l62 



NA TURE 



\7uly 2, 1874 



vibrating rod had blinded me, and it was only after long reason- 

 ing, forced upon me by the presence of independent harmonics, 

 not upon any theory belonging to a reed (whose first harmonic 

 would be higlier than an octave twelftli), that my faith was shaken. 

 Then, conceiving the idea of this principle of action, I looked, 

 hoping to find my reasoning confirmed ; yet, let me confess it, 

 the first sight of the reality startled me not a little with self-con- 

 fusion. Here was an every-day fact, constantly before me it had 

 been, beautiful in its simplicity, waiting to be acknowledged, and 

 I so stupidly blind as not to see it. Vary the experiment, repeat 

 it again and again, and the fact will be confirmed beyond possi- 

 bility of doubt, that, the length of reed remaining unaltered, if 

 by extraneous influence the pitch of the note is lowered whilst 

 the pipe is speaking, correspondingly with the changing sound 

 the path of the air-reed will be lengthened ; or conversely if the 

 pitch be raised, simultaneously with the quickened velocity, the 

 air-recd will be seen to shorten its stroke ; no swelling of tone 

 gaining power with gain of amplitude ; not the counterpart of a 

 metallic reed, nor acting as a tuning-fork. The creature of air, 

 it times itself to the element that sustains it. This aero-rhythmic 

 law provides the only way possible to the air-reed to work out 

 the transmutations of energy essential to its functions ; the con- 

 stitution of air necessitates the conformity in mechanical rela- 

 tions. 



Another remarkable demonstration falls to this theory — that 

 the note of every open organ-pipe is not .single but is a concord, 

 always consists of a duality of tone ; the two distinct tones of the 

 air-reed and of the pipe may be separated and again blended at 

 pleasure. 



Also that the harmonics or over- tones may in favourable pipes 

 be brought on at will without alteration of the pressure of blow- 

 ing ; that likewise, when a pipe, instead of continuing to sound 

 its fundamental, is unsteady, and gives its harmonic, the pipe 

 being said to "fly off to its octave," the notion implied is 

 erroneous ; it can be rendered visible that the air-reed leaps back 

 to its octave speed, and by its superior strength compels the pipe 

 to follow in accord. The expression "leaps back," is delibe- 

 rately used, for the native pitch of the air-reed is far higher than 

 the harmonics of the pipe. 



Add to these the still more singular feature of three different 

 velocities concurring to produce in an open organ-pipe the one 

 fundamental tone, which we call its pitch, the super-nodal wave 

 having one velocity, and the sub-nodal wave having for its course 

 and recourse two differing rates of progression. The motion of 

 vihratioit is an aclivily timpcyed by rests. In every wind-instru- 

 ment we perceive intimations that the period of rest is originally 

 governed by the special structure of each, and experiment shows 

 that we can arbitrarily limit or prolong it; this variable ratio of 

 rest to activity is to be taken into account in all calculate! times 

 and velocities. In forming a true conception of the behaviour of 

 musical reeds, and in tracing out the process of tone-making in 

 organ- pipes and other wind-instruments, the modifying influence 

 of the "rest" between the vibrations announces itself as of viial 

 importance. If the doctrine is strange, it is not unnatural. The 

 action of the heart furnishes a parallel instance — contraction, 

 ddatation, pause — the three making up the rhythmic period of 

 the heart's beat, and their relative duration varying with the indi- 

 vidual organisation. 



The foregoing affirmations are preparative. It will not be 

 possible to condense into one letter the evidence and arguments 

 supporting them, but if they are borne in mind during the pro- 

 gress of the exposition, the bearing of each new fact on theory 

 will be more reidily seen, and the ainr and purpose of the 

 reasoning be apprehended even in its incomplete stages. 



There is one significant question which it occurs to me has 

 never yet been asked ; that the node is to be found in all longi- 

 tudinal vibration of rod or pipe is undoubted ; that there is a 

 displacement of a node in an open organ-pipe is an accepted 

 fact— but wdiy, in rod or pipe, why is there a node at all ? The 

 question will wait. 



Now to the experimental pipe. Suppose we have before us 

 an open diapason organ-pipe, of section rectangular, length 

 7ft. 6 in., interior breadth 45 in., depth 6 in., area of mouth 

 4.J in. by 4 in., pilch C.C. — the half wave-length for this pitch is 

 8ft. Sin. in the atmosphere. The wind-way is a narrow fissure, 

 barely the twcnly-f nirth of an inch wide ; on the inner margin 

 of this wind-way we place a card or plate, covering interiorily 

 the whole area of the embouchure, and then we admit the 

 wind-current at the foot of the pipe from the organ-bellows. 



Premising that the swift sequence of action is delayed for 

 convenience of our anilysis, we notice that the stream of air, 



and as yet it is nothing more, is directed slightly diverging from 

 the vertical, and sufficiently to cause it to glide up the inclined 

 plane of the lip. This stream is the life-force of the sound. 

 " That everybody knows." True they may. But how many 

 ever think, if they know, that its force is that of a storm-wind 

 driving along at the rate of sixty miles an Iiour. The anemo- 

 meter or wind-gauge proves it to be so, and that moreover in 

 some stops of large organs the pressure per foDt given by the 

 bellows is equal to that of a hurricane. 



If now the jilate be removed from the back of the embouchure, 

 the stream is instantaneously Irmsformel into an air-moulded 

 reed. There is gradation in the change, the order of which may 

 be worked out, leaving the sound as Shelley says " waiting to be 

 born." 



The velocity of fassa!;e is to become endowed with a new 

 power, the velocity of vibration. How is this investiture accom- 

 plished? How afterwards does the transversal vibration of the 

 aeroplastic reed call into existence the longitudinal vibration of 

 the air-column of the pipe ? 



The isolated reed, before any change takes place, haj no 

 innate tendency to swerve fro.n uprightness, of itself it can neither 

 blow in nor out, nor can the atmosphere influence it, for that is 

 equal on both sides ; the air-column within the pipe is at rest, 

 it has no self-stimulating power of vibration, and to disturb its 

 equilibrium some internal exciting cause is needed which shall 

 produce, with determination of priority, condensation or rarefac- 

 tion. It is obvious that the reed as it now stands has no power 

 to produce a condensation, it does not strike against the sharp 

 edge, it simply asserts its own upward-rushing force. The reed 

 must be bent before it will vibrate. To cause this flexure the 

 only alternative is rarefaction. Tire act of rarefying occupies 

 time, it takes place within the pipe, is not spontaneous, but is 

 induced by some previous .act, therefore the provocation belongs 

 to the reed. In velocitous rush over the mouth, its dense stream 

 making around itself a rarefied atmosphere, it causes the approach 

 of the quiescent column, carries off all the particles of air lying 

 in the nearest layers, and would go on abstracting indefinitely 

 if there were no counterbalancing causes coming into operation, 

 but it brings down upon itself the power that bends it ; suction 

 bv veloi-itv has created a partial vacuum ; the air-column, pressing 

 outwards with the impetus of expansion, begins to bend the reed 

 over, the excited air-particles of the interior not only press for- 

 ward to fill the places of the lost, but eagerly crowd out upon 

 the top of the reed, irresistibly sucked into the zone of r.rrefaction 

 around the mouth, a region where velocity has ensured least 

 pressure, and through this same " law of least pressure," there 

 is a loss of support to the under surface of the reed, favouring 

 the curve of flexure, the pressure varying and diminishing from 

 the root upward. 



As yet we have no vibration, for simultaneously with the 

 exterior action the interior rarefaction is extending high upward, 

 the air-particles are rallying from further distances, awakened by 

 the agitation of those in advance, throughout the whole length 

 and breadth of the pipe, uneasy as bees in a hive ; whilst the par- 

 ticles are swarming toward the mouth, they are drawing away 

 from the main body of their supports, their own elastic energy 

 i; dianinishing, they are more and more thinned in numbers, and 

 tlie new levies come up to the front exhausted of their early 

 vigour. Now is the supreme moment of the reed's advantage, 

 its watchful ally, the extern.al air, pierces the weakest line just 

 under the sharp edge of the lip, and dashing in as a wave of 

 condensation with cumulative pressure, drives back the outflow- 

 ing wave, and would restore equilibrium but that the air-column, 

 still advancing, and pressed forward in consequence by the in- 

 road of the upper air, meets it in full shock ere it has reached 

 midway ; meanwhile the air-reed, rising with vigour to recover 

 its upright position, and following after its .ally in the w.ake of 

 the retreating column, slightly overpasses its own line, enters 

 the pipe momentarily to be cast out again, for the wave of 

 rarefaction is returning and vibration is established. The in- 

 vading wave has been repulsed at the spot hereafter memorable 

 as the node, and the conflict renewed and continued will chronicle 

 no victory to either unless other and foreign forces are brought 

 in, for, as I shall show, we have resources within command 

 enab'ing us to sway the equipoise and give supremacy to the 

 reed. 



" I do suppose," as Dr. Hooke says in his talk on "springy 

 bodies," "I do suppose the particles" behave, and that the 

 action takes place in the manner I have described ; the analogy 

 is not strained, nor have I used one phrase in association of ideas 

 which I do not think fully justified by the physical relations of 



