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spread from the centre al certain intervals
from each other Now if, while this one system OF
waves is propagaed another pebble be let fall in the
same place, that Will produce different system Of
waveets-either greater or less Yet the TWO will
90 on To be spread over the surface OF the wa,ei,
nor will they interfere with each other-the one
passing over the other. Yet the eye perceives
both distinctly. This is the case with the pulss-
tions in the air, where thsre are two different
sounds. The number of pulsaiions for each minute.
received by the ear from the long string il only
half si he number received from the short one;
and the intermediate PulsatoEs are broken. The
consonsnce Of the two sounds depends on The CO.
incidence OF every ether vibration in the short
string with every Yibraiion in the long one


Tnese obserya,ions lead to an inqniry As TO the
power We possess OF counting the number OF these
vibrations. have told yol that this admits OF
strict mathematical computation bu, a. this
not be exhibited proi;ably;o TO miscellaneous au-
1ieace We must have recourse to another means OF
deiermiaing it which does admir- 1t popular expla


ration | do this tbs more willingly "a it viii
bring TO your notice most beautiful lttle philo-o-
phical instrument called the !Sir-H>. by which thu
vibrations may be counted and registered Invented
bv French NOBLE the Baron CAGNoXD


Tour. Il msy be described in this Sup
pose metallic tube. open at the end ike "a srgan
pipe TO ascend to an orifc. ihrosgh which the air
in it MAY make is escape. wo circular plates,
one directly behind the other. 30 arraHged that
the air from the tube escape only by passing
through holes PLACED around the outside OF ;ne
circles at short intervals from zach other Oae OF
these plates Is fixed in IL position the other by
revolving the holes pass first. directly be
tore the holes in the other in which position the
air NAV escape and then before the spaces between
the holes in the hinder circle when The air Is in
,crrupted and cannot escaPe) Imagine the circle
then to be turned rapidly the air VIII escape wher
the hole. in tsetwo directly opposite each Other


and be Interrupted while passing from one to the
other; 50 that it will be discharged in series Of
pufi, and if the motion Of the revolving plate be
regular the pul,aion- Of the air will be regular
and il the motion be sufficiently rapid musica.
sound viii be produced. Nav, If by any means,
the motian Of the plate can be regulated, we can
make the puisations succeed each other what
rate We please and thus if it be RAPID the note
produced will be nigh; il slow it will be low. But
something still remains we must have the means
of couatin. the number al pulsations in a minute
and nothing can be more simple or beautiful than
the arrangement for this purpose. On the axis OF
the circle i toothed wkee whic. imParts motion
,ohands which plays upon dial, like those Of clock


For every revolution OF the circle the hand passes
over one of The ten divisions the dial tina;
in ten revolutions of the circle The hand vii. have
passed completely round the dial. Now another
dial is so connected with the frat that com
plete revolution of the hand Of the first shall cause
The land Of the second 10 pass aver one division
and ten revolutions of the first will cause one of
The second There is still third dial, revo-
luton of the hand of which corresponds with ten
Of the second OF course, with one hundred of the
first. \ fourth is also provided. revolution of
The hand OF which corresponds with ten of the
third, one hundred ,f the second and one thou
sand of the first. [, will be seen that the system
of decimal notation is here completely preserved
Now in order to count the number OF revolutions
of the circle and consequently the number of vi
pratons of the air, all have II do is to watch
the hand the fourth dial plate. Let Us
see how this il TO be applied. II the tube be
connected in any way with the bellows OF an
prgan that air may be driven through it,
it will cause the circle TO revolve with greater
or less rapidly, and musical sound will ibe
produced The question is to know how many
vibrations are necessary TO produce, for instance
the note 4, or any other note of the musical scale.
We have nothing TO do bu, to 60 on giving greater
and greater velocity to the circle until the musical
sound produced is found BY the ear 10 be the note
required; then observe the number OF revolutions
of the dial hand for any period OF time, as for a
minute, and you have the number ut vibrations
necessary for any note in the musical scale. II you
wish to test the principle Of the octave with this
instrument. in the first place give a motion to the
circle sufficient sound the note, say d, and note
the number of vibrations then soun1 the octave
Of the note. and YOU will h2d the number
l.. a. Il,
former case. Hare then il is p:o,ed by expert
ment that the octave vbratcs twice is fa,, the
elementary note.


Having thus endeavored briefly to explain the
principles on which depends the agreeable sensa-
tons produced by the sounding OF note with lis
octavc. will now present one or two other COM
hinations and hope there are a sulicien; num-
Der of persons wh0 know enough Of music to follow
me upon the staff to render the explanation which
must be somewhat dry, not altogether uniutcrcst-
ing. explained that every other vibra' ion in the
octave corresponds with avery vibration in the eIe-
nen,ary note. Ii, now, you take the two octayes
above the first you have -four notes rising one above


the other; the second vibration in the second note,
The fourth vibration in the third noe. and jhe
eighth vibration in the fourth note. will coincide
WITH each vibration OF the first elementary note,
and ou The senes of ocaycs produces lis
agreeable effect. then by the concordance OF the
hrst, secocd, fourth, eighth sixteenth, e., vbra
tions, with each vibration OF the elementary note.


When the string Is divided into thirds, and two
of them sounded, We get what is called 6ftL;
and the agreeable sensation in this arises
from two vibrations ii the fundamental note cor
responding with three Of the other. Consequently
every second vibration of tue occurs at tho
same moment as the third vibration of the other,
and the concordant vibrations the second and
thrd on the two strings. The TWO adjacen'
strings of violin sounded together svc ffth,
which is peculiarly rich and harmonious chord.