302 



NA TURE 



[Feb. 19, 1874 



the attention of the investigator, be he student or teacher. Why 

 it should have been passed by as though its meaning were not 

 worth wrestling for is incomprehensible. Since Savart wrote 

 no light has been thrown on this singular phenomenon, for the 

 explanation which has been aflorded (presently to be quoted), 

 cannot be called in any degree satisfactory. In the illustrations 

 of nodal division given in various scientific works there is a 

 puzzling contiariety hardly to be accounted for except on the 

 supposition that our engravers are as niggardly conservative in 

 design as the buried Egyptians, or that the engravings themselves 

 are the cherished heirlooms ol our publishers. In one work a 

 representation of the manometrical nodal division after Kcenig will 

 be given, but cairjully corrected and revised by the aid of a pair of 

 compasses ; in another a beautifully accurate copy of the original, 

 so lopped to suit the size of the page that much mental eflort 

 and distortion of reasoning are incumbent on the reader in vain 

 attempts to bring the engraving into harmony with the accom- 

 panying text, young eyes are mystified, it needs cold *' well-worn 

 eyes " to appreciate these fine economics ot the publishing art ; 

 in another the manometrical nodal positions will be properly 

 defined and, by some nrgligent inconsistency, on an opposite 

 page an organ-pipe be depicted, admirably exact to theoretical 

 localisation, in direct contradictiun of knowledge. Faults of this 

 kind should not be allowed to pass, they weaken faith in the 

 teacher and are harassing to the inquirer. 



KiEnig in his own illustrations represents the displacement ol 

 the node as it is indicated under experiment, for this one condi- 

 tion of truth to nature had been too often before him in his 

 manometric flames to allow ot his disregarding its iaithlul por- 

 traiture. The dilTerence he shows to exist as to position corre- 

 sponds very closely with that we arrive at by other means, by 

 calculation of scales and by the practical teachings of experi- 

 mental study of the relations and arrangements of organ-pipes. 

 Of the cause of the displacement Kcenig offers no elucidation. 



The following explanation is quoted from Prof. Airy's treatise 

 on "Sound and Atmospheric Vibrations." In the section on 

 open organ-pipes he says : — 



"It was found by Mr. Hopkins that the node next the open 

 mouth of the pipe was some .v hat less distant from it than that 

 given by theory, or, which amounts to the same thing, that the 

 place where the air has always the same density as the external 

 air is not exactly at the pipe's mouth but somewhat exterior 

 to it." 



The extent of the disparity would be but very imperfectly con^. 

 prehended under this vague delineation. Other authors have 

 attempted explanation, in substance the same as the above, to 

 account for the disparity ; the summary of the whole is, that 

 science brings forward no better plea than the surmise of a pro- 

 bable place, somewhat exterior to the mouth, which the air-wave 

 of the Imtvr half o{ the pipe has to attain before it can be properly 

 said to be completed in length. Truly an illogical conclusion if this 

 line of reasoning is carried out. In common fairness the upper 

 IialJ of the pipe may claim to be credited with a reasonalile 

 amount of wave-prolongation, seeing that at the higher orifice 

 the internal column of air pulsates the atmosphere with far greater 

 vigour than at the mouth, and consequently that for a similar 

 attainment of density the due addition of wave-length would only 

 serve to increase the disparity in relation to the lialf lielmv the 

 node. 



A displacement of some sort thus receives acknowleJgment 

 although as yet the variability of the node is unsuspected. 



The actual extent of the disparity between the " unequal 

 halves " can be ascertained. It is subject to laws of relation of 

 as definite a character as are found in other dynamical problems 

 when the elements of calculation are delicately defined. An ap- 

 proximate estimate will be sufficient for the present purpose. For 

 avoidance of the inconvenient " unequal halves " it will be per- 

 mitted me to coin two simple terms as more distinctively repre- 

 sentative, and to speak of them as super-nodal and sub-nodal. 



II a standard open diapason pipe be made for some designed 

 pitch, whatever that pitch may be, it may safely be predicted 

 that the pipe will stand considerably short of the full theoretical 

 length ; ajsthetlcally judged for musical quality, it ought to be 

 about one-eigtith less, a difference much affecting the veracity of 

 scientific argument. 



Doubtless it would be somewhat a. novelty for a scientific lec- 

 turer to tell his audience that one-eighth of the whole wave- 

 length was lost by cunvcrsiun into organ-pipe vibrations, yet, 

 unless he innocently accepts the ironical reply of Galileo on the 

 pump question, that " perhaps Nature is indifferent to a few 



feet," he is strictly in this dilemma : if the pipe is a natural stan- 

 dard of wave-length, the velocity of sound in air computed on 

 the basis of the pipe's length falls very lar short indeed of the 

 philosophical estimate, 1,125 feet per second ; on this ruling the 

 latter should be pronounced to be irreconcileably wrong, o>- else 

 the frank admission made that there is nu " necessity of relation " 

 that the wave-length in an organ-pipe, giving a defined pitch, 

 and the wave-length in the free air corresponding to that note 

 should be identical. 



Taking the several classes of pipes, from the Diapason to the 

 Vox Angelica, ranging from the pipes of the most vigorous to 

 those of the softest intonation, the amount of difference from full 

 measure varies from one-eighth to one-twelfth less than that which 

 theory demands. The loss is mainly due to the cause which en- 

 forces nodal displacement. 



Our immediate inquiry is, what is the extent of displacement 

 of the node, and what its variability? Divide the lengih of the 

 already reduced pipe into seven equal parts, and the unequal 

 halves will be in the ratio of 4 to 3 Four parts belonging to 

 the super-nodal half, and three parts to the sub-nodal half, sub- 

 ject to a relative variability, according to the position of the pipe 

 in the range of octaves, and subject to a fluctuating variability 

 determined by force of wind, diameter of pipe, character of scale, 

 relative size of mouth, mode of voicing, and other details, chang- 

 ing the proportion, perhaps, to 6 : 5, or even to 7:6. What- 

 ever the extent of the variability, change in result rigidly follows 

 change in details, with a calculable value. When, instead of 

 the fundamental note, the pipe vibrates in harmonic nodal divi- 

 sions, the lowest half-segment takes upon itself almost the whole 

 difference, and not merely a proportional share .in comparison 

 with its segmental relation to the whole pipe. A remarkable 

 fact, but one fully accounted for in that which I have termed the 

 aero-plasiic reed theory (Nature, vol. viii. p. 25) for it is easy to 

 me visibly to demonstrate that the harmonic-independent and the 

 harmonic-concomitant are originated in the pipe by totally diffe- 

 rent natural processes. 



The nodal difference detected by Mr. W. Hopkins was much 

 smaller in extent, but there is an important distinction not to be 

 overlooked : his experiments (recorded in the Transactions of the 

 Cambridge Philosophical Society, vol. 5) were not made with 

 organ-pipes, but with glass tubes supported in position over a 

 glass plate, the plate being set in vibration by friction. He ex- 

 pressly rejected organ-pipes by reason of their intractibility and 

 of the difficulty ot obtaining results from them of the nature 

 desired. 



In like manner we continually find experimentalists rejecting 

 organ-pipes as insubordinate pupils ; they prefer dumb pipes and 

 the artificial speech by tuning-forks, and having obtained such 

 negative evidence, make a clean transfer of their conclusions to 

 all argumentative reasonings and expositions of the nature and 

 functions of the original, living, speaking organ-pipes. The 

 Hon. M. Strutt, in his paper on the Theory of Resonance, printed 

 in Phil. Trans. Nov. 1870, says : — 



" Independently of these difficulties, the theory of pipes or 

 other resonators made to speak by a stream of air directed against 

 a sharp edge is not sufficiently understood to make this method 

 of investigation satisfactory. For this reason I have entirely 

 abandoned this method of causing the resonators to speak in my 

 experiments, and have relied on other indications to fix the 

 pitch." 



Prof. Airy is as evidently dissatisfied with the state of theory and 

 experiment, using such phrases as these : " the matter, however, 

 demands more complete explanation;" "that obscure subject, 

 the production of musical vibrations in a ])ipe by a simple blast 

 of air ;'' " possibly when the mathematical calculus is farther 

 advanced, this may be shown," &c. Beyond the province of 

 mathematical analysis his survey is keen, and with foresight of 

 tlie results of possible experiments. 



At the present date our best authorities are in effect repeating 

 the assertion of Blot that "the paiticular properties of the 

 vibrations of confined air in tubes are not yet sufficiently ex- 

 plained." The disturbing influence of some unknown agency 

 may be discerned in Dulong's experiments of filling organ-jiipes 

 with various gases, and estimating the velocity of sound in these 

 gases by the pitch produced. Similar experiments on this 

 method are referred to by Herschel, and he, noticing how the 

 results gave for hydrogen gas a velocity differing by one-fourth 

 from that which theoretically had been calculated, could only 

 account for it by supposing an impurity in the gas used for the 

 experiments. There is little need to resort to the supposition of 



