 
