UNIVERSITY OF CALIFORNIA, 
 
 DEPARTMENT OF CIVIL ENGINEERING 
 
 BERKELEY, CALIFORNIA 
 
CHARLES DERLETH, Jr. 
 
 2134 WEBSTER STREET, 
 
 BERKELEY, CAU 
 
 UNIVERSITY OF CALIFORNIA, 
 
 DEPARTMENT OF CIVIL ENGI NEERI NG 
 
 BERKELEY, CALIFORNIA 
 
 
SOUND. 
 
 BY 
 
 JOHN TYNDALL, D.C.L., LL.D., F.R.S., 
 
 V PEOPE88OE OP NATURAL PHILOSOPHY 
 
 IN THE BOTAL INSTITtmON OF GEE AT BETTAIN- 
 
 THIRD EDITION, REVISED AND ENLARGED. 
 
 NEW YORK: 
 D. APPLETON AKD COMPANY, 
 
 1, 3, AND 5 BOND STREET. 
 1 884. 
 

 Engineerirg 
 Library 
 
 Engineering 
 Library 
 
TO TEE MEMORY 
 
 OF 
 
 MY FRIEND EIOHARD DAWES, 
 
 LATE DEAN OF HEBEFOBD, 
 
 THIS BOOK IS DEDICATED. 
 
 J. T. 
 
 785377 
 
PREFACE 
 
 THE THIED EDITION. 
 
 IN preparing this new edition of " Sound," I have 
 carefully gone over the last one ; amended, as far as pos- 
 sible, its defects of style and matter, and paid at the same 
 time respectful attention to the criticisms and suggestions 
 which the former editions called forth. 
 
 The cases are few in which I have been content to re- 
 produce what I have read of the works of acousticians. 
 I have sought to make myself experimentally familiar 
 with the ground occupied ; trying, in all cases, to present 
 the illustrations in the form and connection most suitable 
 for educational purposes. 
 
 Though bearing, it may be, an undue share of the im- 
 perfection which cleaves to all human effort, the work has 
 already found its way into the literature of various nations 
 of diverse intellectual standing. Last year, for example, 
 a new German edition was published " under the special 
 supervision " of Helmholtz and Wiedemann. That men 
 so eminent, and so overladen with official duties, should 
 add to these the labor of examining and correcting every 
 proof-sheet of a work like this, shows that they consider 
 it to be what it was meant to be a serious attempt to im- 
 
6 PREFACE. 
 
 prove the public knowledge of science. It is especially 
 gratifying to me to be thus assured that not in England 
 alone has the book met a public want, but also in that 
 learned land to which I owe my scientific education. 
 
 Before me, on the other hand, lie two volumes of fools- 
 cap size, curiously stitched, and printed in characters the 
 meaning of which I am incompetent to penetrate. Here 
 and there, however, I notice the familiar figures of the for- 
 mer editions of " Sound." For these volumes I am in- 
 debted to Mr. John Fryer, of Shanghai, who, along with 
 them, favored me, a few weeks ago, with a letter from 
 which the following is an extract : " One day," writes Mr. 
 Fryer, " soon after the first copy of your work on Sound 
 reached Shanghai, I was reading it in my study, when an 
 intelligent official, named Hsii-chung-hu, noticed some of 
 the engravings and asked me to explain them to him. He 
 became so deeply interested in the subject of Acoustics, 
 that nothing would satisfy him but to make a translation. 
 Since, however, engineering and other works were then 
 considered to be of more practical importance by the 
 higher authorities, we agreed to translate your work 
 during our leisure time every evening, and publish it 
 separately ourselves. Our translation, however, when com- 
 pleted, and shown to the higher officials, so much inter- 
 ested them, and pleased them, that they at once ordered 
 it to be published at the expense of the Government, and 
 sold at cost price. The price is four hundred and eighty 
 copper cash per copy, or about one shilling and eightpence. 
 This will give you an idea of the cheapness of native 
 printing." 
 
PREFACE. 7 
 
 Mr. Fryer adds that his Chinese friend had no diffi- 
 culty in grasping every idea in the book. 
 
 The new matter of greatest importance which has been 
 introdtfced into this edition is an account of an investiga- 
 tion which, during the two past years, I have had the honor 
 of conducting in connection with the Elder Brethren of 
 the Trinity House. Under the title " Eesearches on the 
 Acoustic Transparency of the Atmosphere, in Eelation to 
 the Question of Fog-signaling," the subject is treated in 
 Chapter VII. of this volume. It was only by Govern- 
 mental appliances that such an investigation could have 
 been made ; and it gives me pleasure to believe that not 
 only have the practical objects of the inquiry been secured, 
 but that a crowd of scientific errors, which for more than 
 a century and a half have surrounded this subject, have 
 been removed, their place being now taken by the sure 
 and certain truth of Nature. In drawing up the account 
 of this laborious inquiry, I aimed at linking the observa- 
 tions so together, that they alone should offer a substantial 
 demonstration of the principles involved. Further labors 
 enabled me to bring the whole inquiry within the firm 
 grasp of experiment ; and thus to give it a certainty which, 
 without this final guarantee, it could scarcely have enjoyed. 
 
 Immediately after the publication of the first brief ab- 
 stract of the investigation, it was subjected to criticism. 
 To this I did not deem it necessary to reply, believing 
 that the grounds of it would disappear in presence of the 
 full account. The only opinion to which I thought it 
 right to defer was to some extent a private one, commu- 
 
8 PREFACE. 
 
 nicated to me by Prof. Stokes. He considered that I had, 
 in some cases, ascribed too exclusive an influence to the 
 mixed currents of aqueous vapor and air, to the neglect 
 of differences of temperature. That differences of tem- 
 perature, when they come into play, are an efficient cause 
 of acoustic opacity, I never doubted. In fact, aerial re- 
 flection arising from this cause is, in the present inquiry, 
 for the first time made the subject of experimental demon- 
 stration. What the relative potency of differences of tem- 
 perature and differences due to aqueous vapor, in the cases 
 under consideration, may be, I do not venture to state ; 
 but as both are active, I have, in Chapter YIL, referred 
 to them jointly as concerned in the production of those 
 " acoustic clouds " to which the stoppage of sound in the 
 atmosphere is for the most part due. 
 
 Subsequently, however, to the publication of the full 
 investigation another criticism appeared, to which, in con- 
 sideration of its source, I would willingly pay all respect 
 and attention. In this criticism, which reached me first 
 through the columns of an American newspaper, differ- 
 ences in the amounts of aqueous vapor, and differences of 
 temperature, are alike denied efficiency as causes of acous- 
 tic opacity. At a meeting of the Philosophical Society of 
 "Washington the emphatic opinion had, it was stated, been 
 expressed that I was wrong in ascribing the opacity of the 
 atmosphere to its flocculence, the really efficient cause 
 being refraction. This view appeared to me so obviously 
 mistaken that I assumed, for a time, the incorrectness of 
 the newspaper account. 
 
PREFACE. 9 
 
 Recently, however, I have been favored with the " He- 
 port of the United States Lighthouse Board for 1874," in 
 which the account just referred to is corroborated. A 
 brief reference to the Report will here suffice. Major 
 Elliott, the accomplished officer and gentleman referred 
 to at page 261, had published a record of his visit of in- 
 spection to this country, in which he spoke, with a per- 
 fectly enlightened appreciation of the facts, of the differ- 
 ences between our system of lighthouse illumination and 
 that of the United States. He also embodied in his Re- 
 port some account of the investigation on fog-signals, 
 the initiation of which he had witnessed, and indeed aided, 
 at the South Foreland. 
 
 On this able Report of their own officer the Lighthouse 
 Board at Washington make the following remark : " Al- 
 though this account is interesting in itself and to the public 
 generally, yet, being addressed to the Lighthouse Board of 
 the United States, it would tend to convey the idea that 
 the facts which it states were new to the Board, and that 
 the latter had obtained no results of a similar kind ; while 
 a reference to the appendix to this report 1 will show that 
 the researches of our Lighthouse Board have been much 
 more extensive on this subject than those of the Trinity 
 House, and that the latter has established no facts of prac- 
 tical importance which had not been previously observed 
 and used by the former." 
 
 The " appendix " here referred to is from the pen of 
 the venerable Prof. Joseph Henry, chairman of the Light- 
 
 1 It will be borne in mind that the Washington Appendix was published 
 nearly a year after my Report to the Trinity House. 
 
10 PREFACE. 
 
 house Board at Washington. To his credit be it recorded 
 that at a very early period in the history of fog-signaling 
 Prof. Henry reported in favor of Daboll's trumpet, though 
 he was opposed by one of his colleagues on the ground 
 that " fog-signals were of little importance, since the mari- 
 ner should know his place by the character of his sound- 
 ings." In the appendix, he records the various efforts 
 made in the United States with a view to the establish- 
 ment of fog-signals. He describes experiments on bells, 
 and on the employment of reflectors to reinforce their 
 sound. These, though effectual close at hand, were found 
 to be of no use at a distance. He corrects current errors 
 regarding steam-whistles, which by some inventors were 
 thought to act like ringing bells. He cites the opinion of 
 the Kev. Peter Ferguson, that sound is better heard in fog 
 than in clear air This opinion is founded on observations 
 of the noise of locomotives ; in reference to which it may 
 be said that others have drawn from similar experiments 
 diametrically opposite conclusions. On the authority of 
 Captain Keeney he cites an occurrence, " in the first part 
 of which the captain was led to suppose that fog had a 
 marked influence in deadening sound, though in a subse- 
 quent part he came to an opposite conclusion." Prof. 
 Henry also describes an experiment made during a fog at 
 Washington, in which he employed " a small bell rung by 
 clock-work, the apparatus being the part of a moderator 
 lamp, intended to give warning to the keepers when the 
 supply of oil ceased. The result of the experiment was, 
 he affirms, contrary to the supposition of absorption of 
 the sound by the fog." This conclusion is not founded 
 
PREFACE. 11 
 
 on comparative experiments, but on observations made 
 in the fog alone ; for, adds Prof. Henry, " the change 
 in the condition of the atmosphere, as to temperature and 
 the motion of the air, before the experiment could be re- 
 peated in clear weather, rendered the result not entirely 
 satisfactory." 
 
 This, I may say, is the only experiment on fog which I 
 have found recorded in the appendix. 
 
 In 1867 the steam-siren was mounted at Sandy Hook, 
 and examined by Prof. Henry. He compared its action 
 with that of a Daboll trumpet, employing for this purpose 
 a stretched membrane covered with sand, and placed at 
 the small end of a tapering tube which concentrated the 
 sonorous motion upon the membrane. The siren proved 
 most powerful. "At a distance of 50, the trumpet pro- 
 duced a decided motion of the sand, while the siren gave 
 a similar result at a distance of 58." Prof. Henry also 
 varied the pitch of the siren, and found that in asso- 
 ciation with its trumpet 400 impulses per second yielded 
 the maximum sound ; while the best result with the un- 
 aided siren was obtained when the impulses were 360 a 
 second. Experiments were also made on the influence of 
 pressure ; from which it appeared that when the pressure 
 varied from 100 Ibs. to 20 Ibs., the distance reached by 
 the sound (as determined by the vibrating membrane) 
 varied only in the ratio of 61 to 51. Prof. Henry also 
 showed the sound of the fog-trumpet to be independent 
 of the material employed in its construction ; and he 
 furthermore observed the decay of the sound when the 
 angular distance from the axis of the instrument was 
 
12 PREFACE. 
 
 increased. Further observations were made by Prof. 
 Henry and his colleagues in August, 1873, and in August 
 and September, 1874. In the brief but interesting account 
 of these experiments a hypothetical element appears, 
 which is absent from the record of the earlier observations. 
 
 It is quite evident from the foregoing that, in regard 
 to the question of fog-signaling, the Lighthouse Board 
 of Washington have not been idle. Add to this the fact 
 that their eminent chairman gives his services gratuitously, 
 conducting without fee or reward experiments and obser- 
 vations of the character here revealed, and I think it will 
 be conceded that he not only deserves well of his own 
 country, but also sets his younger scientific contempora- 
 ries, both in his country and ours, an example of high- 
 minded devotion. 
 
 I was quite aware, in a general way, that labors like 
 those now for the first time made public had been con- 
 ducted in the United States, and this knowledge was not 
 without influence upon my conduct. The first instru- 
 ments mounted at the South Foreland were of English 
 manufacture ; and I, on various accounts, entertained a 
 strong sympathy for their able constructor, Mr. Holmes. 
 From the outset, however, I resolved to suppress such 
 feelings, as well as all other extraneous considerations, 
 individual or national ; and to aim at obtaining the best 
 instruments, irrespective of the country which produced 
 them. In reporting, accordingly, on the observations of 
 May 19 and 20, 1873 (our first two days at the South Fore- 
 land), these were my words to the Elder Brethren of the 
 Trinity House : 
 
PREFACE. 13 
 
 " In view of the reported performance of horns and 
 whistles in other places, the question arises whether those 
 mounted at the South Foreland, and to which the fore- 
 going remarks refer, are of the best possible description. 
 ... I think our first duty is to make ourselves acquainted 
 with the best instruments hitherto made, no matter where 
 made ; and then, if home genius can transcend them, to 
 give it all encouragement. Great and unnecessary expense 
 may be incurred, through our not availing ourselves of the 
 results of existing experience. 
 
 " I have always sympathized, and I shall always sym- 
 pathize, with the desire of the Elder Brethren to encourage 
 the inventor who first made the magneto-electric light 
 available for lighthouse purposes. I regard his aid and 
 counsel as, in many respects, invaluable to the corporation. 
 But, however original he may be, our duty is to demand 
 that his genius shall be expended in making advances on 
 that which has been already achieved elsewhere. If the 
 whistles and horns that we heard on the 19th and 20th be 
 the very best hitherto constructed, my views have been 
 already complied with; but if they be not and I am 
 strongly inclined to think that they are not then I would 
 submit that it behooves us to have the best, and to aim at 
 making the South Foreland, both as regards light and 
 sound, a station not excelled by any other in the world." 
 
 On this score it gives me pleasure to say that I never 
 had a difficulty with the Elder Brethren. They agreed 
 with me ; and two powerful steam-whistles, the one from 
 Canada, the other from the United States, together with 
 a steam-siren also an American instrument were in due 
 
14 PREFACE. 
 
 time mounted at the South Foreland. It will be seen in 
 Chapter VII. that my strongest recommendation applies 
 to an instrument for which we are indebted to the United 
 States. 
 
 In presence of these facts, it will hardly be assumed 
 that I wish to withhold from the Lighthouse Board of 
 Washington any credit that they may fairly claim. My 
 desire is to be strictly just ; and this desire compels me 
 to express the opinion that their Report fails to estab- 
 lish the inordinate claim made in its first paragraph. 
 It contains observations, but contradictory observations ; 
 while as regards the establishment of any principle which 
 should reconcile the conflicting results, it leaves our con- 
 dition unimproved. 
 
 But I willingly turn aside from the discussion of 
 " claims " to the discussion of science. Inserted, as a kind 
 of intrusive element, into the Report of Prof. Henry, 
 is a second Report by General Duane, founded on an ex- 
 tensive series of observations made by him in 1870 and 
 1871. After stating with distinctness the points requir- 
 ing decision, the general makes the following remarks : 
 
 " Before giving the results of these experiments, some 
 facts will be stated which will explain the difficulties of 
 determining the power of a fog-signal. 
 
 "There are six steam fog- whistles on the coast of 
 Maine : these have been frequently heard at a distance of 
 twenty miles, and as frequently cannot be heard at the dis- 
 tance of two miles, and this with no perceptible difference 
 in the state of the atmosphere. 
 
 " The signal is often heard at a great distance in one 
 
PREFACE. 15 
 
 direction, while in another it will be scarcely audible at 
 the distance of a mile. This is not the effect of wind, as 
 the signal is frequently heard much farther against the 
 wind than with it. 1 For example, the whistle on Cape 
 Elizabeth can always be distinctly heard in Portland, a 
 distance of nine miles, during a heavy northeast snow- 
 storm, the wind blowing a gale directly from Portland 
 toward the whistle. 8 
 
 " The most perplexing difficulties, however, arise from 
 the fact that the signal often appears to be surrounded by 
 a belt, varying in radius from one to one and a half mile, 
 from which the sound appears to be entirely absent. Thus, 
 in moving directly from a station the sound is audible for 
 the distance of a mile, is then lost for about the same dis- 
 tance, after which it is again distinctly heard for a long 
 time. This action is common to all ear-signals, and has 
 been at times observed at all the stations, at one of which 
 the signal is situated on a bare rock twenty miles from 
 the mainland, with no surrounding objects to affect the 
 sound." 
 
 It is not necessary to assume here the existence of a 
 "belt," at some distance from the station. The passage 
 of an acoustic cloud over the station itself would produce 
 the observed phenomenon. 
 
 Passing over the record of many other valuable observa- 
 
 1 That is to say, homogeneous air with an opposing wind, is frequently 
 more favorable to sound than non-homogeneous air with a favoring wind. 
 We made the same experience at the South Foreland. J. T. 
 
 2 Had this observation been published, it could only have given me 
 pleasure to refer to it in my recent writings. It is a striking confirmation of 
 my observations on the Mer de Glace in 1 859. 
 
16 PREFACE. 
 
 tions, in the Eeport of General Duane, I come to a few 
 very important remarks which have a direct bearing upon 
 the present question : 
 
 " From an attentive observation," writes the general, 
 " during three years, of the fog-signals on this coast, and 
 from the reports received from the captains and pilots of 
 coasting vessels, I am convinced that, in some conditions 
 of the atmosphere, the most powerful signals will be at 
 times unreliable. 1 
 
 " Now it frequently occurs that a signal which, under 
 ordinary circumstances, would be audible at the distance of 
 fifteen miles, cannot be heard from a vessel at the dis- 
 tance of a single mile. This is probably due to the reflec- 
 tion mentioned by Humboldt. 
 
 " The temperature of the air over the land where the 
 fog-signal is located being very different from that over 
 the sea, the sound, in passing from the former to the latter, 
 undergoes reflection at their surface of contact. The cor- 
 rectness of this view is rendered more probable by the 
 fact that, when the sound is thus impeded in the direction 
 of the sea, it has been observed to be much stronger 
 inland. 
 
 "Experiments and observation lead to the conclusion 
 that these anomalies in the penetration and direction of 
 sound from fog-signals are to be attributed mainly to the 
 want of uniformity in the surrounding atmosphere, and 
 that snow, rain, and fog, and the direction of the wind, 
 
 1 Had I been aware of its existence I might have used the language of 
 General Duane to express my views on the point here adverted to. See 
 Chap. VII., pp. 319-320. 
 
PREFACE. 17 
 
 have much less influence than has been generally sup- 
 posed." 
 
 The Keport of General Duane is marked throughout 
 by fidelity to facts, rare sagacity, and soberness of specu- 
 lation. The last three of the paragraphs just quoted, 
 exhibit, in my opinion, the only approach to a true expla- 
 nation of the phenomena which the Washington Keport 
 reveals. At this point, however, the eminent Chairman 
 of the Lighthouse Board strikes in with the following 
 criticism : 
 
 "In the foregoing I differ entirely in opinion from 
 General Duane, as to the cause of extinction of powerful 
 sounds being due to the unequal density of the atmos- 
 phere. The velocity of sound is not at all affected by 
 barometric pressure; but if the difference in pressure is 
 caused by a difference in heat, or by the expansive power 
 of vapor mingled with the air, a slight degree of obstruc- 
 tion of sound may be observed. But this effect we think 
 is entirely too minute to produce the results noted by 
 General Duane and Dr. Tyndall, while we shall find in the 
 action of currents above and below a true and efficient 
 cause." 
 
 I have already cited the remarkable observation of 
 General Duane, that with a snow-storm from the north- 
 east blowing against the sound, the signal at Cape Eliza- 
 beth is always heard at Portland, a distance of nine miles. 
 The observations at the South Foreland, where the sound 
 has been proved to reach a distance of more than twelve 
 miles against the wind, backed by decisive experiments, 
 reduce to certainty the surmises of General Duane. It 
 
18 PREFACE. 
 
 has, for example, been proved that a couple of gas-flames 
 placed in a chamber can, in a minute or two, render its 
 air so non-homogeneous as to cut a sound practically off ; 
 while the same sound passes without sensible impediment 
 through showers of paper-scraps, seeds, bran, rain-drops, 
 and through fumes and fogs of the densest description. 
 The sound also passes through thick layers of calico, silk, 
 serge, flannel, baize, close felt, and through pads of cotton- 
 net impervious to the strongest light. 
 
 As long, indeed, as the air on which snow, hail, rain, 
 or fog is suspended is homogeneous, so long will sound 
 pass through the air, sensibly heedless of the suspended 
 matter. 1 This point is illustrated upon a large scale by 
 my own observations on the Her de Glace, and by those 
 of General Duane, at Portland, which prove the snow- 
 laden air from the northeast to be a highly homogeneous 
 medium. Prof. Henry thus accounts for the fact that 
 the northeast snow-wind renders the sound of Cape Eliza- 
 beth audible at Portland: In the higher regions of the 
 atmosphere he places an ideal wind, blowing in a direc- 
 tion opposed to the real one, which always accompanies 
 the latter, and which more than neutralizes its action. In 
 speculating thus he bases himself on the reasoning of 
 Prof. Stokes, according to which a sound-wave moving 
 against the wind is tilted upward. The upper, and op- 
 posing wind, is invented for the purpose of tilting again 
 the already lifted sound-wave downward. Prof. Henry 
 does not explain how the sound-wave recrosses the hos- 
 
 1 This does not seem more surprising than the passage of light, or radi- 
 ant heat, through rock-salt. 
 
PREFACE. 19 
 
 tile lower current, nor does he give any definite notion 
 of the conditions under which it can be shown that it will 
 reach the observer. 
 
 This, so far as I know, is the only theoretic gleam 
 cast by the Washington Report on the conflicting results 
 which have hitherto rendered experiments on fog-signals 
 so bewildering. I fear it is an ignis fatuus, instead of a 
 safe guiding light. Prof. Henry, however, boldly applies 
 the hypothesis in a variety of instances. But he dwells 
 with particular emphasis upon a case of non-reciprocity 
 which he considers absolutely fatal to my views regarding 
 the flocculence of the atmosphere. The observation was 
 made on board the steamer City of Richmond, during a 
 thick fog in a night of 1872. " The vessel was approach- 
 ing Whitehead from the southwestward, when, at a dis- 
 tance of about six miles from the station, the fog-signal, 
 which is a 10-inch steam-whistle, was distinctly perceived, 
 and continued to be heard with increasing intensity of 
 sound until within about three miles, when the sound sud- 
 denly ceased to be heard, and was not perceived again 
 until the vessel approached within a quarter of a mile of 
 the station, although from conclusive evidence, furnished 
 by the keeper, it was shown that the signal had been 
 sounding during the whole time." 
 
 But while the 10-inch shore-signal thus failed to make 
 itself heard at sea, a 6-inch whistle on board the steamer 
 made itself heard on shore. Prof. Henry thus turns this 
 fact against me. "It is evident," he writes, "that this 
 result could not be due to any mottled condition or want 
 of acoustic transparency in the atmosphere, since this 
 
20 PREFACE. 
 
 would absorb the sound equally in both directions." Had 
 the observation been made in a still atmosphere, this argu- 
 ment would, at one time, have had great force. But the 
 atmosphere was not still, and a sufficient reason for the 
 observed non-reciprocity is to be found in the recorded 
 fact that the wind was blowing against the shore-signal, 
 and in favor of the ship-signal. 
 
 But the argument of Prof. Henry, on which he places 
 his main reliance, would be untenable, even had the air 
 been still. By the very aerial reflection which he prac- 
 tically ignores, reciprocity may be destroyed in a calm 
 atmosphere. In proof of this assertion I would refer him 
 to a short paper on " Acoustic Keversibility," printed at 
 the end of this volume. 1 The most remarkable case of 
 non-reciprocity on record, and which, prior to the demon- 
 stration of the existence and power of acoustic clouds, 
 remained an insoluble enigma, is there shown to be capable 
 of satisfactory solution. These clouds explain perfectly 
 the " abnormal phenomena " of Prof. Henry. Aware of 
 their existence, the falling off and subsequent recovery of 
 a signal-sound, as noticed by him and General Duane, is 
 no more a mystery, than the interception of the solar light 
 by a common cloud, and its restoration after the cloud has 
 moved or melted away. 
 
 The clue to all the difficulties and anomalies of this 
 question is to be found in the aerial echoes, the significance 
 of which has been overlooked by General Duane, and mis- 
 interpreted by Prof. Henry. And here a word might be 
 
 1 Also " Proceedings of the Royal Society," vol. xxiii., p. 159, and " Pro- 
 ceedings of the Royal Institution," vol. vii., p. 344. 
 
PREFACE. 21 
 
 said with regard to the injurious influence still exercised 
 by authority in science. The affirmations of the highest 
 authorities, that from clear air no sensible echo ever comes, 
 were so distinct, that my mind for a time refused to enter- 
 tain the idea. Authority caused me for weeks to depart 
 from the truth, and to seek counsel among delusions. On 
 the day our observations at the South Foreland began, I 
 heard the echoes. They perplexed me. I heard them 
 again and again, and listened to the explanations offered 
 by some ingenious persons at the Foreland. They were 
 an " ocean-echo : " this is the very phraseology now used 
 by Prof. Henry. They were echoes " from the crests and 
 slopes of the waves : " these are the words of the hypoth- 
 esis which he now espouses. Through a portion of the 
 month of May, through the whole of June, and through 
 nearly the whole of July, 1873, I was occupied with these 
 echoes ; one of the phases of thought then passed through, 
 one of the solutions then weighed in the balance and found 
 wanting, being identical with that which Prof. Henry now 
 offers for acceptation. 
 
 But though it thus deflected me from the proper track, 
 shall I say that authority in science is injurious? !N"ot 
 without some qualification. It is not only injurious, but 
 deadly, when it cows the intellect into fear of questioning 
 it. But the authority which so merits our respect as to 
 compel us to test and overthrow all its supports, before 
 accepting a conclusion opposed to it, is not wholly noxious. 
 On the contrary, the disciplines it imposes may be in the 
 highest degree salutary, though they may end, as in the 
 present case, in the ruin of authority. The truth thus 
 
22 PREFACE. 
 
 established is rendered firmer by our struggles to reach 
 it. I groped day after day, carrying this problem of aerial 
 echoes in my mind ; to the weariness, I fear, of some of 
 my colleagues who did not know my object. The ships 
 and boats afloat, the "slopes and crests of the waves," the 
 visible clouds, the cliffs, the adjacent lighthouses, the ob- 
 jects landward, were all in turn taken into account, and 
 all in turn rejected. 
 
 With regard to the particular notion which now finds 
 favor with Prof. Henry, it suggests the thought that his 
 observations, notwithstanding their apparent variety and 
 extent, were really limited as regards the weather. For 
 did they, like ours, embrace weather of all kinds, it is not 
 likely that he would have ascribed to the sea-waves an 
 action which often reaches its maximum intensity when 
 waves are entirely absent. I will not multiply instances, 
 but confine myself to the definite statement that the 
 echoes have often manifested an astonishing strength 
 when the sea was of glassy smoothness. On days when 
 the echoes were powerful, I have seen the southern cu- 
 muli mirrored in the waveless ocean, in forms almost as 
 definite as the clouds themselves. By no possible appli- 
 cation of the law of incidence and reflection could the 
 echoes from such a sea return to the shore ; and if we ac- 
 cept for a moment a statement which Prof. Henry seems 
 to indorse, that sound-waves of great intensity, when they 
 impinge upon a solid or liquid surface, do not obey the 
 law of incidence and reflection, but " roll along the surface 
 like a cloud of smoke," it only increases the difficulty. 
 Such a " cloud," instead of returning to the coast of Eng- 
 
 
PREFACE. 23 
 
 land, would, in our case, have rolled toward the coast of 
 France. Nothing that I could say in addition could 
 strengthen the case here presented. I will only add one 
 further remark. When the sun shines uniformly on a 
 smooth sea, thus producing a practically uniform distribu- 
 tion of the aerial currents to which the echoes are due, the 
 direction in which the trumpet-echoes reach the shore is 
 always that in which the axis of the instrument is pointed. 
 At Dungeness this was proved to be the case through- 
 out an arc of 210 an impossible result, if the direc- 
 tion of reflection were determined by that of the ocean 
 waves. 
 
 Kightly interpreted and followed out, these aerial 
 echoes lead to a solution which penetrates and reconciles 
 the phenomena from beginning to end. On this point I 
 would stake the issue of the whole inquiry, and to this 
 point I would, with special earnestness, direct the atten- 
 tion of the Lighthouse Board of Washington. Let them 
 prolong their observations into calm weather : if their at- 
 mosphere resembles ours which I cannot doubt then I 
 affirm that they will infallibly find the echoes strong on 
 days when all thought of reflection " from the crests and 
 slopes of the waves " must be discarded. The echoes afford 
 the easiest access to the core of this question, and it is for 
 this reason that I dwell upon them thus emphatically. It 
 requires no refined skill or profound knowledge to master 
 the conditions of their production ; and these once mas- 
 tered, the Lighthouse Board of Washington will find them- 
 selves in the real current of the phenomena, outside of 
 which I say it with respect they are now vainly specu- 
 
24 PREFACE. 
 
 lating. The acoustic deportment of the atmosphere in 
 haze, fog, sleet, snow, rain, and hail, will be no longer a 
 mystery: even those " abnormal phenomena" which are 
 now referred to an imaginary cause, or reserved for future 
 investigation, will be found to fall naturally into place, as 
 illustrations of a principle as simple as it is universal. 
 
 "With the instruments now at our disposal, wisely 
 established along our coasts, I venture to think that the 
 saving of property, in ten years, will be an exceedingly 
 large multiple of the outlay necessary for the establish- 
 ment of such signals. The saving of life appeals to the 
 higher motives of humanity." Such were the words with 
 which I wound up my Report on Fog-signals. 1 One year 
 after their utterance, the Schiller goes to pieces on the 
 Scilly rocks. A single calamity covers the predicted mul- 
 tiple, while the sea receives three hundred and thirty-three 
 victims. As regards the establishment of fog-signals, 
 energy has been hitherto paralyzed by their reputed un- 
 certainty. We now know both the reason and the range 
 of their variations ; and such knowledge places it within 
 our power to prevent disasters like the recent one. The 
 inefficiency of bells, which caused their exclusion from 
 our inquiry, was sadly illustrated in the case of the 
 
 Schiller. 
 
 JOHN TYNDALL. 
 
 ROYAL INSTITUTION, June, 1875. 
 
 1 See page 320 of this volume. 
 
PREFACE 
 
 TO 
 
 THE FIRST EDITION". 
 
 IN tlie following pages I have tried to render the science 
 of Acoustics interesting to all intelligent persons, including 
 those who do not possess any special scientific culture. 
 
 The subject is treated experimentally throughout, and 
 I have endeavored so to place each experiment before the 
 reader, that he should realize it as an actual operation. 
 My desire, indeed, has been to give distinct images of the 
 various phenomena of acoustics, and to cause them to be 
 seen mentally in their true relations. 
 
 I have been indebted to the kindness of some of my 
 English friends for a more or less complete examination 
 of the proof-sheets of this work. To my celebrated Ger- 
 man friend Clausius, who has given himself the trouble of 
 reading the proofs from beginning to end, my especial 
 thanks are due and tendered. 
 
 There is a growing desire for scientific culture through- 
 out the civilized world. The feeling is natural, and, 
 under the circumstances, inevitable. For a power which 
 influences so mightily the intellectual and material action 
 of the age, could not fail to arrest attention and challenge 
 examination. In our schools and universities a movement 
 
26 PREFACE. 
 
 in favor of science has begun which, no doubt, will end 
 in the recognition of its claims, both as a source of knowl- 
 edge and as a means of discipline. If by showing, how- 
 ever inadequately, the methods and results of physical 
 science to men of influence, who derive their culture from 
 another source, this book should indirectly aid in pro- 
 moting the movement referred to, it will not have been 
 written in vain. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 The Nerves and Sensation. Production and Propagation of Sonorous Mo- 
 tion. Experiments on Sounding Bodies placed in Vacuo. Deadening of 
 Sound by Hydrogen. Action of Hydrogen on the Voice. Propagation 
 of Sound through Air of Varying Density. Reflection of Sound. Echoes. 
 Refraction of Sound. Diffraction of Sound ; Case of Erith Village and 
 Church. Influence of Temperature on Velocity. Influence of Density 
 and Elasticity. Newton's Calculation of Velocity. Thermal Changes 
 produced by the Sonorous Ware. Laplace's Correction of Newton's 
 Formula. Ratio of Specific Heats at Constant Pressure and at Constant 
 Volume deduced from Velocities of Sound. Mechanical Equivalent of 
 Heat deduced from this Ratio. Inference that Atmospheric Air possesses 
 no Sensible Power to radiate Heat. Velocity of Sound in Different Gases. 
 Velocity in Liquids and Solids. Influence of Molecular Structure on 
 the Velocity of Sound . page 31 
 
 SUMMARY OF CHAPTER 1 73 
 
 CHAPTER II. 
 
 Physical Distinction between Noise and Music. A Musical Tone produced by 
 Periodic, Noise produced by Unperiodic, Impulses. Production of Musi- 
 cal Sounds by Taps. Production of Musical Sounds by Puffs. Definition 
 of Pitch in Music. Vibrations of a Tuning-Fork ; their Graphic Repre- 
 sentation on Smoked Glass. Optical Expression of the Vibrations of a 
 Tuning-Fork. Description of the Siren. Limits of the Ear ; Highest and 
 Deepest Tones. Rapidity of Vibration determined by the Siren. Deter- 
 mination of the Lengths of Sonorous Waves. Wave-Lengths of the Voice 
 in Man and Woman. Transmission of Musical Sounds through Liquids 
 and Solids 77 
 
 SUMMARY OF CHAPTER II. ... .110 
 
CONTENTS. 
 
 CHAPTER III. 
 
 Vibration of Strings. How employed in Music. Influence of Sound-Boards 
 Laws of Vibrating Strings. Combination of Direct and Reflected Pulses. 
 Stationary and Progressive Waves. Nodes and Ventral Segments. 
 Application of Results to the Vibrations of Musical Strings. Experiments 
 of Melde. Strings set in Vibration by Tuning-Forks. Laws of Vibration 
 thus demonstrated. Harmonic Tones of Strings. Definition of Timbre 
 or Quality, of Overtones and Clang. Abolition of Special Harmonics. 
 Conditions which affect the Intensity of the Harmonic Tones. Optical 
 Examination of the Vibrations of a Piano-Wire . . page 113 
 
 SUMMARY OF CHAPTER III 162 
 
 CHAPTEE IV. 
 
 Vibrations of a Rod fixed at Both Ends : its Subdivisions and Corresponding 
 Overtones. Vibrations of a Rod fixed at One End. The Kaleidophone. 
 The Iron Fiddle and Musical Box. Vibrations of a Rod free at Both Ends. 
 The Claque-bois and Glass Harmonica. Vibrations of a Tuning-Fork : its 
 Subdivision and Overtones. Vibrations of Square Plates. Chladni's Dis- 
 coveries. Wheatstone's Analysis of the Vibrations of Plates. Chladni's 
 Figures. Vibrations of Disks and Bells. Experiments of Faraday and 
 Strehlke 156 
 
 SUMMARY OF CHAPTER IV. . 186 
 
 CHAPTER V. 
 
 Longitudinal Vibrations of a Wire. Relative Velocities of Sound in Brass 
 and Iron. Longitudinal Vibrations of Rods fixed at One End. Of Rods 
 free at Both Ends. Divisions and Overtones of Rods vibrating longitu- 
 dinally. Examination of Vibrating Bars by Polarized Light. Deter- 
 mination of Velocity of Sound in Solids. Resonance. Vibrations of 
 Stopped Pipes : their Divisions and Overtones. Relation of the Tones 
 of Stopped Pipes to those of Open Pipes. Condition of Column of Air 
 within a Sounding Organ-Pipe. Reeds and Reed-Pipes. The Voice. 
 Overtones of the Vocal Chords. The Vowel Sounds. Kundt's Experi- 
 ments. New Methods of determining the Velocity of Sound . 188 
 
 SUMMARY OF CHAPTER V 239 
 
 CHAPTEE VI. 
 
 Singing Flames. Influence of the Tube surrounding the Flame. In- 
 fluence of Size of Flame. Harmonic Notes of Flames. Effect of 
 
CONTENTS. 29 
 
 Unisonant Notes on Singing Flames. Action of Sound on Naked 
 Flames. Experiments with Fish-Tail and Bat's-Wing Burners. Ex- 
 periments on Tall Flames. Extraordinary Delicacy of Flames as 
 Acoustic Reagents. The Yowel-Flame. Action of Conversational 
 Tones upon Flames. Action of Musical Sounds on Smoke-Jets. 
 Constitution of Water-Jets. Plateau's Theory of the Resolution of 
 a Liquid Vein into Drops. Action of Musical Sounds on Water- 
 Jets. A Liquid Vein may compete in Point of Delicacy with the 
 Ear page 244 
 
 SUMMABY OF CHAPTER VI. . 284 
 
 CHAPTER VII. 
 
 RESEARCHES ON THE ACOUSTIC TRANSPARENCY OF THE ATMOSPHERE IN RELA- 
 TION TO THE QUESTION OF FOG-SIGNALLING. 
 
 PART L 
 
 Introduction. Instruments and Observations. Contradictory Results from 
 the 19th of May to the 1st of July inclusive. Solution of Contradic- 
 tions. Aerial Reflection and its Causes. Aerial Echoes. Acoustic 
 Clouds. Experimental Demonstration of Stoppage of Sound by Aerial 
 Reflection 28T 
 
 PART II. 
 
 INVESTIGATION OF THE CAUSES WHICH HAVE HITEERTO BEEN SUPPOSED EF- 
 FECTIVE IN PREVENTING THE TRANSMISSION OF SOUND THROUGH THE 
 ATMOSPHERE. 
 
 Action of Hail and Rain. Action of Snow. Action of Fog ; Observations 
 in London. Experiments on Artificial Fogs. Observations on Fogs at 
 the South Foreland. Action of Wind. Atmospheric Selection. Influ- 
 ence of Sound-Shadow 320 
 
 SUMMARY OF CHAPTER VII. , 361 
 
 CHAPTEE VIII. 
 
 Law of Vibratory Motions in Water and Air. Superposition of Vibra- 
 tions. Interference of Sonorous Waves. Destruction of Sound by 
 Sound. Combined Action of Two Sounds nearly in Unison with each 
 other. Theory of Beats. Optical Illustration of the Principle of In- 
 terference. Augmentation of Intensity by Partial Extinction of Vi- 
 brations. Resultant Tones. Conditions of their Production. Experi- 
 
30 CONTENTS. 
 
 mental Illustrations. Difference-Tones and Summation-Tones. Theo- 
 ries of Young and Helmboltz page 354 
 
 SUMMARY OF CHAPTER VIII. 383 
 
 CHAPTEE IX. 
 
 Combination of Musical Sounds. The smaller the Two Numbers which ex- 
 press the Ratio of their Rates of Vibration, the more perfect is the 
 Harmony of Two Sounds. Notions of the Pythagoreans regarding Musi- 
 cal Consonance. Euler's Theory of Consonance. Theory of Helm- 
 holtz. Dissonance due to Beats. Interference of Primary Tones and of 
 Overtones. Sympathetic Vibrations. Mechanism of Hearing. Schultze's 
 Bristles. The Otolites. Cord's Fibres. Graphic Representation of 
 Consonance and Dissonance. Musical Chords. The Diatonic Scale. 
 Optical illustration of Musical Intervals. Lissajous's Figures. Various 
 Modes of Illustrating the Composition of Vibrations . . . 385 
 
 SUMMARY OF CHAPTER IX. 423 
 
 APPENDIX I. 
 
 ON THE INFLUENCE OF MUSICAL SOUNDS ON THE FLAME OF A JET OF COAL-GAS. 
 BY JOHN LE CONTE, M. D 427 
 
 APPENDIX II. 
 
 ON ACOUSTIC REVERSIBILITY 432 
 
 INDEX 44 1 
 
 ILLUSTRATIONS. 
 
 FOG-SIREN ... Frontispiece 
 
 OHLADNI to face p. 108 
 
S OUND. 
 
 CHAPTEE I. 
 
 The Nerves and Sensation. Production and Propagation of Sonorous Mo- 
 tion. Experiments on Sounding Bodies placed in Vacuo. Deadening of 
 Sound by Hydrogen. Action of Hydrogen on the Voice. Propagation 
 of Sound through Air of Varying Density. Reflection of Sound. Echoes. 
 Refraction of Sound. Diffraction of Sound ; Case of Erith Village and 
 Church. Influence of Temperature on Velocity. Influence of Density 
 and Elasticity. Newton's Calculation of Velocity. Thermal Changes 
 produced by the Sonorous Wave. Laplace's Correction of Newton's 
 Formula. Ratio of Specific Heats at Constant Pressure and at Constant 
 Volume deduced from Velocities of Sound. Mechanical Equivalent of 
 Heat deduced from this Ratio. Inference that Atmospheric Air possesses 
 no Sensible Power to radiate Heat. Velocity of Sound in Different Gases. 
 Velocity m Liquids and Solids. Influence of Molecular Structure on 
 the Velocity of Sound. 
 
 1. Introduction : Character of Sonorous Motion. 
 Experimental Illustrations. 
 
 THE various nerves of the human body have their ori- 
 gin in the brain, which is the seat of sensation. When 
 the finger is wounded, the sensor nerves convey to the 
 brain intelligence of the injury, and if these nerves be 
 severed, however serious the hurt may be, no pain is 
 experienced. "We have the strongest reason for believing 
 that what the nerves convey to the brain is in all cases 
 motion. The motion here meant is not, however, that of 
 
32 SOUND. 
 
 the netfve as a r whole> but of its molecules or smallest 
 particles. 1 
 
 ' DiHeromV -tierces -are appropriated to the transmission 
 of different kinds of molecular motion. The nerves of 
 taste, for example, are not competent to transmit the 
 tremors of light, nor is the optic nerve competent to 
 transmit sonorous vibrations. For these a special nerve 
 is necessary, which passes from the brain into one of the 
 cavities of the ear, and there divides into a multitude of 
 filaments. It is the motion imparted to this, the auditory 
 nerve, which, in the brain, is translated into sound. 
 
 Applying a flame to a small collodion balloon which con- 
 tains a mixture of oxygen and hydrogen, the gases explode, 
 and every ear in this room is conscious of a shock, which 
 we name a sound. How was this shock transmitted from 
 the balloon to our organs of hearing ? Have the exploding 
 gases shot the air-particles against the auditory nerve as 
 a gun shoots a ball against a target ? No doubt, in the 
 neighborhood of the balloon, . there is to some extent a 
 propulsion of particles ; but no particle of air from the 
 vicinity of the balloon reached the ear of any person here 
 present. The process was this : When the flame touched 
 the mixed gases they combined chemically, and their 
 union was accompanied by the development of intense 
 heat. The heated air expanded suddenly, forcing the 
 surrounding air violently away on all sides. This motion 
 of the air close to the balloon was rapidly imparted 
 to that a little farther off, the air first set in motion 
 coming at the same time to rest. The air, at a little dis- 
 tance, passed its motion on to the air at a greater distance, 
 and came also in its turn to rest. Thus each shell of air, 
 if I may use the term, surrounding the balloon took up 
 
 1 The rapidity with which an impression is transmitted through the 
 nerves, as first determined by Helmholtz, and confirmed by Du Bois-Rey- 
 mond, is 93 feet a second. 
 
PRODUCTION AND PROPAGATION OF SOUND. 33 
 
 the motion of the shell next preceding, and transmitted it 
 to the next succeeding shell, the motion being thus propa- 
 gated as a pulse or wave through the air. 
 
 The motion of the pulse must not be confounded with 
 the motion of the particles which at any moment constitute 
 the pulse. For while the wave moves forward through 
 considerable distances, each particular particle of air makes 
 only a small excursion to and fro. 
 
 The process may be rudely represented by the propa- 
 gation of motion through a row of glass balls, such as are 
 employed in the game of solitaire. Placing the balls 
 along a groove thus, Fig. 1, each of them touching its 
 neighbor, and urging one of them against the end of the 
 
 row : the motion thus imparted to the first ball is delivered 
 up to the second, the motion of the second is delivered up 
 to the third, the motion of the third is imparted to the 
 fourth ; each ball, after having given up its motion, re- 
 turning itself to rest. The last ball only of the row flies 
 away. In a similar way is sound conveyed from particle 
 to particle through the air. The particles which fill the 
 cavity of the ear are finally driven against the tympanic 
 membrane, which is stretched across the passage leading 
 from the external air toward the brain. This membrane, 
 which closes outwardly the " drum " of the ear, is thrown 
 into vibration, its motion is transmitted to the ends of the 
 auditory nerve, and afterward along that nerve to the 
 
34: SOUND. 
 
 brain, where the vibrations are translated into sound. 
 How it is that the motion of the nervous matter can thus 
 excite the consciousness of sound is a mystery which the 
 human mind cannot fathom. 
 
 The propagation of sound may be illustrated by another 
 homely but useful illustration. I have here five young 
 assistants, A, B, c, D, and E, Fig. 2, placed in a row, one 
 behind the other, each boy's hands resting against the 
 back of the boy in front of him. E is now foremost, and 
 A finishes the row behind. I suddenly push A, A pushes 
 B, and regains his upright position ; B pushes c ; c pushes 
 D ; D pushes E ; each boy, after the transmission of the 
 push, becoming himself erect. E, having nobody in front, 
 
 is thrown forward. Had he been standing on the edge of 
 a precipice, he would have fallen over ; had he stood in 
 contact with a window, he would have broken the glass ; 
 had he been close to a drum-head, he would have shaken 
 the drum. We could thus transmit a push through a row 
 of a hundred boys, each particular boy, however, only 
 swaying to and fro. Thus, also, we send sound through 
 the air, and shake the drum of a distant ear, while each 
 particular particle of the air concerned in the transmission 
 of the pulse makes only a small oscillation. 
 
 But we have not yet extracted from our row of boys 
 all that they can teach us. When A is pushed he may yield 
 languidly, and thus tardily deliver up the motion to his 
 
A SONOROUS WAVE. 35 
 
 neighbor B. B may do the same to c, c to D, and D to E. 
 In this way the motion might be transmitted with com- 
 parative slowness along the line. But A, when pushed, 
 may, by a sharp muscular effort and sudden recoil, deliver 
 up promptly his motion to B, and come himself to rest ; B 
 may do the same to c, c to D, and D to E, the motion be- 
 ing thus transmitted rapidly along the line. Now this 
 sharp muscular effort and sudden recoil is analogous to 
 the elasticity of the air in the case of sound. In a wave 
 of sound, a lamina of air, when urged against its neigh- 
 bor lamina, delivers up its motion and recoils, in virtue 
 of the elastic force exerted between them ; and the more 
 rapid this delivery and recoil, or in other words the greater 
 the elasticity of the air, the greater is the velocity of the 
 sound. 
 
 A very instructive mode of illustrating the transmission 
 of a sound-pulse is furnished by the apparatus represented 
 in Fig. 3, devised by my assistant, Mr. Cottrell. It con- 
 
 FIG. 8. 
 
 
 
 e 
 
 fcu 
 
 f EC 
 
 I 
 
 r F 
 
 
 = -= ^ 
 
 
 
 
 sists of a series of wooden balls separated from each other 
 by spiral springs. On striking the knob A, a rod attached 
 to it impinges upon the first ball B, which transmits its 
 motion to c, thence it passes to E, and so on through the 
 entire series. The arrival at D is announced by the shock 
 of the terminal ball against the wood, or, if we wish, by the 
 ringing of a bell. Here the elasticity of the air is repre- 
 sented by that of the springs. The pulse may be rendered 
 slow enough to be followed by the eye. 
 
 Scientific education ought to teach us to see the in- 
 visible as well as the visible in nature, to picture with the 
 vision of the mind those operations which entirely elude 
 
36 SOUND. 
 
 bodily vision ; to look at the very atoms of matter in mo- 
 tion and at rest, and to follow them forth, without ever 
 once losing sight of them, into the world of the senses, and 
 see them there integrating themselves in natural phenom- 
 ena. With regard to the point now under consideration, 
 we must endeavor to form a definite image of a wave 
 of sound. We ought to see mentally the air-particles 
 when urged outward by the explosion of our balloon 
 crowding closely together; but immediately behind this 
 condensation we ought to see the particles separated more 
 widely apart. We must, in short, to be able to seize the 
 conception that a sonorous wave consists of two portions, 
 in the one of which the air is more dense, and in the other 
 of which it is less dense than usual. A condensation and 
 a rarefaction, then, are the two constituents of a wave of 
 sound. This conception shall be rendered more complete 
 in our next lecture. 
 
 2. Experiments in Vacuo, in Hydrogen, and on Moun- 
 tains. 
 
 That air is thus necessary to the propagation of sound 
 Was proved by a celebrated experiment made before the 
 Eoyal Society, by a philosopher named Hawksbee, in 1705. 1 
 He so fixed a bell within the receiver of an air-pump that 
 he could ring the bell when the receiver was exhausted. 
 Before the air was withdrawn the sound of the bell was 
 heard within the receiver ; after the air was withdrawn the 
 sound became so faint as to be hardly perceptible. An 
 arrangement is before you which enables us to repeat in a 
 very perfect manner the experiment of Hawksbee. With- 
 in this jar, GO', Fig. 4, resting on the plate of an air-pump 
 is a bell, B, associated with clock-work. 2 After the jar has 
 
 1 And long previously by Robert Boyle. 
 
 8 A very effective instrument, presented to the Royal Institution by Mr. 
 Warren De La Rue. 
 
BELL IN VACUO. 
 
 FIG. 4. 
 
 been exhausted as perfectly as possible, I release, by means 
 of a rod, rr', which passes air-tight through the top of the 
 vessel, the detent which holds the hammer. It strikes, 
 and you see it striking, but only those close to the bell can 
 hear .the sound. Hydrogen gas, which you know is four- 
 teen times lighter than air, is now allowed to enter the 
 vessel. The sound of the bell is not augmented by the 
 presence of this attenuated gas, though the receiver is now 
 full of it. By working the pump, the atmosphere round 
 the bell is rendered still more 
 attenuated. In this way we 
 obtain a vacuum more perfect 
 than that of Hawksbee, and 
 this is important, for it is 
 the last traces of air that are 
 chiefly effective in this ex- 
 periment. You now see the 
 hammer pounding the bell, but 
 you hear no sound. Even 
 w r hen the ear is placed against 
 the exhausted receiver, not 
 the faintest tinkle is heard. 
 Observe also that the bell is 
 suspended by strings, for if it 
 were allowed to rest upon the 
 plate of the air - pump, the 
 vibrations would be communi- 
 cated to the plate, and thence 
 transmitted to the air outside. 
 Permitting the air to enter the jar with as little noise as 
 possible, you immediately hear a feeble sound, which 
 grows louder as the air becomes more dense, until finally 
 every person in this large assembly distinctly hears the 
 ringing of the bell. 1 
 
 1 By directing the beam of an electric lamp on glass bulbs filled with a 
 
38 SOUND. 
 
 Sir John Leslie found hydrogen singularly incompe- 
 tent to act as the vehicle of the sound of a bell rung in the 
 gas. More than this, he emptied a receiver like that be- 
 fore you of half its air, and plainly heard the ringing of 
 the bell. On permitting hydrogen to enter the half-filled 
 receiver until it was wholly filled, the sound sank until it 
 was scarcely audible. This result remained an enigma 
 until it received a simple and satisfactory explanation at 
 the hands of Prof. Stokes. When a common pendulum 
 oscillates it tends to form a condensation in front and a 
 rarefaction behind. But it is only a tendency ; the mo- 
 tion is so slow, and the air is so elastic, that it moves away 
 in front before it is sensibly condensed, and fills the space 
 behind before it can become sensibly dilated. Hence 
 waves or pulses are not generated by the pendulum. It 
 requires a certain sharpness of shock to produce the con- 
 densation and rarefaction which constitute a wave of sound 
 in air. 
 
 The more elastic and mobile the gas, the more able 
 will it be to move away in front and to fill the space 
 behind, and thus to oppose the formation of rarefactions 
 and condensations by a vibrating body. Now hydrogen is 
 much more mobile than air ; and hence the production of 
 sonorous waves in it is attended with greater difficulty 
 than in air. A rate of vibration quite competent to pro- 
 duce sound-waves in the one may be wholly incompetent 
 to produce them in the other. Both calculation and obser- 
 vation prove the correctness of this explanation, to which 
 we shall again refer. 
 
 At great elevations in the atmosphere sound is sensibly 
 diminished in loudness. De Saussure thought the explo- 
 sion of a pistol at the summit of Mont Blanc to be about 
 
 mixture of equal volumes of chlorine and hydrogen, I have caused the bulbs 
 to explode in vacuo and in air. The difference, though not so striking as I 
 at first expected, was perfectly distinct. 
 
EFFECT OF HYDROGEN UPOX THE VOICE. 39 
 
 equal to that of a common cracker below. I have several 
 times repeated this experiment ; first, in default of any- 
 thing better, with a little tin cannon, the torn remnants of 
 which are now before you, and afterward with pistols. 
 What struck me was the absence of that density and sharp- 
 ness in the sound which characterize it at lower elevations. 
 The pistol-shot resembled the explosion of a champagne 
 bottle, but it was still loud. The withdrawal of half an 
 atmosphere does not very materially affect our ringing 
 bell, and air of the density found at the top of Mont Blanc 
 is still capable of powerfully affecting the auditory nerve. 
 That highly attenuated air is able to convey sound of 
 great intensity is forcibly illustrated by the explosion of 
 meteorites at elevations where the tenuity of the atmos- 
 phere must be almost infinite. Here, however, the initial 
 disturbance must be exceedingly great. 
 
 The motion of sound, like all other motion, is enfeebled 
 by its transference from a light body to a heavy one. 
 When the receiver which has hitherto covered our bell is 
 removed, you hear how much more loudly it rings in the 
 open air. When the bell was covered the aerial vibra- 
 tions were first communicated to the heavy glass jar, and 
 afterward by the jar to the air outside ; a great diminution 
 of intensity being the consequence. The action of hydro- 
 gen gas upon the voice is an illustration of the same 
 kind. The voice is formed by urging air from the lungs 
 through an organ called the larynx, where it is thrown 
 into vibration by the vocal chords which thus generate 
 sound. But when the lungs are filled with hydrogen, 
 the vocal chords on speaking produce a vibratory motion 
 in the hydrogen, which then transfers the motion to the 
 outer air. By this transference from a light gas to a heavy 
 one the voice is so weakened as to become a mere squeak. 1 
 
 1 It may be that the gas fails to throw the vocal chords into sufficiently 
 strong vibration. The laryngoscope might decide this question. 
 
40 SOUND. 
 
 The intensity of a sound depends on the density of the 
 air in which the sound is generated, and not on that of the 
 air in which it is heard. 1 Supposing the summit of Mont 
 Blanc to be equally distant from the top of the Aiguille 
 Yerte and the bridge at Chamouni ; and supposing two 
 observers stationed, the one upon the bridge and the other 
 upon the Aiguille : the report of a cannon fired on Mont 
 Blanc would reach both observers with the same intensity, 
 though in the one case the sound would pursue its way 
 through the rare air above, while in the other it would de- 
 scend through the denser air below. Again, let a straight 
 line equal to that from the bridge at Chamouni to the 
 summit of Mont Blanc be measured along the earth's sur- 
 face in the valley of Chamouni, and let two observers be 
 stationed, the one on the summit and the other at the end 
 of the line : the report of a cannon fired on the bridge 
 would reach both observers with the same intensity, though 
 in the one case the sound would be propagated through 
 the dense air of the valley, and in the other case would 
 ascend through the rarer air of the mountain. Finally, 
 charge two cannon equally, and fire one of them at Cha- 
 mouni and the other at the top of Mont Blanc : the one 
 fired in the heavy air below may be heard above, while the 
 one fired in the light air above is unheard below. 
 
 3. Intensity of Sound. Law of Inverse Squares. 
 
 In the case of our exploding balloon the wave of 
 sound expands on all sides, the motion produced by the 
 explosion being thus diffused over a continually augment- 
 ing mass of air. It is perfectly manifest that this cannot 
 occur without an enfeeblement of the motion. Take the 
 case of a thin shell of air with a radius of one foot, 
 reckoned from the centre of explosion. A shell of air of 
 the same thickness, but of two feet radius, will contain 
 
 1 Poisson, "M6canique," vol. ii., p. 707. 
 
INTENSITY OF SOUND. 41 
 
 four times the quantity of matter ; if its radius be three 
 feet, it will contain nine times the quantity of matter ; if 
 four feet, it will contain sixteen times the quantity of 
 matter, and so on. Thus the quantity of matter set in 
 motion augments as the square of the distance from the 
 centre of explosion. The intensity or loudness of sound 
 diminishes in the same proportion. We express this law 
 by saying that the intensity of the sound varies inversely 
 as the square of the distance. 
 
 Let us look at the matter in another light. The me- 
 chanical effect of a ball striking a target depends on two 
 things the weight of the ball, and the velocity with which 
 it moves. The effect is proportional to the weight simply ; 
 but it is proportional to the square of the velocity. The 
 proof of this is easy, but it belongs to ordinary mechanics, 
 rather than to our present subject. Now what is true of 
 the cannon-ball striking a target is also true of an air- 
 particle striking the tympanum of the ear. Fix your at- 
 tention upon a particle of air as the sound-wave passes 
 over it; it is urged from its position of rest toward a 
 neighbor particle, first with an accelerated motion, and 
 then with a retarded one. The 'force which first urges it 
 is opposed by the resistance of the air, which finally stops 
 the particle and causes it to recoil. At a certain point of 
 its excursion the velocity of the particle is its maximum. 
 The intensity of the sound is proportional to the square 
 of this maximum velocity. 
 
 The distance through which the air-particle moves to 
 and fro, when the sound-wave passes it, is called the am- 
 plitude of the vibration. The intensity of the sound is 
 proportional to the square of the amplitude. 
 
 4. Confinement of Sound-waves in Tubes. 
 
 This weakening of the sound, according to the law of 
 inverse squares, would not take place if the sound-wave 
 
2 SOUND. 
 
 were so confined as to prevent its lateral diffusion. By 
 sending it through, a tube with a smooth interior surface 
 we accomplish this, and the wave thus confined may be 
 transmitted to great distances with very little diminution 
 of intensity. Into one end of this tin tube, fifteen feet 
 long, I whisper in a manner quite inaudible to the people 
 nearest to me, but a listener at the other end hears me 
 distinctly. If a watch be placed at one end of the tube, 
 a person at the other end hears the ticks, though nobody 
 else does. At the distant end of the tube is now placed a 
 lighted candle, 0, Fig. 5. When the hands are clapped at 
 this end, the flame instantly ducks down at the other. 
 
 FIG. 5. 
 
 It is not quite extinguished, but it is forcibly depressed. 
 When two books, B B', Fig. 5, are clapped together, the 
 candle is blown out. 1 You may here observe, in a rough 
 way, the speed with which the sound-wave is propagated. 
 The instant the clap is heard the flame is extinguished. 
 I do not say that the time required by the sound to travel 
 this tube is immeasurably short, but simply that the in- 
 terval is too short for your senses to appreciate it. 
 
 That it is a pulse and not a puff of air is proved by 
 filling one end of the tube with the smoke of brown paper. 
 On clapping the books together no trace of this smoke is 
 ejected from the other end. The pulse has passed through 
 both smoke and air without carrying either of them along 
 with it. 
 
 1 To converge the pulse upon the flame, the tube was caused to end in 
 a cone. 
 
TRANSMISSION OF SOUND THROUGH TUBES. 43 
 
 An effective mode of throwing the propagation of a 
 pulse through air has been devised by my assistant. The 
 two ends of a tin tube fifteen feet long are stopped by 
 sheet India-rubber stretched across them. At one end, 0, 
 a hammer with a spring handle rests against the India- 
 rubber ; at the other end is an arrangement for the striking 
 of a bell, c. Drawing back the hammer e to a distance 
 measured on the graduated circle and liberating it, the 
 generated pulse is propagated through the tube, strikes 
 the other end, drives away the cork termination a of the 
 
 FIG. 6. 
 
 lever a 5, and causes the hammer b to strike the bell. 
 The rapidity of propagation is well illustrated here. When 
 hydrogen (sent through the India-rubber tube H) is substi- 
 tuted for air the bell does not ring. 
 
 The celebrated French philosopher, Biot, observed the 
 transmission of sound through the empty water-pipes of 
 Paris, and found that he could hold a conversation in a 
 low voice through an iron tube 3,120 feet in length. The 
 lowest possible whisper, indeed, could be heard at this dis- 
 tance, while the firing of a pistol into one end of the tube 
 quenched a lighted candle at the other. 
 
 5. The Reflection of Sound. Resemblances to Light. 
 
 The action of sound thus illustrated is exactly the same 
 as that of light and radiant heat. They, like sound, are 
 
4A: SOUND. 
 
 wave-motions. Like sound they diffuse themselves in 
 space, diminishing in intensity according to the same law. 
 Like sound also, light and radiant heat, when sent through 
 a tube with a reflecting interior surface, may be conveyed 
 to great distances with comparatively little loss. In fact, ' 
 every experiment on the reflection of light has its anal- 
 ogy in the reflection of sound. On yonder gallery stands 
 an electric lamp, placed close to the clock of this lecture- 
 room. An assistant in the gallery ignites the lamp, and 
 directs its powerful beam upon a mirror placed here be- 
 hind the lecture-table. By the act of reflection the diver- 
 gent beam is converted into this splendid luminous cone 
 traced out upon the dust of the room. The point of con- 
 vergence being marked and the lamp extinguished, I place 
 my ear at that point. Here every sound-wave sent forth by 
 the clock and reflected by the mirror is gathered up, and 
 the ticks are heard as if they came, not from the clock, but 
 from the mirror. Let us stop the clock, and place a watch 
 w, Fig. Y, at the place occupied a moment ago by the elec- 
 
 trie light. At this great distance the ticking of the 
 watch is distinctly heard. The hearing is much aided by 
 introducing the end f of a glass funnel into the ear, the 
 funnel here acting the part of an ear-trumpet. We know, 
 
REFLECTION OF SOUND BY MIRRORS. 4.5 
 
 moreover, that in optics the positions of a body and of its 
 image are reversible. When a candle is placed at this lower 
 focus, you see its image on the gallery above, and I have 
 only to turn the mirror on its stand to make the image of 
 the flame fall upon any one of the row of persons who occupy 
 the front seat in the gallery. Kemoving the candle, and 
 putting the watch, w, Fig. 8, in its place, the person on 
 whom the light fell distinctly hears the sound. When 
 the ear is assisted by the glass funnel, the reflected ticks 
 of the clock in our first experiment are so powerful as to 
 suggest the idea of something pounding against the tym- 
 panum, while the direct ticks are scarcely, if at all, heard. 
 
 FIG. 8. 
 
 One of these two parabolic mirrors, n n', Fig. 9, is placed 
 upon the table, the other, m m' ', being drawn up to the 
 ceiling of this theatre ; they are five-and-twenty feet apart. 
 When the carbon-points of the electric light are placed in 
 the focus a of the lower mirror and ignited, a fine lumi- 
 nous cylinder rises like a pillar to the upper mirror, which 
 brings the parallel beam to a focus. At that focus is seen 
 a spot of sunlike brilliancy, due to the reflection of the 
 light from, the surface of a watch, w, there suspended. 
 The watch is ticking, but in my present position I do not 
 
SOUND. 
 
 hear it. At this lower focus, a, however, we have the energy 
 of every sonorous wave converged. Placing the ear at a, 
 the ticking is as audible as if the watch were at hand ; the 
 sound, as in the former case, appearing to proceed, not 
 from the watch itself, but from the lower mirror. 1 
 
 Curved roofs and ceilings and bellying sails act as 
 mirrors upon sound. In our old laboratory, for example, 
 
 the singing of a kettle 
 seemed, in certain po- 
 sitions, to come, not 
 from the fire on which 
 it was placed, but from 
 the ceiling. Incon- 
 venient secrets have 
 been thus revealed, an 
 instance of which has 
 been cited by Sir John 
 Herschel. 9 In one of 
 the cathedrals in Sicily 
 the confessional was 
 so placed that the 
 whispers of the peni- 
 tents were reflected by 
 the curved roof, and 
 brought to a focus at 
 a distant part of the 
 edifice. The focus was 
 discovered by accident, 
 and for some time the 
 person who discovered it took pleasure in hearing, and in 
 
 1 It is recorded that a bell placed on an eminence in Heligoland failed, 
 on account of its distance, to be heard in the town. A parabolic reflector 
 placed behind the bell, so as to reflect the sound-waves in the direction of 
 the long, sloping street, caused the strokes of the bell to be distinctly heard 
 at all times. This observation needs verification. 
 
 8 " Encyclopedia Metropolitana," art. " Sound." 
 
ECHOES. 47 
 
 bringing his friends to hear, utterances intended for the 
 priest alone. One day, it is said, his own wife occupied 
 the penitential stool, and both he and his friends were 
 thus made acquainted with secrets which were the reverse 
 of amusing to one of the party. 
 
 When a sufficient interval exists between a direct and 
 a reflected sound, we hear the latter as an echo. 
 
 Sound, like light, may be reflected several times in 
 succession, and, as the reflected light under these circum- 
 stances becomes gradually feebler to the eye, so the suc- 
 cessive echoes become gradually feebler to the ear. In 
 mountain-regions this repetition and decay of sound pro- 
 duce wonderful and pleasing effects. Visitors to Killarney 
 will remember the flne echo in the Gap of Dunloe. When 
 a trumpet is sounded in the proper place in the Gap, the 
 sonorous waves reach the ear in succession after one, two, 
 three, or more reflections from the adjacent cliifs, and thus 
 die away in the sweetest cadences. There is a deep cul-de- 
 sac, called the Ochsenthal, formed by the great cliffs of 
 the Engelhorner, near Rosenlaui, in Switzerland, where 
 the echoes warble in a wonderful manner. The sound of 
 the Alpine horn, echoed from the rocks of the Wetterhorn 
 or the Jungfrau, is in the first instance heard roughly. 
 But by successive reflections the notes are rendered more 
 soft and flute-like, the gradual diminution of intensity 
 giving the impression that the source of sound is retreat- 
 ing farther and farther into the solitudes of ice and snow. 
 The repetition of echoes is also in part due to the fact that 
 the reflecting surfaces are at different distances from the 
 hearer. 
 
 In large, unfurnished rooms the mixture of. direct and 
 reflected sound sometimes produces very curious effects. 
 Standing, for example, in the gallery of the Bourse at 
 Paris, you hear the confused vociferation of the excited 
 multitude below. You see all the motions of their lips 
 3 
 
48 SOUND. 
 
 as well as of their hands and arms. You know they are 
 speaking often, indeed, with vehemence, but what they 
 say you know not. The voices mix with their echoes into 
 a chaos of noise, out of which no intelligible utterance can 
 emerge. The echoes of a room are materially damped by 
 its furniture. The presence of an audience may also ren- 
 der intelligible speech possible where, without an audience, 
 the definition of the direct voice is destroyed by its echoes. 
 On the 16th of May, 1865, having to lecture in the Senate 
 House of the University of Cambridge, I first made some 
 experiments as to the loudness of voice necessary to fill the 
 room, and was dismayed to find that a friend, placed at a 
 distant part of the hall, could not follow me because of the 
 echoes. The assembled audience, however, so quenched 
 the sonorous waves, that the echoes were practically absent, 
 and my voice was plainly heard in all parts of the Senate 
 House. 
 
 Sounds are also said to be reflected from the clouds. 
 Arago reports that, when the sky is clear, the report of a 
 cannon on an open plain is short and sharp, while a cloud 
 is sufficient to produce an echo like the rolling of distant 
 thunder. The subject of aerial echoes will be subsequently 
 treated at length, when it will be shown that Arago's con- 
 clusion requires correction. 
 
 Sir John Herschel, in his excellent article " Sound," in 
 the " Encyclopaedia Metropolitana," has collected with 
 others the following instances of echoes. An echo in 
 Woodstock Park repeats seventeen syllables by day and 
 twenty by night; one, on the banks of the Lago del 
 Lupo, above the fall of Terni, repeats fifteen. The tick of 
 a watch may be heard from one end of the abbey church 
 of St. Albans to the other. In Gloucester Cathedral, a 
 gallery of an octagonal form conveys a whisper seventy- 
 five feet across the nave. In the whispering-gallery of 
 St. Paul's, the faintest sound is conveyed from one side to 
 
REFRACTION OF SOUND BY LENSES. 4.9 
 
 the other of the dome, but is not heard at any inter- 
 mediate point. At Carisbrook Castle, in the Isle of 
 Wight, is a well two hundred and ten feet deep and 
 twelve wide. The interior is lined by smooth masonry ; 
 when a pin is dropped into the well it is distinctly heard 
 to strike the water. Shouting or coughing into this well 
 produces a resonant ring of some duration. 1 
 
 6. Refraction of Sound, 
 
 Another important analogy between sound and light 
 has been established by M, Sondhauss. 2 When a large 
 lens is placed in front of our lamp, the lens compels the 
 rays of light that fall upon it to deviate from their direct 
 and divergent course, and to form a convergent cone 
 behind it. This refraction of the luminous beam is a con- 
 sequence of the retardation suffered by the light in passing 
 
 FIG. 10, 
 
 through the glass. Sound may be similarly refracted by 
 causing it to pass through a lens which retards its motion. 
 Such a lens is formed when we fill a thin balloon with 
 some gas heavier than air. A collodion balloon, B, Fig. 
 10, filled with carbonic-acid gas, the envelope being so 
 
 1 Placing himself close to the upper part of the wall of the London 
 Colosseum, a circular building one hundred and thirty feet in diameter, Mr. 
 Wheatstone found a word pronounced to be repeated a great many times. 
 A single exclamation appeared like a peal of laughter, while the tearing of a 
 piece of paper was like the patter of hail. 
 
 2 Poggcndorff^s Annalen, vol. Ixxxv., p. 378 ; Philosophical Magazine^ 
 vol, v., p. 73. 
 
50 SOUND. 
 
 thin as to yield readily to the pulses which strike against 
 it, answers the purpose. 1 A watch, w, is hung up close to 
 the lens, beyond which, and at a distance of four or five 
 feet from the lens, is placed the ear, assisted by the glass 
 funnel f f. By moving the head about, a position is 
 soon discovered in which the ticking is particularly loud. 
 This, in fact, is the focus of the lens. If the ear be 
 moved from this focus the intensity of the sound falls ; 
 if, when the ear is at the focus, the balloon be removed, 
 the ticks are enfeebled ; on replacing the balloon their 
 force is restored. The lens, in fact, enables us to hear 
 the ticks distinctly when they are perfectly inaudible to 
 the unaided ear. 
 
 How a sound-wave is thus converged may be compre- 
 hended by reference to Fig. 11. Let m o n o" be a section 
 of the sound-lens, and a b a portion of a sonorous wave ap- 
 FIG lt proaching it from a distance. 
 
 a 5 The middle point, 0, of the 
 
 wave first touches the lens, 
 and is first retarded by it. 
 By the time the ends a and 
 5, still moving through air, 
 reach the balloon, the middle 
 point 0, pursuing its way 
 through the heavier gas withr 
 
 a/ B' in, will have only reached o f . 
 
 The wave is therefore broken at o' / and the direction of 
 motion being at right angles to the face of the wave, the 
 two halves will encroach upon each other. This conver- 
 gence of the two halves of the wave is augmented on quit- 
 ting the lens. For when o' has reached 0", the two ends a 
 and 5 will have pushed forward to a greater distance, say 
 to a' and ft. Soon afterward the two halves of the wave 
 will cross each other, or in other words come to a focus, 
 
 1 Thin India-rubber balloons also form excellent sound-lenses. 
 
DIFFRACTION OF SOUND ERITH EXPLOSION. 51 
 
 the air at the focus being agitated by the sum of the mo- 
 tions of the two waves. 1 
 
 7. Diffraction of Sound: illustrations offered by great 
 Explosions. 
 
 When a long sea-roller meets an isolated rock in its 
 passage, it rises against the rock and embraces it all round. 
 Facts of this nature caused Newton to reject the undula- 
 tory theory of light. He contended that if light were a 
 product of wave-motion we could have no shadows, be- 
 cause the waves of light would propagate themselves 
 round opaque bodies as a wave of water round a rock. It 
 has been proved since his time that the waves of light do 
 bend round opaque bodies ; but with that we have nothing 
 now to do. A sound-wave certainly bends thus round an 
 obstacle, though as it diffuses itself in the air at the back 
 of the obstacle it is enfeebled in power, the obstacle thus 
 producing a partial shadow of the sound. A railway-train 
 passing through cuttings and long embankments exhibits 
 great variations in the intensity of the sound. The inter- 
 position of a hill in the Alps suffices to diminish materi- 
 ally the sound of a cataract ; it is able sensibly to extin- 
 guish the tinkle of the cow-bells. Still the sound-shadow 
 is but partial, and the marker at the rifle-butts never fails 
 to hear the explosion, though he is well protected from the 
 ball. A striking example of this diffraction of a sonorous 
 wave was exhibited at Erith after the tremendous explosion 
 of a powder magazine which occurred there in 1864. The 
 village of Erith was some miles distant from the magazine, 
 but in nearly all cases the windows were shattered ; and it 
 was noticeable that the windows turned away from the 
 origin of the explosion suffered almost as much as those 
 
 1 For the sake of simplicity, the wave is shown broken at o' and its two 
 halves straight. The surface of the wave, however, is really a curve, with 
 its concavity turned in the direction of its propagation. 
 
52 SOUND. 
 
 which faced it. Lead sashes were employed in Erith 
 Church, and these, being in some degree flexible, enabled 
 the windows to yield to pressure without much fracture of 
 the glass. As the sound-wave reached the church it sepa- 
 rated right and left, and, for a moment, the edifice was 
 clasped by a girdle of intensely compressed air, every 
 window in the church, front and back, being bent inward. 
 After compression, the air within the church no doubt 
 dilated, tending to restore the windows to their first condi- 
 tion. The bending in of the windows, however, produced 
 but a small condensation of the whole mass of air within 
 the church ; the recoil was therefore feeble in comparison 
 with the pressure, and insufficient to undo what the latter 
 had accomplished. 
 
 8. Velocity of Sound: relation to Density and Elas- 
 ticity of Air. 
 
 Two conditions determine the velocity of propagation 
 of a sonorous wave ; namely, the elasticity and the density 
 of the medium through which the wave passes. The elas- 
 ticity of air is measured by the pressure which it sustains 
 or can hold in equilibrium. At the sea-level this pressure 
 is equal to that of a stratum of mercury about thirty 
 inches high. At the summit of Mont Blanc the baro- 
 metric column is not much more than half this height ; 
 and, consequently, the elasticity of the air upon the sum- 
 mit of the mountain is not much more than half what it is 
 at the sea-level. 
 
 If we could augment the elasticity of air, without at 
 the same time augmenting its density, we should augment 
 the velocity of sound. Or, if allowing the elasticity to 
 remain constant we could diminish the density, we should 
 augment the velocity. Now, air in a closed vessel, where 
 it cannot expand, has its elasticity augmented by heat, 
 while its density remains unchanged. Through such heated 
 
INFLUENCE OF TEMPERATURE ON VELOCITY. 53 
 
 air sound travels more rapidly than through cold air. Again, 
 air free to expand has its density lessened by wanning, its 
 elasticity remaining the same, and through such air sound 
 travels more rapidly than through cold air. This is the 
 case with our atmosphere when heated by the sun. 
 
 The velocity of sound in air, at the freezing tempera- 
 ture^ is 1,090 feet a second. 
 
 At all lower temperatures the velocity is less than this, 
 and at all higher temperatures it is greater. The late M. 
 Wertheim has determined the velocity of sound in air of 
 different temperatures, and here are some of his results : 
 
 Temperature Velocity of 
 
 of air. sound. 
 
 0-5 centigrade 1,089 feet. 
 
 2-10 " 1,091 " 
 
 8-5 " 1,109 " 
 
 12-0 " 1,113 " 
 
 26-6 " 1,140 " 
 
 At a temperature of half a degree above the freezing- 
 point of water the velocity is 1,089 feet a second ; at a 
 temperature of 26*6 degrees, it is 1,140 feet a second, or 
 a difference of 51 feet for 26 degrees ; that is to say, an 
 augmentation of velocity of nearly two feet for every sin- 
 gle degree centigrade. 
 
 With the same elasticity the density of hydrogen gas 
 is much less than that of air, and the consequence is that 
 the velocity of sound in hydrogen far exceeds its velocity 
 in air. The reverse holds good for heavy carbonic-acid 
 gas. If density and elasticity vary in the same proportion, 
 as the law of Boyle and Mariotte proves them to do in air 
 when the temperature is preserved constant, they neutralize 
 each other's effects ; hence, if the temperature were the 
 same, the velocity of sound upon the summits of the high- 
 est Alps would be the same as that at the mouth of the 
 Thames. But, inasmuch as the air above is colder than 
 that below, the actual velocity on the summits of the moun- 
 
54: SOUND. 
 
 tains is less than that at the sea-level. To express this re- 
 sult in stricter language, the velocity is directly propor- 
 tional to the square root of the elasticity of the air ; it is 
 also inversely proportional to the square root of the den- 
 sity of the air. Consequently, as in air of a constant 
 temperature elasticity and density vary in the same pro- 
 portion, and act oppositely, the velocity of sound is not 
 affected by a change of density, if unaccompanied by a 
 change of temperature. 
 
 There is no mistake more common than to suppose the 
 velocity of sound to be augmented by density. The mis- 
 take has arisen from a misconception of the fact that in 
 solids and liquids the velocity is greater than in gases. 
 But it is the higher elasticity of those bodies, in relation 
 to their density, that causes sound to pass rapidly through 
 them. Other things remaining the same, an augmentation 
 of density always produces a diminution of velocity. Were 
 the elasticity of water, which is measured by its compressi- 
 bility, only equal to that of air, the velocity of sound in 
 water, instead of being more than quadruple the velocity 
 in air, would be only a small fraction of that velocity. 
 Both density and elasticity, then, must be always borne in 
 mind ; the velocity of sound being determined by neither 
 taken separately, but by the relation of the one to the 
 other. The effect of small density and high elasticity is 
 exemplified in an astonishing manner by the luminiferous 
 ether, which transmits the vibrations of light not at the 
 rate of so many feet, but at the rate of nearly two hundred 
 thousand miles a second. 
 
 Those who are unacquainted with the details of scien- 
 tific investigation have no idea of the amount of labor 
 expended in the determination of those numbers on which 
 important calculations or inferences depend. They have 
 no idea of the patience shown by a Berzelius in deter- 
 mining atomic weights ; by a Regnault in determining 
 
DETERMINATION OF VELOCITY. 55 
 
 coefficients of expansion ; or by a Joule in determining 
 the mechanical equivalent of heat. There is a morality 
 brought to bear upon such matters which, in point of se- 
 verity, is probably without a parallel in any other domain 
 of intellectual action. Thus, as regards the determination 
 of the velocity of sound in air, hours might be filled with 
 a simple statement of the efforts made to establish it with 
 precision. The question has occupied the attention of 
 experimenters in England, France, Germany, Italy, and 
 Holland. But to the French and Dutch philosophers we 
 owe the application of the last refinements of experimental 
 skill to the solution of the problem. They neutralized 
 effectually the influence of the wind ; they took into 
 account barometric pressure, temperature, and hygrometric 
 condition. Sounds were started at the same moment from 
 two distant stations, and thus caused to travel from station 
 to station through the self-same air. The distance between 
 the stations was determined by exact trigonometrical ob- 
 servations, and means were devised for measuring with the 
 utmost accuracy the time required by the sound to pass 
 from the one station to the other. This time, expressed 
 in seconds, divided into the distance expressed in feet, gave 
 1,090 feet per second as the velocity of sound through air 
 at the temperature of centigrade. 
 
 The time required by light to travel over all terrestrial 
 distances is practically zero ; and in the experiments just 
 referred to the moment of explosion was marked by the 
 flash of a gun, the time occupied by the sound in passing 
 from station to station being the interval observed between 
 the appearance of the flash and the arrival of the sound. 
 The velocity of sound in air once established, it is plain 
 that we can apply it to the determination of distances. 
 By observing, for example, the interval between the ap- 
 pearance of a flash of lightning and the arrival of the ac- 
 companying thunder-peal, we at once determine the dis- 
 
56 SOUND. 
 
 tance of the place of discharge. It is only when the inter- 
 val between the flash and peal is short that danger from 
 lightning is to be apprehended. 
 
 9. Theoretic Velocity calculated by Newton. 
 Laplacds Correction. 
 
 We now come to one of the most delicate points in the 
 whole theory of sound. The velocity through air has been 
 determined by direct experiment ; but knowing the elas- 
 ticity and density of the air, it is possible, without any 
 experiment at all, to calculate the velocity with which a 
 sound-wave is transmitted through it. Sir Isaac Newton 
 made this calculation, and found the velocity at the freez- 
 ing temperature to be 916 feet a second. This is about 
 one-sixth less than actual observation had proved the 
 velocity to be, and the most curious suppositions were 
 FHJ. 12. made to account for the discrepancy. Newton 
 himself threw out the conjecture that it was only 
 in passing from .particle to particle of the air that 
 sound required time for its transmission ; that it 
 moved instantaneously through the particles them- 
 selves. He then supposed the line along which 
 sound passes to be occupied by air-particles for 
 one-sixth of its extent, and thus he sought to make 
 good the missing velocity. The very art and 
 ingenuity of this assumption were sufficient to 
 throw doubt on it ; other theories were therefore 
 advanced, but the great French mathematician 
 Laplace was the first to completely solve the 
 enigma. I shall now endeavor to make you 
 thoroughly acquainted with his solution. 
 
 Into this strong cylinder of glass, T u, Fig. 
 12, which is accurately bored, and quite smooth 
 within, fits an air-tight piston. By pushing the 
 piston down, I condense the air beneath it, heat being at 
 
NEWTON'S CALCULATIONS OF VELOCITY. 57 
 
 the same time developed. A scrap of amadou attached 
 to the bottom of the piston is ignited by the heat gener- 
 ated by compression. If a bit of cotton wool dipped 
 into bisulphide of carbon be attached to the piston, when 
 the latter is forced down, a flash of light, due to the igni- 
 tion of the bisulphide of carbon vapor, is observed within 
 the tube. It is thus proved that when air is compressed 
 heat is generated. By another experiment it may be shown 
 that when air is rarefied cold is developed. This brass 
 box contains a quantity of condensed air. I open the cock, 
 and permit the air to discharge itself against a suitable 
 thermometer ; the sinking of the instrument immediately 
 declares the chilling of the air. 
 
 All that you have heard regarding the transmission of 
 a sonorous pulse through air is, I trust, still fresh in your 
 minds. As the pulse advances it squeezes the particles of 
 air together, and two results follow from this compression. 
 Firstly, its elasticity is augmented through the mere aug- 
 mentation of its density. Secondly, its elasticity is aug- 
 mented by the heat of compression. It was the change of 
 elasticity which resulted from a change of density that 
 Newton took into account, and he entirely overlooked the 
 augmentation of elasticity due to the second cause just 
 mentioned. Over and above, then, the elasticity involved 
 in Newton's calculation, we have an additional elasticity 
 due to changes of temperature produced by the sound-wave 
 itself. When both are taken into account, the calculated 
 and the observed velocities agree perfectly. 
 
 But here, without due caution, we may fall into the 
 gravest error. In fact, in dealing with Nature, the mind 
 must be on the alert to seize all her conditions ; otherwise 
 we soon learn that our thoughts are not in accordance with 
 her facts. It is to be particularly noted that the augmen- 
 tation of velocity due to the changes of temperature pro- 
 duced by the sonorous wave itself is totally different from 
 
58 SOUND. 
 
 the augmentation arising from the heating of the general 
 mass of the air. The average temperature of the air is 
 unchanged by the waves of sound. We cannot have a con- 
 densed pulse without having a rarefied one associated with 
 it. But in the rarefaction, the temperature of the air is 
 as much lowered as it is raised in the condensation. Sup- 
 posing, then, the atmosphere parceled out into such con- 
 densations arid rarefactions, with their respective tempera- 
 tares, an extraneous sound passing through such an atmos- 
 phere would be as much retarded in the latter as accel- 
 erated in the former, and no variation of the average 
 velocity could result from such a distribution of temper- 
 ature. 
 
 Whence, then, does the augmentation pointed out by- 
 Laplace arise ? I would ask your best attention while I 
 endeavor to make this knotty point clear to you. If air 
 be compressed it becomes smaller in volume ; if the press- 
 ure be diminished, the volume expands. The force 
 which resists compression, and which produces expansion, 
 is the elastic force of the air. Thus an external pressure 
 squeezes the air-particles together ; their own elastic force 
 holds them asunder, and the particles are in equilibrium 
 when these two forces are in equilibrium. Hence it is 
 that the external pressure is a measure of the elastic force. 
 Let the middle row of dots, Fig. 13, represent a series of 
 air-particles in a state of quiescence between the points a 
 and x. Then, because of the elastic force exerted between 
 the particles, if any one of them be moved from its posi- 
 tion of rest, the motion will be transmitted through the 
 entire series. Supposing the particle a to be driven by the 
 prong of a tuning-fork, or some other vibrating body, tow- 
 ard x, so as to be caused finally to occupy the position a' 
 in the lowest row of particles : at the instant the excur- 
 sion of a commences, its motion begins to be transmitted 
 to b. In the next following moments ft transmits the 
 
LAPLACE'S CORRECTION OF NEWTON'S FORMULA. 59 
 
 motion to <?, c to <#, d to 0, and so on. So that by the 
 time a has reached the position a ', the motion will have 
 been propagated to some point o' of the line of particles 
 more or less distant from a'. The entire series of particles 
 between a 1 and o r is then in a state of condensation. The 
 distance a! o' ', over which the motion has traveled during 
 the excursion of a to #', will depend upon the elastic 
 force exerted between the particles. Fix your attention 
 on any two of the particles, say a and b. The elastic 
 force between them may be figured as a spiral spring, and 
 it is plain that the more flaccid this spring the more 
 sluggish would be the communication of the motion from 
 
 p. is. 
 
 a to b while the stiffer the spring the more prompt would 
 be the communication of the motion. What is true of a 
 and 5 is true for every other pair of particles between a 
 and o. Now the spring between every pair of these par- 
 ticles is suddenly stiffened by the heat developed along 
 the line of condensation, and hence the velocity of prop- 
 agation is augmented by this heat. Eeverting to our 
 old experiment with the row of boys, it is as if, by the 
 very act of pushing his neighbor, the muscular rigidity 
 of each boy's arm was increased, thus enabling him to 
 deliver his push more promptly than he would have done 
 without this increase of rigidity. The condensed portion 
 of a sonorous wave is propagated in the manner here 
 described, and it is plain that the velocity of propagatioD 
 is augmented by the heat developed in the condensation. 
 
60 SOUND. 
 
 Let us now turn our thoughts for a moment to the 
 propagation of the rarefaction. Supposing, as before, the 
 middle row a x to represent the particles of air in equilib- 
 rium under the pressure of the atmosphere, and suppose 
 the particle a to be suddenly drawn to the right, so as to 
 occupy the position a" in the highest line of dots : a" is 
 immediately followed by I", 1)" by c' 1 ', c" by d' 1 ', d" by e" ; 
 and thus the rarefaction is propagated backward toward 
 x'\ reaching a point o" in the line of particles by the time 
 a has completed its motion to the right. Now, why does 
 1)" follow a" when a" is drawn away from it ? Manifestly 
 because the elastic force exerted between V and a" is less 
 than that between W and c" . In fact, ~b" will be driven 
 after a" by a force equal to the difference of the two 
 elasticities between a" and 1}" and between W and c". The 
 same remark applies to the motion of o" after J", to that 
 of d" after c", in fact, to the motion of each succeeding 
 particle when it follows its predecessor. The greater the 
 difference of elasticity on the two sides of any particle the 
 more promptly will it follow its predecessor. And here 
 observe what the cold of rarefaction accomplishes. In ad- 
 dition to the diminution of the elastic force between a" 
 and V by the withdrawal of a!' to a greater distance, there 
 is a further diminution due to the lowering of the tem- 
 perature. The cold developed augments the difference of 
 elastic force on which the propagation of the rarefaction 
 depends. Thus we see that because the heat developed in 
 the condensation augments the rapidity of the condensa- 
 tion, and because the cold developed in the rarefaction 
 augments the rapidity of the rarefaction, the sonorous 
 wave, which consists of a condensation and a rarefaction, 
 must have its velocity augmented by the heat and the cold 
 which it develops during its own progress. 
 
 It is worth while fixing your attention here upon the 
 fact that the distance a' o' to which the motion has been 
 
RATIO OF SPECIFIC HEATS OF AIR. 61 
 
 propagated while a is moving to the position of may be 
 vastly greater than that passed over in the same time by 
 the particle itself. The excursion of a! may not be more 
 than a small fraction of an inch, while the distance to which 
 the motion is transferred during the time required by a' to 
 perform this small excursion may be many feet, or even 
 many yards. If this point should not appear altogether 
 plain to you now, it will appear so by-and-by. 
 
 10. Ratio of Specific Heats of Air deduced from 
 Velocity of Sound. 
 
 Having grasped this, even partially, I will ask you to 
 accompany me to a remote corner of the domain of physics, 
 with the view, however, of showing that remoteness does 
 not imply discontinuity. Let a certain quantity of air 
 at a temperature of 0, contained in a perfectly inexpan- 
 sible vessel, have its temperature raised 1. Let the same 
 quantity of air, placed in a vessel which permits the air 
 to expand when it is heated the pressure on the air be- 
 ing kept constant during its expansion also have its tem- 
 perature raised 1. The quantities of heat employed in 
 the two cases are different. The one quantity expresses 
 what is called the specific heat of air at constant volume ; 
 the other the specific heat of air at constant pressure. 1 
 It is an instance of the manner in which apparently un- 
 related natural phenomena are bound together, that from 
 the calculated and observed velocities of sound in air we 
 can deduce the ratio of these two specific heats. Squaring 
 ISTewton's theoretic velocity and the observed velocity, and 
 dividing the greater square by the less, we obtain the ratio 
 referred to. Calling the specific heat at constant volume 
 C v , and that at constant pressure C p ; calling, moreover, 
 
 1 See " Heat as a Mode of Motion," chap. iii. 
 
62 SOUND. 
 
 Newton's calculated velocity Y, and the observed velocity 
 V', Laplace proved that- 
 
 o Y /a 
 ^ z : Y a 
 
 Inserting the values of Y and Y 7 in this equation, and 
 making the calculation, we find 
 
 g , ,. 
 
 Thus, without knowing either the specific heat at con- 
 stant volume or at constant pressure, Laplace found the 
 ratio of the greater of them to the less to be 1'42. It is 
 evident from the foregoing formulae that the calculated 
 velocity of sound, multiplied by the square root of this 
 ratio, gives the observed velocity. 
 
 But there is one assumption connected with the deter- 
 mination of this ratio, which must be here brought clearly 
 forth. It is assumed that the heat developed by compres- 
 sion remains in the condensed portion of the wave, and 
 applies itself there to augment the elasticity ; that no por- 
 tion of it is lost by radiation. If air were a powerful 
 radiator, this assumption could not stand. The heat de- 
 veloped in the condensation could not then remain in the 
 condensation. It would radiate all round, lodging itself 
 for the most part in the chilled and rarefied portion of the 
 wave, which would be gifted with a proportionate power 
 of absorption. Hence the direct tendency of radiation 
 would be to equalize the temperatures of the different 
 parts of the wave, and thus to abolish the increase of ve- 
 locity which called forth Laplace's correction. 1 
 
 1 In fact, the prompt abstraction of the motion of heat from the condensa- 
 tion, and its prompt communication to the rarefaction by the contiguous 
 luminiferous ether, would prevent the former from ever rising so high, or the 
 latter from .ever falling so low, in temperature as it would do if the power of 
 radiation was absent. 
 
MECHANICAL EQUIVALENT OF HEAT. 63 
 
 11. Mechanical Equivalent of Heat deduced from 
 Velocity of Sound. 
 
 The question, then, of the correctness of this ratio in- 
 volves the other and apparently incongruous question, 
 whether atmospheric air possesses any sensible radiative 
 power. If the ratio be correct, the practical absence of 
 radiative power on the part of air is demonstrated. How 
 then are we to ascertain whether the ratio is correct or 
 not ? By a process of reasoning which illustrates still fur- 
 ther how natural agencies are intertwined. It was this 
 ratio, looked at by a man of genius, named Mayer, which 
 helped him to a clearer and a grander conception of the 
 relation and interaction of the forces of inorganic and or- 
 ganic nature than any philosopher up to his time had at- 
 tained. Mayer was the first to see that the excess 0*4-2 of 
 the specific heat at constant pressure over that at constant 
 volume was the quantity of heat consumed in the work per- 
 formed by the expanding gas. Assuming the air to be 
 confined laterally and to expand in a vertical direction, in 
 which direction it would simply have to lift the weight of 
 the atmosphere, he attempted to calculate the precise 
 amount of heat consumed in the raising of this or any other 
 weight. He thus sought to determine the " mechanical 
 equivalent " of heat. In the combination of his data his 
 mind was clear, but for the numerical correctness of these 
 data he was obliged to rely upon the experimenters of his 
 age. Their results, though approximately correct, were not 
 so correct as the transcendent experimental ability of Re- 
 gnault, aided by the last refinements of constructive skill, 
 afterward made them. Without changing in the slightest 
 degree the method of his thought or the structure of his 
 calculation, the simple introduction of the exact numerical 
 data into the formula of Mayer brings out the true me- 
 chanical equivalent of heat. 
 
64: SOUND. 
 
 But how are we able to speak thus confidently of the 
 accuracy of this equivalent ? We are enabled to do so by 
 the labors of an Englishman, who worked at this subject 
 contemporaneously with Mayer ; and who, while animated 
 by the creative genius of his celebrated German brother, 
 enjoyed also the opportunity of bringing the inspirations 
 of that genius to the test of experiment. By the immortal 
 experiments of Mr. Joule, the mutual convertibility of me- 
 chanical work and heat was first conclusively established. 
 And " Joule's equivalent," as it is rightly called, consider- 
 ing the amount of resolute labor and skill expended in its 
 determination, is almost identical with that derived from 
 the formula of Mayer. 
 
 12. Absence of Radiative Power of Air deduced from 
 Velocity of Sound. 
 
 Consider now the ground we have trodden, the curious 
 labyrinth of reasoning and experiment through which we 
 have passed. We started with the observed and calculated 
 velocities of sound in atmospheric air. We found Laplace, 
 by a special assumption, deducing from these velocities 
 the ratio of the specific heat of air at constant pressure to 
 its specific heat at constant volume. We found Mayer 
 calculating from this ratio the mechanical equivalent of 
 heat ; finally, we found Joule determining the same 
 equivalent by direct experiments on the friction of solids 
 and liquids. And what is the result ? Mr. Joule's experi- 
 ments prove the result of Mayer to be the true one ; they 
 therefore prove the ratio determined by Laplace to be 
 the true ratio ; and, because they do this, they prove at 
 the same time the practical absence of radiative power in 
 atmospheric air. It seems a long step from the stirring 
 of water, or the rubbing together of iron plates in Joule's 
 experiments, to the radiation of the atoms of our atmos- 
 
ABSENCE OP KADIATIVE POWER IN AIR. 65 
 
 phere ; both questions are, however, connected by the line 
 of reasoning here followed out. 
 
 But the true physical philosopher never rests content 
 with an inference when an experiment to verify or contra- 
 vene it is possible. The foregoing argument is clinched 
 by bringing the radiative power of atmospheric air to a 
 direct test. When this is done, experiment and reasoning 
 are found to agree ; air being proved to be a body sensibly 
 devoid of radiative and absorptive power. 1 
 
 But here the experimenter on the transmission of sound 
 through gases needs a word of warning. In Laplace's day, 
 and long subsequently, it was thought that gases of all 
 kinds possessed only an infinitesimal power of radiation ; 
 but that this is not the case, is now well established. It 
 would be rash to assume that, in the case of such bodies as 
 ammonia, aqueous vapor, sulphurous acid, and olefiant gas, 
 their enormous radiative powers do not interfere with the 
 application of the formula of Laplace. It behooves us to 
 inquire whether the ratio of the two specific heats deduced 
 from the velocity of sound in these bodies is the true ratio ; 
 and whether, if the true ratio could be found by other 
 methods, its square root, multiplied into the calculated 
 velocity, would give the observed velocity. From the 
 moment heat first appears in the condensation and cold in 
 the rarefaction of a sonorous wave in any of those gases, 
 the radiative power comes into play to abolish the differ- 
 ence of temperature. The condensed part of the wave is 
 on this account rendered more flaccid and the rarefied part 
 Less flaccid than it would otherwise be, and with a suffi- 
 ciently high radiative power the velocity of sound, instead 
 of coinciding with that derived from the formula* of La- 
 place, must approximate to that derived from the more 
 simple formula of Newton. 
 
 1 " Heat a Mode of Motion," chap, x 
 
06 SOUND. 
 
 13. Velocity of Sound through Gases, Liquids, 
 and Solids. 
 
 To complete our knowledge of the transmission of sound 
 through gases, a table is here added from the excellent re- 
 searches of Dulong, who employed in his experiments a 
 method which shall be subsequently explained : 
 
 VELOCITY OF SOUND IN GASES AT THE TEMPERATURE OF C. 
 
 Velocity. 
 
 Air 1,092 feet. 
 
 Oxygen 1,040 
 
 Hydrogen 4,164 
 
 Carbonic acid 858 
 
 Carbonic oxide 1,107 
 
 Protoxide of nitrogen 859 
 
 Olefiant gas 1,030 
 
 According to theory, the velocities of sound in oxygen 
 and hydrogen are inversely proportional to the square roots 
 of the densities of the two gases. We here find this theo- 
 retic deduction verified by experiment. Oxygen being six- 
 teen times heavier than hydrogen, the velocity of sound in 
 the latter gas ought, according to the above law, to be four 
 times its velocity in the former ; hence, the velocity in oxy- 
 gen being 1,040, in hydrogen calculation would make it 
 4,160. Experiment, we see, makes it 4,164. 
 
 The velocity of sound in liquids may be determined 
 theoretically, as Newton determined its velocity in air; 
 for the density of a liquid is easily determined, and its 
 elasticity can be measured by subjecting it to compression. 
 In the case of water, the calculated and the observed 
 velocities agree so closely as to prove that the changes of 
 temperature produced by a sound-wave in water have no 
 sensible influence upon the velocity. In a series of mem- 
 orable experiments in the lake of Geneva, MM. Colladon 
 and Sturm determined the velocity of sound through 
 water, and made it 4,708 feet a second. By a mode of 
 
VELOCITY IN GASES, LIQUIDS, AND SOLIDS. 
 
 67 
 
 experiment which you will subsequently be able to com- 
 prehend, the late M. Wertheim determined the velocity 
 through various liquids, and in the following table I have 
 collected his results : 
 
 TRANSMISSION OF SOUND THROUGH LIQUIDS. 
 
 Name of Liquid. 
 
 Temperature. 
 
 Velocity. 
 
 
 15 C. 
 
 Feet. 
 
 4,714 
 
 u 
 
 30 
 
 5,013 
 
 (( (( 
 
 60 
 
 6,657 
 
 Sea-water (artificial) . 
 
 20 
 
 4,768 
 
 
 18 
 
 5,132 
 
 Solution of sulphate of soda . . 
 
 20 
 
 5,194 
 
 
 22 
 
 5,230 
 
 Solution of nitrate of soda. . . 
 
 21 
 
 5,477 
 
 Solution of chloride of calcium . . 
 
 23 
 
 6,493 
 
 Common alcohol . . 
 
 20 
 
 4,218 
 
 Absolute alcohol . 
 
 23 
 
 3,804 
 
 Spirits of turpentine 
 
 24 
 
 3,976 
 
 
 
 
 3,801 
 
 
 
 
 We learn from this table that sound travels with dif- 
 ferent velocities through different liquids; that a salt 
 dissolved in water augments the velocity, and that the 
 salt which produces the greatest augmentation is chloride 
 of calcium. The experiments also teach us that in water, 
 as in air, the velocity augments with the temperature. At 
 a temperature of 15 C., for example, the velocity in Seine 
 water is 4,714 feet, at 30 it is 5,013 feet, and at 60 
 5,657 feet a second. 
 
 I have said that from the compressibility of a liquid, 
 determined by proper measurements, the velocity of sound 
 through the liquid may be deduced. Conversely, from the 
 velocity of sound in a liquid, the compressibility of the 
 liquid may be deduced. Wertheim compared a series of 
 compressibilities deduced from his experiments on sound 
 with a similar series obtained directly by M. Grassi. The 
 agreement of both, exhibited in the following table, is a 
 
SOUND. 
 
 strong confirmation of the accuracy of the method pursued 
 by Wertheim : 
 
 Cubic compressibility 
 
 Sea-water.. ... . 
 
 from "Wertheim's 
 velocity of sound. 
 
 0*0000467 
 
 from the direct 
 experiments of 
 M. Grassi. 
 
 0-0000436 
 
 Solution of common salt 
 
 0-0000349 
 
 0-0000321 
 
 " carbonate of soda. . 
 nitrate of soda. . . 
 
 . . 0-0000337 
 . . 0-0000301 
 
 0-0000297 
 0'0000295 
 
 Absolute alcohol 
 
 . . 0-0000947 
 
 0-0000991 
 
 Sulphuric ether.. . 
 
 0-0001002 
 
 0-0001110 
 
 The greater the resistance which a liquid offers to com- 
 pression, the more promptly and forcibly will it return 
 to its original volume after it has been compressed. The 
 less the compressibility, therefore, the greater is the elas- 
 ticity, and consequently, other things being equal, the 
 greater the velocity of sound through the liquid. 
 
 We have now to examine the transmission of sound 
 through solids. Here, as a general rule, the elasticity, as 
 compared with the density, is greater than in liquids, and 
 consequently the propagation of sound is more rapid. In 
 the following table the velocity of sound through various 
 metals, as determined by Wertheim, is recorded : 
 
 VELOCITY OF SOUND THROUGH METALS, 
 
 Name of Metal. 
 
 At 20" 0. 
 
 At 100 0. 
 
 At 200 C. 
 
 Lead 
 
 4,030 
 
 3 951 
 
 
 Gold 
 
 6 717 
 
 5 640 
 
 5 619 
 
 Silver 
 
 8,553 
 
 8,658 
 
 8 127 
 
 Copper. . 
 
 11 666 
 
 10802 
 
 9 690 
 
 Platinum 
 
 8,815 
 
 8,437 
 
 8 C79 
 
 Iron 
 
 16 822 
 
 17 386 
 
 16483 
 
 Iron wire (ordinary) 
 
 16 130 
 
 16 728 
 
 
 Cast steel 
 
 16 8^7 
 
 16,153 
 
 15 709 
 
 Steel wire (Englieli) 
 
 15 470 
 
 17 201 
 
 16 394 
 
 Steel wire 
 
 16023 
 
 16443 
 
 
 
 
 
 
 As a general rule, the velocity of sound through metals 
 is diminished by augmented temperature ; iron is, how- 
 ever, a striking exception to this rule, but it is only within 
 
INFLUENCE OF MOLECULAR STRUCTURE. 69 
 
 certain limits an exception. While, for example, a rise 
 of temperature from 20 to 100 0. in the case of copper 
 causes the velocity to fall from 11,666 to 10,802, the same 
 rise produces in the case of iron an increase of velocity 
 from 16,882 to 17,386. Between 100 and 200, however, 
 we see that iron falls from the last figure to 15,483. In 
 iron, therefore, up to a certain point, the elasticity is aug- 
 mented by heat ; beyond that point it is lowered. Silver 
 is also an example of the same kind. 
 
 The difference of velocity in iron and in air may be il- 
 lustrated by the following instructive experiment : Choose 
 one of the longest horizontal bars employed for fencing in 
 Hyde Park ; and let an assistant strike the bar at one end 
 while the ear of the observer is held close to the bar at a 
 considerable distance from the point struck. Two sounds 
 will reach the ear in succession ; the first being transmit- 
 ted through the iron and the second through the air. This 
 effect was obtained by M. Biot, in his experiments on the 
 iron water-pipes of Paris. 
 
 The transmission of sound through a solid depends 
 on the manner in which the molecules of the solid are 
 arranged. If the body be homogeneous and without 
 structure, sound is transmitted through it equally well in 
 all directions. But this is not the case when the body, 
 whether inorganic like a crystal or organic like a tree, 
 possesses a definite structure. This is also true of other 
 things than sound. Subjecting, for example, a sphere of 
 wood to the action of a magnet, it is not equally affected 
 in all directions. It is repelled by the pole of the magnet, 
 but it is most strongly repelled when the force acts along 
 the fibre. Heat also is conducted with different facilities 
 in different directions through wood. It is most freely 
 conducted along the fibre, and it passes more freely across 
 the ligneous layers than along them. Wood, therefore, 
 possesses three unequal axes of calorific conduction. 
 
70 
 
 SOUND. 
 
 These, established by myself, coincide with the axes of 
 elasticity discovered by Savart. MM. Wertheim and 
 Chevandier have determined the velocity of sound along 
 these three axes and obtained the following results : 
 
 VELOCITY OP SOUND IN WOOD, 
 
 Name of Wood. 
 
 Along Fibre. 
 
 Across Kings. 
 
 Along Kings. 
 
 Acacia . ... 
 
 15 467 
 
 4 840 
 
 4 436 
 
 Fir 
 
 15 218 
 
 4 382 
 
 2 572 
 
 Beech 
 
 10965 
 
 6028 
 
 4 643 
 
 Oak 
 
 12,622 
 
 5,036 
 
 4 229 
 
 Pine 
 
 10 900 
 
 4 611 
 
 2 605 
 
 Elm 
 
 13,516 
 
 4 665 
 
 3 324 
 
 Sycamore . . 
 
 14 639 
 
 4 916 
 
 3 728 
 
 Ash 
 
 15,314 
 
 4 567 
 
 4 142 
 
 Alder 
 
 15 306 
 
 4 491 
 
 3 423 
 
 Aspen . 
 
 16 677 
 
 5 297 
 
 2 987 
 
 Maple 
 
 13 472 
 
 5 047 
 
 3 401 
 
 Poplar ... 
 
 14050 
 
 4 600 
 
 3 444 
 
 
 
 
 
 FIG. 14. 
 
 Separating a cube from the bark-wood of a good-sized 
 tree, where the rings for a short distance may be regarded 
 
 as straight: then, if A R, Fig. 
 14, be the section of the tree, 
 the velocity of the sound in 
 the direction m n, through 
 such a cube, is greater than 
 in the direction a b. 
 
 The foregoing table strik- 
 ingly illustrates the influence 
 of molecular structure. The 
 great majority of crystals show 
 differences of the same kind. 
 Such bodies, for the most part, 
 
 have their molecules arranged in different degrees of 
 proximity in different directions, and where this occurs 
 there are sure to be differences in the transmission and 
 manifestation of heat, light, electricity, magnetism, and 
 sound. 
 
HOOKE'S ANTICIPATION OF THE STETHOSCOPE. 71 
 
 14. Hookas Anticipation of the Stethoscope. 
 
 I will conclude this lecture on the transmission of sound 
 through gases, liquids, and solids, by a quaint and beauti- 
 ful extract from the writings of that admirable thinker, 
 Dr. Robert Hooke. It will be noticed that the philosophy 
 of the stethoscope is enunciated in the following passage, 
 and another could hardly be found which illustrates so 
 well that action of the scientific imagination which, in all 
 great investigators, is the precursor and associate of ex- 
 periment : 
 
 " There may also be a possibility," writes Hooke, " of 
 discovering the internal motions and actions of bodies by 
 the sound they make. Who knows but that, as in a watch, 
 we may hear the beating of the balance, and the running 
 of the wheels, and the striking of the hammers, and the 
 grating of the teeth, and multitudes of other noises : 
 who knows, I say, but that it may be possible to discover 
 the motions of the internal parts of bodies, whether ani- 
 mal, vegetable, or mineral, by the sound they make ; that 
 one may discover the works performed in the several 
 offices and shops of a man's body, and thereby discover 
 what instrument or engine is out of order, what works are 
 going on at several times, and lie still at others, and the 
 like ; that in plants and vegetables one might discover by 
 the noise the pumps for raising the juice, the valves for 
 stopping it, and the rushing of it out of one passage into 
 another, and the like ? I could proceed further, but me- 
 thinks I can hardly forbear to blush when I consider how 
 the most part of men will look upon this : but, yet again, 
 I have this encouragement, not to think all these things 
 utterly impossible, though never so much derided by the 
 generality of men, and never so seemingly mad, foolish, 
 and phantastic, that as the thinking them impossible can- 
 not much improve rny knowledge, so the believing them 
 possible may, perhaps, be an occasion of taking notice of 
 
72 SOUND. 
 
 such things as another would pass by without regard as 
 useless. And somewhat more of encouragement I have 
 also from experience, that I have been able to hear very 
 plainly the beating of a man's heart, and it is common to 
 hear the motion of wind to and fro in the guts, and other 
 small vessels ; the stopping of the lungs is easily discov- 
 ered by the wheezing, the stopping of the head by the 
 humming and whistling noises, the slipping to and fro of 
 the joints, in many cases, by crackling, and the like, as to 
 the working or motion of the parts one among another ; 
 methinks I could receive encouragement from hearing the 
 hissing noise made by a corrosive menstruum in its opera- 
 tion, the noise of fire in dissolving, of water in boiling, of 
 the parts of a bell after that its motion is grown quite in- 
 visible as to the eye, for to me these motions and the other 
 seem only to differ secundum magis minus, and so to their 
 becoming sensible they require either that their motions 
 be increased, or that the organ be made more nice and 
 powerful to sensate and distinguish them." 
 
 NOTE ON THE DIFFRACTION OF SOUND. 
 
 The recent explosion of a powder-laden barge in the Regent's Park 
 produced effects similar to those mentioned in 7. The sound-wave bent 
 round houses and broke the windows at the back, the coalescence of dif- 
 ferent portions of the wave at special points being marked by intensified 
 local action. Close to the place where the explosion occurred the uncon- 
 gumed gunpowder was in the wave, and, as a consequence, the dismantled 
 gate-keeper's lodge was girdled all round by a black belt of carbon. 
 
SUMMARY. 73 
 
 SUMMARY OF CHAPTER I. 
 
 THE sound of an explosion is propagated as a wave or 
 pulse through the air. 
 
 This wave impinging upon the tympanic membrane 
 causes it to shiver, its tremors are transmitted to the au- 
 ditory nerve, and along the auditory nerve to the brain, 
 where it announces itself as sound. 
 
 A sonorous wave consists of two parts, in one of which 
 the air is condensed, and in the other rarefied. 
 
 The motion of the sonorous wave must not be con- 
 founded with the motion of the particles which at any 
 moment form the wave. During the passage of the wave 
 every particle concerned in its transmission makes only a 
 small excursion to and fro. 
 
 The length of this excursion is called the amplitude of 
 the vibration. 
 
 Sound cannot pass through a vacuum. 
 
 A certain sharpness of shock, or rapidity of vibration, 
 is needed for the production of sonorous waves in air. It 
 is still more necessary in hydrogen, because the greater 
 mobility of this light gas tends to prevent the formation 
 of condensations and rarefactions. 
 
 Sound is in all respects reflected like light ; it is also 
 refracted like light ; and it may, like light, be condensed 
 by suitable lenses. 
 
 Sound is also diffracted, the sonorous wave bending 
 round obstacles ; such obstacles, however, in part shade off 
 the sound. 
 
 Echoes are produced by the reflected waves of sound. 
 
74: SOUND. 
 
 In regard to sound and the medium through which 
 it passes, four distinct things are to be borne in mind 
 intensity, velocity, elasticity, and density. 
 
 The intensity is proportional to the square of the am- 
 plitude as above defined. 
 
 It is also proportional to the square of the maximum 
 velocity of the vibrating air-particles. 
 
 "When sound issues from a small body in free air, the 
 intensity diminishes as the square of the distance from 
 the body increases. 
 
 If the wave of sound be confined in a tube with a 
 smooth interior surface, it may be conveyed to great dis- 
 tances without sensible loss of intensity. 
 
 The velocity of sound in air depends on the elasticity 
 of the air in relation to its density. The greater the elas- 
 ticity the swifter is the propagation ; the greater the den- 
 sity the slower is the propagation. 
 
 The velocity is directly proportional to the square root 
 of the elasticity ; it is inversely proportional to the square 
 root of the density. 
 
 Hence, if elasticity and density vary in the same pro- 
 portion, the one will neutralize the other as regards the 
 velocity of sound. 
 
 That they do vary in the same proportion is proved 
 by the law of Boyle and Mariotte ; hence the velocity of 
 sound in air is independent of the density of the air. 
 
 But that this law shall held good, it is necessary that 
 the dense air and the rare air should have the same tem- 
 perature. 
 
 The intensity of a sound depends upon the density of 
 the air in which it is generated, but not on that of the air 
 in which it is heard. 
 
 The velocity of sound in air of the temperature C, is 
 1,090 feet a second ; it augments nearly 2 feet for every 
 degree centigrade added to its temperature. 
 
SUMMARY. 75 
 
 Hence, given the velocity of sound in air, the tempera- 
 ture of the air may be readily calculated. 
 
 The distance of a fired cannon or of a discharge of 
 lightning may be determined by observing the interval 
 which elapses between the flash and the sound. 
 
 From the foregoing, it is easy to see that if a row of 
 soldiers form a circle, and discharge their pieces all at the 
 same time, the sound will be heard as a single discharge 
 by a person occupying the centre of the circle. 
 
 But if the men form a straight row, and if the observer 
 stand at one end of the row, the simultaneous discharge 
 of the men's pieces will be prolonged to a kind of roar. 
 
 A discharge of lightning along a lengthy cloud may in 
 this way produce the prolonged roll of thunder. The roll 
 of thunder, however, must in part at least be due to echoes 
 from the clouds. 
 
 The pupil will find no difficulty in referring many 
 common occurrences to the fact that sound requires a sen- 
 sible time to pass through any considerable length of air. 
 For example, the fall of the axe of a distant woodcutter 
 is not simultaneous with the sound of the stroke. A com- 
 pany of soldiers marching to music along a road cannot 
 march in time, for the notes do not reach those in front 
 and those behind simultaneously. 
 
 In the condensed portion of a sonorous wave the air is 
 above, in the rarefied portion of the wave it is below, its 
 average temperature. 
 
 This change of temperature, produced by the passage 
 of the sound-wave itself, virtually augments the elasticity 
 of the air, and makes the velocity of sound about -J-th 
 greater than it would be if there were no change of tem- 
 perature. 
 
 The velocity found by Newton, who did not take thia 
 change of temperature into account, was 916 feet a second. 
 
 Laplace proved that by multiplying Newton's velocity 
 
76 SOUND. 
 
 by the square root of the ratio of the specific heat of air at 
 constant pressure to its specific heat at constant volume, 
 the actual or observed velocity is obtained. 
 
 Conversely, from a comparison of the calculated and 
 observed velocities, the ratio of the two specific heats may 
 be inferred. 
 
 The mechanical equivalent of heat may be deduced 
 from this ratio ; it is found to be the same as that estab- 
 lished by direct experiment. 
 
 This coincidence leads to the conclusion that atmos- 
 pheric air is devoid of any sensible power to radiate heat. 
 Direct experiments on the radiative power of air establish 
 the same result. 
 
 The velocity of sound in water is more than four times 
 its velocity in air. 
 
 The velocity of sound in iron is seventeen times its 
 velocity in air. 
 
 The velocity of sound along the fibre of pine-wood is 
 ten times its velocity in air. 
 
 The cause of this great superiority is that the elastici- 
 ties of the liquid, the metal, and the wood, as compared 
 with their respective densities, are vastly greater than the 
 elasticity of air in relation to its density. 
 
 The velocity of sound is dependent to some extent 
 upon molecular structure. In wood, for example, it is 
 conveyed with different degrees of rapidity in different 
 directions. 
 
CHAPTEE II. 
 
 Physical Distinction between Noise and Music. A Musical Tone produced by 
 Periodic, Noise produced by Unperiodic, Impulses. Production of Musi- 
 cal Sounds by Taps. Production of Musical Sounds by Puffs. Definition 
 of Pitch in Music. Vibrations of a Tuning-Fork ; their Graphic Repre- 
 sentation on Smoked Glass. Optical Expression of the Vibrations of a 
 Tuning-Fork. Description of the Siren. Limits of the Ear ; Highest and 
 Deepest Tones. Rapidity of Vibration determined by the Siren. Deter- 
 mination of the Lengths of Sonorous Waves. Wave-Lengths of the Voice 
 in Man and Woman. Transmission of Musical Sounds through Liquids 
 and Solids 
 
 1. Musical Sounds. 
 
 IN our last chapter we considered the propagation 
 through air of a sound of momentary duration. "We have 
 to-day to consider continuous sounds, and to make our- 
 selves in the first place acquainted with the physical dis- 
 tinction between noise and music. As far as sensation 
 goes, everybody knows the difference between these two 
 things. But we have now to inquire into the causes of 
 sensation, and to make ourselves acquainted with the con- 
 dition of the external air which in one case resolves itself 
 into music and in another into noise. 
 
 We have already learned that what is loudness in our 
 sensations is outside of us nothing more than width of 
 swing, or amplitude, of the vibrating air-particles. Every 
 other real sonorous impression of which we are conscious 
 has its correlative without, as a mere form or state of the 
 atmosphere. Were our organs sharp enough to see the 
 motions of the air through which an agreeable voice is 
 passing, we might see stamped upon that air the conditions 
 
78 SOUND. 
 
 of motion on which the sweetness of the voice depends. 
 In ordinary conversation, also, the physical precedes and 
 arouses the psychical ; the spoken language, which is to 
 give us pleasure or pain, which is to rouse us to anger or 
 soothe us to peace, existing for a time, between us and 
 the speaker, as a purely mechanical condition of the inter- 
 vening air. 
 
 Noise affects us as an irregular succession of shocks. 
 We are conscious while listening to it of a jolting and 
 jarring of the auditoiy nerve, while a musical sound 
 flows smoothly and without asperity or irregularity. How 
 is this smoothness secured ? By rendering the impulses 
 received l}y the tympanic membrane perfectly periodic. 
 A periodic motion is one that repeats itself. The mo- 
 tion of a common pendulum, for example, is periodic, 
 but its vibrations are far too sluggish to excite sonorous 
 waves. To produce a musical- tone we must have a body 
 which vibrates with the unerring regularity of the pendu- 
 lum, but which can impart much sharper and quicker 
 shocks to the air. 
 
 Imagine the first of a series of pulses following each 
 other at regular intervals, impinging upon the tympanic 
 membrane. It is shaken by the shock ; and a body once 
 shaken cannot come instantaneously to rest. The human 
 ear, indeed, is so constructed that the soiiorous motion 
 vanishes with extreme rapidity, but its disappearance is 
 not instantaneous; and if the motion imparted to the 
 auditory nerve by each individual pulse of our series con- 
 tinue until the arrival of its successor, the sound will not 
 cease at all. The effect of every shock will be renewed 
 before it vanishes, and the recurrent impulses will link 
 themselves together to a continuous musical sound. The 
 pulses, on the contrary, which produce noise, are of irreg- 
 ular strength and recurrence. The action of noise upon 
 the ear has been well compared to that of a flickering light 
 
NOISE AND MUSIC. 79 
 
 upon the eye, both being painful through the sudden and 
 abrupt changes which they impose upon their respective 
 nerves. 
 
 The only condition necessary to the production of a 
 musical sound is that the pulses should succeed each other 
 in the same interval of time. JSTo matter what its origin 
 may be, if this condition be fulfilled the sound becomes mu- 
 sical. If a watch, for example, could be caused to tick with 
 sufficient rapidity say one hundred times a second the 
 ticks would lose their individuality and blend to a musical 
 tone. And if the strokes of a pigeon's wings could be 
 accomplished at the same rate, the progress of the bird 
 through the air would be accompanied by music. In the 
 humming-bird the necessary rapidity is attained ; and when 
 we pass on from birds to insects, where the vibrations are 
 more rapid, we have a musical note as the ordinary accom- 
 paniment of the insects' flight. 1 The puffs of a locomotive 
 at starting follow each other slowly at first, but they soon 
 increase so rapidly as to be almost incapable of being 
 counted. If this increase could continue up to fifty or 
 sixty puffs a second, the approach of the engine would be 
 heralded by an organ-peal of tremendous power. 
 
 2. Musical Sounds produced by Taps. 
 
 Galileo produced a musical sound by passing a knife 
 over the edge of a piastre. The minute serration of the 
 coin indicated the periodic character of the motion, which 
 consisted of a succession of taps quick enough to produce 
 sonorous continuity. Every schoolboy knows how to pro- 
 duce a note with his slate-pencil. I will not call it musical, 
 because this term is usually associated with pleasure, and 
 the sound of the pencil is not pleasant. 
 
 The production of a musical sound by taps is usually 
 
 1 According to Burmeister, through the injection and ejection of air into 
 and from the cavity of the chest 
 
80 
 
 SOUND. 
 
 effected by causing the teeth of a rotating wheel to strike 
 in quick succession against a card. This was first illus- 
 trated by the celebrated Robert Hooke, 1 and nearer our 
 own day by the eminent French experimenter Savart. 
 
 FI&. 15. vve will confine ourselves to 
 
 homelier modes of illustration. 
 This gyroscope is an instru- 
 ment consisting mainly of a 
 heavy brass ring, d, Fig. 15, 
 loading the circumference of 
 a disk, through which, and at 
 right angles to its surface, 
 passes a steel axis, delicately 
 supported at its two ends. By 
 coiling a string round the axis, 
 and drawing it vigorously out, 
 the ring is caused to spin 
 rapidly ; and along with it ro- 
 tates a small-toothed wheel, w. 
 On touching this wheel with 
 the edge of a card c, a musical 
 sound of exceeding shrillness 
 is produced. I place my thumb 
 for a moment against the ring ; the rapidity of its rotation 
 is thereby diminished, and this is instantly announced by 
 
 1 On July 27, 1681, " Mr. Hooke showed an experiment of making musi- 
 cal and other sounds by the help of teeth of brass wheels ; which teeth were 
 made of equal bigness for musical sounds, but of unequal for vocal sounds." 
 (Birch's " History of the Royal Society," p. 96, published in 1757.) 
 
 The following extract is taken from the " Life of Hooke," which precedes 
 his "Posthumous Works," published in 1705, by Richard Waller, Secretary 
 of the Royal Society : " In July the same year he (Dr. Hooke) showed a way 
 of making musical and other sounds by the striking of the teeth of several 
 brass wheels, proportionally cut as to their numbers, and turned very fast 
 round, in which it was observable that the equal or proportional stroaks of 
 the teeth, that is, 2 to 1, 4 to 3, etc., made the musical notes, but the unequal 
 stroaks of the teeth more answered the sound of the voice in speaking.'' 
 
MUSICAL SOUNDS PRODUCED BY TAPS. 81 
 
 a lowering of the pitch of the note. By checking the mo- 
 tion still more, the pitch is lowered still further. We are 
 here made acquainted with the important fact that the 
 pitch of a note depends upon the rapidity of its pulses. 1 
 At the end of the experiment you hear the separate taps 
 of the teeth against the card, their succession not being 
 quick enough to produce that continuous flow of sound 
 which is the essence of music. A screw with a milled 
 head attached to a whirling table, and caused to rotate, 
 produces by its taps against a card a note almost as clear 
 and pure as that obtained from the toothed wheel of the 
 gyroscope. 
 
 The production of a musical sound by taps may also be 
 pleasantly illustrated in the following way : In this vice 
 are fixed vertically two pieces of sheet-lead, with their 
 horizontal edges a quarter of an inch apart. I lay a bar 
 of brass across them, permitting it to rest upon the edges, 
 and, tilting the bar a little, set it in oscillation like a see- 
 saw. After a time, if left to itself, it comes to rest. But 
 suppose the bar on touching the lead to be always tilted 
 upward by a force issuing from the lead itself, it is plain 
 that the vibrations would then be rendered permanent. 
 Now such a force is brought into play when the bar is 
 heated. On its then touching the lead the heat is commu- 
 nicated, a sudden jutting upward of the lead at the point 
 of contact being the result. Hence an incessant tilting of 
 the bar from side to side, so long as it continues sufficiently 
 hot. Substituting for the brass bar the heated fire-shovel 
 shown in Fig. 16, the same effect is produced. 
 
 In its descent upon the lead the bar taps it gently, the 
 taps being so slow that you may readily count them. But 
 a mass of metal differently shaped may be caused to 
 
 1 Galileo, finding the number of notches on his metal to be great when 
 the pitch of the note was high, inferred that the pitch depended on the rapidi- 
 ty of the impulses. 
 
82 
 
 SOUND. 
 
 vibrate more briskly, and the taps to succeed each other 
 more rapidly. When such a heated rocker. Fig. 17, is 
 placed upon a block of lead, the taps hasten to a loud rattle. 
 When, with the point of a file, the rocker is pressed against 
 
 FIG. 16. 
 
 the lead, the vibrations are rendered more rapid, and the 
 taps link themselves together to a deep musical tone. 
 A second rocker, which oscillates more quickly than the 
 last, produces music without any other pressure than that 
 
 FIG. IT. 
 
 due to its own weight. Pressing it, however, with the 
 file, the pitch rises, until a note of singular force and 
 purity fills the room. Relaxing the pressure, the pitch 
 
MUSICAL SOUNDS PRODUCED BY PUFFS. 83 
 
 instantly falls ; resuming the pressure, it again rises ; and 
 thus by the alternation of the pressure we obtain great 
 variations of tone. Nor are such rockers essential. Al- 
 lowing one face of the clean, square end of a heated poker 
 to rest upon the block of lead, a rattle is heard ; causing 
 another face to rest upon the block, a clear musical note 
 is obtained. The two faces have been beveled differ- 
 ently by a file, so as to secure different rates of vibration. 1 
 This curious effect was discovered by Schwartz and Tre- 
 velyan. 
 
 3. Musical Sounds produced ~by Puffs. 
 
 Prof. Eobison was the first to produce a musical sound 
 by a quick succession of puffs of air. His device was 
 the first form of an instrument which will soon be intro- 
 duced to you under the name of the siren. Hobison de 
 scribes his experiment in the following words : " A stop- 
 cock was so constructed that it opened and shut the passage 
 of a pipe 720 times in a second. The apparatus was fitted 
 to the pipe of a conduit leading from the bellows to the 
 wind-chest of an organ. The air was simply allowed to 
 pass gently along this pipe by the opening of the cock. 
 When this was repeated 720 times in a second, the sound 
 g in alt was most smoothly uttered, equal in sweetness to 
 
 1 When a rough tide rolls in upon a pebble beach, as at Blackgang Chine 
 or Freshwater Gate, in the Isle of Wight, the rounded stones are carried up 
 the slope by the impetus of the water, and when the wave retreats the peb- 
 bles are dragged down. Innumerable collisions thus ensue of irregular in- 
 tensity and recurrence. The union of these shocks impresses us as a kind 
 of scream. Hence the line in Tennyson's " Maud ; " 
 
 " Now to the scream of a maddened beach dragged down by the wave." 
 The height of the note depends in some measure upon the size of the peb- 
 ble, varying from a kind of roar heard when the stones are large to a 
 scream ; from a scream to a noise resembling that of frying bacon ; and 
 from this, when the pebbles are so small as to approach the state of gravel, 
 to a mere hiss. The roar of the breaking wave itself is mainly due to the 
 explosion of bladders of air. 
 
84 SOUND. 
 
 a clear female voice. "When the frequency was reduced 
 to 360, the sound was that of a clear but rather a harsh 
 man's voice. The cock was now altered in such a manner 
 that it never shut the hole entirely, but left about one- 
 third of it open. "When this was repeated 720 times in a 
 second, the sound was uncommonly smooth and sweet. 
 When reduced to 360, the sound was more mellow than 
 any man's voice of the same pitch." 
 
 But the difficulty of obtaining the necessary speed 
 renders another form of the experiment preferable, A 
 disk of Bristol board, B, Fig. 18, twelve inches in diam- 
 eter, is perforated at equal intervals along a circle near 
 its circumference. The disk, being strengthened by a 
 
 FIQ. 18. 
 
 backing of tin, can be attached to a whirling table, and 
 caused to rotate rapidly. The individual holes then dis- 
 appear, blending themselves into a continuous shaded 
 circle. Immediately over this circle is placed a bent tube, 
 77&, connected with a pair of acoustic bellows. The disk 
 is now motionless, the lower end of the tube being im- 
 mediately over one of the perforations of the disk. If, 
 therefore, the bellows be worked, the wind will pass from 
 m through the hole underneath. But if the disk be turned 
 a little, an unperforated portion of the disk comes under 
 the tube, the current of air being then intercepted. As 
 the disk is slowly turned, successive perforations are 
 brought under the tube, and whenever this occurs a puff 
 of air gets through. On rendering the rotation rapid, 
 
MUSICAL SOUNDS PRODUCED BY PUFFS. 85 
 
 the puffs succeed each other in very quick succession, pro- 
 ducing pulses in the air which blend to a continuous 
 musical note, audible to you all. Mark how the note 
 varies. When the whirling table is turned rapidly the 
 sound is shrill ; when its motion is slackened the pitch 
 immediately falls. If instead of a single glass tube there 
 were two of them, as far apart as two of our orifices, so that 
 whenever the one tube stood over an orifice, the other 
 should stand over another, it is plain that if both tubes 
 were blown through, we should, on turning the disk, get a 
 puff through two holes at the same time. The intensity of 
 the sound would be thereby augmented, but the pitch 
 would remain unchanged. The two puffs issuing at the 
 same instant would act in concert, and produce a greater 
 effect than one upon the ear. And if instead of two tubes 
 we had ten of them, or better still, if we had a tube for 
 every orifice in the disk the puffs from the entire series 
 would all issue, and would be all cut off at the same time. 
 These puffs would produce a note of far greater intensity 
 than that obtained by the alternate escape and interruption 
 of the air from a single tube. In the arrangement now be- 
 fore you, Fig. 19, there are nine tubes through which the air 
 
 FIG. 19. 
 
 is urged through nine apertures, therefore, puffs escape at 
 once. On turning the whirling table, and alternately in- 
 creasing and relaxing its speed, the sound rises and falls 
 like the loud wail of a changing wind. 
 
86 SOUND 
 
 4. Musical Sounds produced ~by a Tuning-fork. 
 
 Various other means may be employed to throw the 
 air into a state of periodic motion. A stretched string 
 pulled aside and suddenly liberated imparts vibrations 
 to the air which succeed each other in perfectly regular 
 intervals. A tuning-fork does the same. When a bow is 
 drawn across the prongs of this tuning-fork, Fig. 20, the 
 resin of the bow enables the hairs to grip the prong, 
 which is thus pulled aside. But the resistance of the prong 
 soon becomes too strong, and it starts suddenly back ; 
 it is, however, immediately laid hold of again by the bow, 
 
 FIG. 20. 
 
 to start back once more as soon as its resistance becomes 
 great enough. This rhythmic process, continually re- 
 peated during the passage of the bow, finally throws the 
 fork into a state of intense vibration, and the result is 
 a musical note. A person close at hand could see the 
 fork vibrating ; a deaf person bringing his hand suffi- 
 ciently near would feel the shivering of the air. Or caus- 
 ing its vibrating prong to touch a card, the taps against 
 the card link themselves, as in the case of the gyroscope, 
 to a musical sound, the fork coming rapidly to rest. What 
 we call silence expresses this absence of motion. 
 
THE TUNING-FORK. 87 
 
 When the tuning-fork is first excited the sound issues 
 from it with maximum loudness, becoming gradually fee- 
 bler as the fork continues to vibrate. A person close to 
 the fork can notice at the same time that the amplitude, 
 or space through which the prongs oscillate, becomes grad- 
 ually less and less. But the most expert ear in this assem- 
 bly can detect no change in the pitch of the note. The 
 lowering of the intensity of a note does not therefore 
 imply the lowering of its pitch. In fact, though the 
 amplitude changes, the rate of vibration remains the same. 
 Pitch and intensity must therefore be held distinctly 
 apart ; the latter depends solely upon the amplitude, the 
 former solely upon the rapidity of vibration. 
 
 This tuning-fork may be caused to write the story of 
 its own motion. Attached to the side of one of its prongs, 
 F, Fig. 21, is a thin strip of sheet-copper which tapers to 
 
 FIG. 21. 
 
 a point. When the tuning-fork is excited it vibrates, 
 and the strip of metal accompanies it in its vibration. 
 The point of the strip being brought gently down upon a 
 piece of smoked glass, it moves to and fro over the smoked 
 surface, leaving a clear line behind. As long as the hand 
 is kept motionless, the point merely passes to and fro 
 over the same line ; but it is plain that we have only to 
 draw the fork along the glass to produce a sinuous line, 
 Fig. 21. 
 
 When this process is repeated without exciting the fork 
 afresh, the depth of the indentations diminishes. The 
 sinuous line approximates more and more to a straight one. 
 
88 
 
 SOUND. 
 
 This is the visual expression of decreasing amplitude. 
 When the sinuosities entirely disappear, the amplitude has 
 become zero, and the sound, which depends upon the am- 
 plitude, ceases altogether. 
 
 To M. Lissajous we are indebted for a very beautiful 
 method of giving optical expression to the vibrations of a 
 tuning-fork. Attached to one of the prongs of a very large 
 fork is a small metallic mirror, F, Fig. 22, the other prong 
 being loaded with a piece of metal to establish equi- 
 librium. Permitting a slender beam of intense light to 
 fall upon the mirror, the beam is thrown back by reflec- 
 
 FIG. 22. 
 
 tion. In my hands is held a small looking-glass, which 
 receives the reflected beam, and from which it is again 
 reflected to the screen, forming a small luminous disk 
 upon the white surface. The disk is perfectly motionless ; 
 but the moment the fork is set in vibration the reflected 
 beam is tilted rapidly up and down, the disk describing a 
 band of light three feet long. The length of the band 
 depends on the amplitude of the vibration, and you see 
 it gradually shorten as the motion of the fork is expended. 
 It remains, however, a straight line as long as the glass 
 is held in a fixed position. But on suddenly turning the 
 
OPTICAL ILLUSTRATIONS. 
 
 89 
 
 glass so as to make the beam travel from left to right over 
 the screen, you observe the straight line instantly resolved 
 into a beautiful luminous ripple m n. A luminous im- 
 pression once made upon the retina lingers there for the 
 tenth of a second ; if then the time required to transfer 
 the elongated image from side to side of the screen be 
 less than the tenth of a second, the wavy line of light 
 will occupy for a moment the whole width of the screen. 
 Instead of permitting the beam from the lamp to issue 
 through a single aperture, it may be caused to issue through 
 two apertures, about half an inch asunder, thus project- 
 ing two disks of light, one above the other, upon the 
 screen. When the fork is excited and the mirror turned, 
 we have a brilliant double sinuous line running over the 
 dark surface, Fig. 23. Turning the diaphragm so as to 
 
 FIG. 23. 
 
 place the two disks beside each other, on exciting the fork 
 and moving the mirror, we obtain a beautiful interlacing 
 of the two sinuous lines, Fig. 24. 
 
 Fio. 24. 
 
 5. The Waves of Sound. 
 
 How are we to picture to ourselves the condition of the 
 air through which this musical sound is passing ? Imagine 
 one of the prongs of the vibrating fork swiftly advancing; 
 it compresses the air immediately in front of it, and when 
 
90 SOUND. 
 
 it retreats it leaves a partial vacuum behind, the process 
 being repeated by every subsequent advance and retreat. 
 The whole function of the tuning-fork is to carve the air 
 into these condensations and rarefactions, and they, as they 
 are formed, propagate themselves in succession through 
 the air. A condensation with its associated rarefaction 
 constitutes, as already stated, a sonorous wave. In water 
 the length of a wave is measured from crest to crest; 
 while, in the case of sound, the wave-length is the distance 
 between two successive condensations. The condensation 
 of the sound-wave corresponds to the crest, while the rare- 
 faction of the sound-wave corresponds to the sinus, or de- 
 pression, of the water-wave. Let the dark spaces, a, 5, <?, 
 d, Fig. 25, represent the condensations, and the light ones, 
 
 a', & ', d ', <#', the rarefactions of the waves issuing from the 
 fork A B : the wave-lenth would then be measured from 
 
 a to 5, from 5 to c, or from c to d. 
 
 6. Definition of Pitch : Determination of Rates of 
 Vibration. 
 
 When two notes from two distinct sources are of the 
 same pitch, their rates of vibration are the same. If, for 
 example, a string yield the same note as a tuning-fork, it 
 is because they vibrate with the same rapidity ; and if a 
 fork yield the same note as the pipe of an organ or the 
 
THE SIREN. 91 
 
 tongue of a concertina, it is because the vibrations of the 
 fork in the one case are executed in precisely the same 
 time as the vibrations of the column of. air, or of the 
 tongue, in the other. The same holds good for the human 
 voice. If a string and a voice yield the same note, it is 
 because the vocal chords of the singer vibrate in the same 
 time as the string vibrates. Is there any way of deter- 
 mining the actual number of vibrations corresponding to 
 a musical note ? Can we infer from the pitch of a string, 
 of an organ-pipe, of a tuning-fork, or of the human voice, 
 the number of waves which it sends forth in a second ? 
 This very beautiful problem is capable of the most com- 
 plete solution. 
 
 7. The Siren : Analysis of the Instrument. 
 
 By the rotation of a perforated pasteboard disk, it has 
 been proved to you that a musical sound is produced by a 
 quick succession of puffs. Had we any means of register- 
 ing the number of revolutions accomplished by that disk 
 in a minute, we should have in it a means of determining 
 the number of puffs per minute due to a note of any deter- 
 minate pitch. The disk, however, is but a cheap substi- 
 tute for a far more perfect apparatus, which requires no 
 whirling table, and which registers its own rotations with 
 the most perfect accuracy. 
 
 I will take the instrument asunder, so that you may 
 see its various parts. A brass tube, , Fig. 26, leads into 
 a round box, c, closed at the top by a brass plate a b. 
 This plate is perforated with four series of holes, placed 
 along four concentric circles. The innermost series con- 
 tains 8, the next 10, the next 12, and the outermost 16 
 orifices. When we blow into the tube t, the air escapes 
 through the orifices, and the problem now before us is to 
 convert these continuous currents into discontinuous puffs. 
 This is accomplished by means of a brass disk d e, also 
 
SOOND. 
 
 P 
 
 FIG. 26. 
 
 perforated with 8, 10, 12, and 16 holes, at the same dis- 
 tances from the centre and with the same intervals be- 
 tween them as those in the top of the box c. Through 
 the centre of the disk passes a steel axis, the two ends of 
 
 which are smoothly beveled 
 off to points at p and p' . 
 My object now is to cause 
 this perforated disk to rotate 
 over the perforated top a b 
 of the box c. You will un- 
 derstand how this is done by 
 observing how the instru- 
 ment is put together. 
 
 In the centre of a b, Fig. 
 26, is a depression x sunk in 
 steel, smoothly polished and 
 intended to receive the end 
 p' of the axis. I place the 
 end p' in this depression, 
 and, holding the axis up- 
 right, bring down upon its 
 upper end p a steel cap, 
 finely polished within, which 
 holds the axis at the top, 
 the pressure both at top and 
 bottom being so gentle, and 
 the polish of the touching 
 surfaces so perfect, that the 
 disk can rotate with an ex- 
 ceedingly small amount of 
 friction. At c, Fig. 27, is 
 the cap which fits on to the upper end of the axisjpj/. 
 In this figure the disk d e is shown covering the top of the 
 cylinder c. You may neglect for the present the wheel- 
 work of the figure. Turning the disk d e slowly round, its 
 
ANALYSIS OF THE SIREN. 
 
 93 
 
 FIG. 27. 
 
 perforations may be caused to coincide or not coincide 
 with those of the cylinder underneath. As the disk turns 
 its orifices come alternately over the perforations of the 
 cylinder, and over the spaces between the perforations. 
 Hence it is plain that if 
 air were urged into c, 
 and if the disk could be 
 caused to rotate at the 
 same time, we should 
 accomplish our object, 
 and carve into puffs the 
 streams of air. In this 
 beautiful instrument 
 the disk is caused to ro- 
 tate by the very air cur- 
 rents which it renders 
 intermittent. This is 
 done by ifhe simple de- 
 vice of causing the per- 
 forations to pass oblique- 
 ly through the top of 
 the cylinder c, and also 
 obliquely, but opposite- 
 ly inclined, through the 
 rotating disk d e. The 
 air is thus caused to is- 
 sue from c, not verti- 
 cally, but in side cur^ 
 rents, which impinge 
 against the disk and 
 drive it round. In this way, by its passage through the 
 siren, the air is moulded into sonorous waves. 
 
 Another moment will make you acquainted with the 
 recording portion of the instrument. At the upper part 
 of the steel axis p p f , Fig. 27, is a screw s, working into a 
 
94 
 
 SOUND. 
 
 pair of toothed wheels (seen when the back of the instru- 
 ment is turned toward you). As the disk and its axis 
 turn, these wheels rotate. In front you simply see two 
 graduated dials, Fig. 28, each furnished with an index like 
 the hand of a clock. These indexes record the number of 
 revolutions executed by the disk in any given time. By 
 pushing the button a or 5 the wheel-work is thrown into 
 or out of action, thus starting or suspending, in a moment, 
 the process of recording. Finally, by the pins m, n, o, p, 
 Fig. 27, any series of orifices in the top of the cylinder c 
 can be opened or closed at pleasure. By pressing m, one 
 series is opened ; by pressing n, another. By pressing two 
 keys, two series of orifices are opened ; by pressing three 
 keys, three series ; and by pressing all the keys, puffs are 
 caused to issue from the four series simultaneously. The 
 perfect instrument is now before you, and your knowledge 
 of it is complete. 
 
 This instrument received the name of siren from its 
 inventor, Cagniard de la Tour. The one now before you 
 
 is the siren as greatly 
 improved by Dove. The 
 pasteboard siren, whose 
 performance you have al- 
 ready heard, was devised 
 by Seebeck, who gave 
 the instrument various 
 interesting forms, and 
 executed with it many 
 important experiments. 
 Let us now make the 
 siren sing. By pressing 
 the key m, the outer series of apertures in the cylinder c 
 is opened, and by working the bellows, the air is caused to 
 impinge against the disk. It begins to rotate, and you 
 hear a succession of puffs which follow each other so 
 
 FIG. 28. 
 
EXPERIMENTS ON PITCH. 95 
 
 slowly that they may be counted. But as the motion aug- 
 ments, the puffs succeed each other with increasing rapid- 
 ity, and at length you hear a deep musical note. As thr 
 velocity of rotation increases the note rises in pitch ; it is 
 now very clear and full, and as the air is urged more vig- 
 orously, it becomes so shrill as to be painful. Here we 
 have a further illustration of the dependence of pitch on 
 rapidity of vibration. I touch the side of the disk and 
 lower its speed ; the pitch falls instantly. Continuing the 
 pressure the tone continues to sink, ending in the discon- 
 tinuous puffs with which it began. 
 
 Were the blast sufficiently powerful and the siren 
 sufficiently free from friction, it might be urged to higher 
 and higher notes, until finally its sound would become 
 inaudible to human ears. This, however, would not prove 
 the absence of vibratory motion in the air ; but would 
 rather show that our auditory apparatus is incompetent to 
 take up and translate into sound vibrations whose rapidity 
 exceeds a certain limit. The ear, as we shall immediately 
 learn, is in this respect similar to the eye. 
 
 By means of this siren we can determine with extreme 
 accuracy the rapidity of vibration of any sonorous body. 
 It may be a vibrating string, an organ-pipe, a reed, or the 
 human voice. Operating delicately, we might even deter- 
 mine from the hum of an insect the number of times it 
 flaps its wings in a second. I will illustrate the subject 
 by determining in your presence a tuning-fork's rapidity 
 of vibration. From the acoustic bellows I urge the air 
 through the siren, and, at the same time, draw my bow 
 across the fork. Both now sound together, the tuning- 
 fork yielding at present the highest note. But the pitch 
 of the siren gradually rises, and at length you hear 
 the " beats " so well known to musicians, which indicate 
 that the two notes are not wide apart in pitch. These 
 beats become slower and slower ; now they entirely 
 5 
 
96 SOUND. 
 
 ranish, both notes blending as it were to a single stream 
 of sound. 
 
 All this time the clock-work of the siren has remained 
 out of action. As the second hand of a watch crosses 
 the number 60, the clock-work is set going by pushing the 
 button a. We will allow the disk to continue its rota- 
 tion for a minute, the tuning-fork being excited from 
 time to time to assure you that the unison is preserved. 
 The second hand again approaches 60 ; as it passes that 
 number the clock-work is stopped by pushing the button "b 
 and then, recorded on the dials, we have the exact number 
 of revolutions performed by the disk. The number is 
 1,440. But the series of holes open during the experi- 
 ment numbers 16 ; for every revolution, therefore, we had 
 16 puffs of air, or 16 waves of sound. Multiplying 1,440 
 by 16, we obtain 23,040 as the number of vibrations exe- 
 cuted by the tuning-fork in a minute. Dividing this by 
 60, we find the number of vibrations executed in a second 
 to be 384. 
 
 8. Determination of Wave-lengths : Time of Vibration. 
 
 Having determined the rapidity of vibration, the length 
 of the corresponding sonorous wave is found with the ut- 
 most facility. Imagine a tuning-fork vibrating in free 
 air. At the end of a second from the time it com- 
 menced its vibrations the foremost wave would have 
 reached a distance of 1,090 feet in air of the freezing 
 temperature. In the air of a room which has a tempera- 
 ture of about 15 C., it would reach a distance of 1,120 
 in a second. In this distance, therefore, are embraced 
 384 sonorous waves. Dividing 1,120 by 384, we find the 
 length of each wave to be nearly 3 feet. Determining in 
 this way the rates of vibration of the four tuning-forks 
 now before you, we find them to be 256, 320, 384, and 
 512 ; these numbers corresponding to wave-lengths of 
 
LENGTHS OF SOUND-WAVES. 97 
 
 4: feet 4 inches, 3 feet 6 inches, 2 feet 11 inches, and 2 feet 
 2 inches respectively. The waves generated by a man's 
 voice in common conversation are from 8 to 12 feet, those 
 of a woman's voice are from 2 to 4 feet in length. Hence 
 a woman's ordinary pitch in the lower sounds of conversa- 
 tion is more than an octave above a man's ; in the higher 
 sounds it is two octaves. 
 
 And here it is important to note that by the term vi- 
 brations are meant complete ones / and by the term sonor- 
 ous wave are meant a condensation and its associated 
 rarefaction. By a vibration an excursion to and fro of 
 the vibrating body is to be understood. Every wave gen- 
 erated by such a vibration bends the tympanic membrane 
 once in and once out. These are the definitions of a vi- 
 bration and of a sonorous wave employed in England and 
 Germany. In France, however, a vibration consists of an 
 excursion of the vibrating body in one direction^ whether 
 to or fro. The French vibrations, therefore, are only the 
 halves of ours, and we therefore call them semi-vibrations. 
 In all cases throughout these chapters, when the word vi- 
 bration is employed without qualification, it refers to com- 
 plete vibrations. 
 
 During the time required by each of those sonorous 
 waves to pass entirely over a particle of air, that piirticle 
 accomplishes one complete vibration. It is at one moment 
 pushed forward into the condensation, while at the next 
 moment it is urged back into the rarefaction. The time 
 required by the particle to execute a complete oscillation 
 is, therefore, that required by the sonorous wave to mow 
 through a distance equal to its own length. Supposing 
 the length of the wave to be eight feet, and the velocity 
 of sound in air of our present temperature to be 1,120 feet 
 a second, the wave in question will pass over its own length 
 of air in xi-g-th of a second : this is the time required by 
 every air-particle that it passes to complete an oscillation 
 
08 SOUND. 
 
 In air of a definite density and elasticity a certain 
 length of wave always corresponds to the same pitch.. 
 But supposing the density or elasticity not to be uniform ; 
 supposing, for example, the sonorous waves from one of 
 our tuning-forks to pass from cold to 'hot air: an instant 
 augmentation of the wave-length would occur, without 
 any change of pitch, for we should have no change in the 
 rapidity with which the waves would reach the ear. Con- 
 versely with the same length of wave the pitch would be 
 higher in hot air than in cold, for the succession of the waves 
 would be quicker. In an atmosphere of hydrogen waves of 
 a certain length would produce a note nearly two octaves 
 higher than waves of the same length in air ; for, in con- 
 sequence of the greater rapidity of propagation, the num- 
 ber of impulses received in a given time in the one case 
 would be nearly four times the number received in the 
 other. 
 
 9. Definition of an Octave. 
 
 Opening the innermost and outermost series of the 
 orifices of our siren, and sounding both of them, either 
 together or in succession, the musical ears present at once 
 detect the relationship of the two sounds. They notice 
 immediately that the sound which issues from the circle of 
 sixteen orifices is the octave of that which issues from the 
 circle of eight. But for every wave sent forth by the lat- 
 ter, two waves are sent forth by the former. In this w T ay 
 we prove that the physical meaning of the term " octave " 
 is, that it is a note produced by double the number of 
 vibrations of its fundamental. By multiplying the vibra- 
 tions of the octave by two, we obtain its octave, and by 
 a continued multiplication of this kind w r e obtain a series 
 of numbers answering to a series of octaves. Starting, 
 for example, from a fundamental note of 100 vibra- 
 tions, we should find, by this continual multiplication, that 
 
LIMITS OF THE HUMAN EAR. 99 
 
 A note five octaves above it would be produced by 3,200 
 
 vibrations. Thus : 
 
 100 Fundamental note. 
 
 2 
 
 200 1st octave. 
 2 
 
 400 2d octave. 
 2 
 
 800 3d octave. 
 
 2 
 
 1600 4th octave. 
 
 2 
 
 3200 5th octave. 
 
 This result is more readily obtained by multiplying the 
 vibrations of the fundamental note by the fifth power of 
 two. In a subsequent chapter we shall return to this 
 question of musical intervals. For our present .purpose 
 it is only necessary to define an octave. 
 
 10. Limits of the Ear ; and of Musical Sounds. 
 
 The ear's range of hearing is limited in both directions. 
 Savart fixed the lower limit at eight complete vibrations a 
 second ; and to cause these slowly recurring vibrations to 
 link themselves together, he was obliged to employ shocks 
 of great power. By means of a toothed wheel and an 
 associated counter, he fixed the upper limit of hearing at 
 24,000 vibrations a second. Helmholtz has recently fixed 
 the lower limit at 16 vibrations, and the higher at 38,000 
 vibrations, a second. By employing very small tuning- 
 forks, the late M. Depretz showed that a sound correspond- 
 ing to 38,000 vibrations a second is audible. 1 Starting 
 from the note 16, and multiplying continually by 2, or 
 
 1 The error of Savart consists, according to Helmholtz, in having adopted 
 an arrangement in which overtones (described in Chapter III.) were mistaken 
 for the fundamental one. 
 
100 SOUND. 
 
 more compendiously raising 2 to the llth power, and mul- 
 tiplying this by 16, we should find that at 11 octaves above 
 the fundamental note the number of vibrations would be 
 32,768. Taking, therefore, the limits assigned by Helm- 
 holtz, the entire range of the human ear embraces about 
 eleven octaves. But all the notes comprised within these 
 limits cannot be employed in music. The practical range 
 of musical sounds is comprised between 40 and 4,000 vibra- 
 tions a second, which amounts, in round numbers, to seven 
 octaves. 1 
 
 The limits of hearing are different in different persons. 
 While endeavoring to estimate the pitch of certain sharp 
 sounds, Dr. Wollaston remarked in a friend a total insensi- 
 bility to the sound of a small organ-pipe, which, in respect 
 to acuteness, was far within the ordinary limits of hearing. 
 The sense of hearing of this person terminated at a note 
 four octaves above the middle E of the pianoforte. The 
 squeak of the bat, the sound of a cricket, even the chirrup 
 of the common house-sparrow, are unheard by some people 
 who for lower sounds possess a sensitive ear. A difference 
 of a single note is sometimes sufficient to produce the 
 change from sound to silence. " The suddenness of the 
 transition," writes "Wollaston, " from perfect hearing to total 
 want of perception, occasions a degree of surprise which 
 
 1 " The deepest tone of orchestra instruments is the E of the double-bass, 
 with 41J vibrations. The new pianos and organs go generally as far as C 1 , 
 with 33 vibrations; new grand pianos may reach A 11 , with 2 7|- vibrations. 
 In large organs a lower octave is introduced, reaching to C u , with 16 vi- 
 brations. But the musical character of all these tones under E is imper- 
 fect, because they are near the limit where the power of the ear to unite the 
 vibrations to a tone ceases. In height the pianoforte reaches to a lr , with 
 8,520 vibrations, or sometimes to C T , with 4,224 vibrations. The highest note 
 of the orchestra is probably the d v of the piccolo flute, with 4,752 vibrations.' 1 
 (Helmholtz, " Tonempfindungen," p. 30.) In this notation we start from C, 
 with 66 vibrations, calling the first lower octave C 1 , and the second C 11 ; and 
 calling the first highest octave c, the second c 1 , the third c 11 , the fourth c 12 , 
 etc. In England the deepest tone, Mr. Macfarren informs me, is not E, but A, 
 a fourth above it. 
 
DRUM OF THE EAR. 101, 
 
 renders an experiment of this kino:' with d series of, small; 
 pipes among several persons rather amusing. It is ominous 
 to observe the change of feeling manifested by various in- 
 dividuals of the party, in succession, as the sounds ap- 
 proach and pass the limits of their hearing. Those who 
 enjoy a temporary triumph are often compelled, in their 
 turn, to acknowledge to how short a distance their little 
 superiority extends." " Nothing can be more surprising," 
 writes Sir John Herschel, " than to see two persons, neither 
 of them deaf, the one complaining of the penetrating 
 shrillness of a sound, while the other maintains there is no 
 sound at all. Thus, while one person mentioned by Dr. 
 Wollaston could but just hear a note four octaves above 
 the middle E of the pianoforte, others have a distinct per- 
 ception of sounds full two octaves higher. The chirrup of 
 the sparrow is about the former limit ; the cry of the bat 
 about an octave above it ; and that of some insects proba- 
 bly another octave." In " The Glaciers of the Alps " I 
 have referred to a case of short auditory range, noticed by 
 myself in crossing the "Wengern Alp in company with a 
 friend. The grass at each side of the path swarmed with 
 insects, which to me rent the air with their shrill chirrup- 
 ing. My friend heard nothing of this, the insect-music 
 lying beyond his limit of audition. 
 
 11. Drum of the Ear. The JE/ustachian Tube. 
 
 Behind the tympanic membrane exists a cavity the 
 drum of the ear in part crossed by a series of bones, and 
 in part occupied by air. This cavity communicates with 
 the mouth by means of a duct called the Eustachian tube. 
 This tube is generally closed, the air-space behind the tym- 
 panic membrane being thus shut off from the external air. 
 If, under these circumstances, the external air becomes 
 denser, it will press the tympanic membrane inward. If, 
 on the other hand, the air outside becomes rarer, while the 
 
102 . , SOUND. 
 
 Eustachian tube remains closed, tlie membrane will be 
 Jpre^efl' GutWkid.-^ Pain is felt in both cases, and partial 
 deafness is experienced. I once crossed tlie Stelvio Pass 
 by night in company with a friend who complained of acute 
 pain in the ears. On swallowing his saliva the pain in- 
 stantly disappeared. By the act of swallowing the Eusta- 
 chian tube is opened, and thus equilibrium is established 
 between the external and internal pressure. 
 
 It is possible to quench the sense of hearing of low 
 sounds by stopping the nose and mouth, and trying to ex- 
 pand the chest, as in the act of inspiration. This effort 
 partially exhausts the space behind the tympanic mem- 
 brane, which is then thrown into a state of tension by the 
 pressure of the outward air. A similar deafness to low 
 sounds is produced when the nose and mouth are stopped, 
 and a strong effort is made to expire. In this case air is 
 forced through the Eustacliian tube into the drum of the 
 ear, the tympanic membrane being distended by the press- 
 ure of the internal air. The experiment may be made in 
 a railway carriage, when 'the low rumble will vanish or be 
 greatly enfeebled, while the sharper sounds are heard with 
 undiminished intensity. Dr. "Wollaston was expert in 
 closing the Eustachian tube, and leaving the space behind 
 the tympanic membrane occupied by either compressed or 
 rarefied air. He was thus able to cause his deafness to 
 continue for any required time without effort on his part, 
 always, however, abolishing it by the act of swallowing. 
 A sudden concussion may produce deafness by forcing air 
 either into or out of the dram of the ear, and this may 
 account for a fact noticed by myself in one of my Al- 
 pine rambles. In the summer of 1858, jumping from 
 a cliff on to what was supposed to be a deep snow-drift, 
 I came into rude collision with a rock which the snow 
 barely covered. The sound of the wind, the rush of the 
 glacier-torrents, and all the other noises which a sunny day 
 
THE DOUBLE SIREN. 103 
 
 awakes upon the mountains, instantly ceased. I could 
 hardly hear the sound of my guide's voice. This deafness 
 continued for half an hour ; at the end of which time the 
 blowing of the nose opened, I suppose, the Eustachian 
 tube, and restored, with the quickness of magic, the innu- 
 merable murmurs which filled the air around me. 
 
 Light, like sound, is excited by pulses or waves ; and 
 lights of different colors, like sounds of different pitch, 
 are excited by different rates of vibration. But in its 
 width of perception the ear exceedingly transcends the 
 eye ; for while the former ranges over eleven octaves, but 
 little more than a single octave is possible to the latter. 
 The quickest vibrations which strike the eye, as light, 
 have only about twice the rapidity of the slowest ; 1 whereas 
 the quickest vibrations which strike the ear, as a musical 
 sound, have more than two thousand times the rapidity 
 of the slowest. 
 
 12. HelmJwltsfs Double Siren. 
 
 Prof. Dove, as we have seen, extended the utility of 
 the siren of Cagniard de la Tour, by providing it with 
 four series of orifices instead of one. By doubling all its 
 parts, Helmholtz has recently added vastly to the power 
 of the instrument. The double siren, as it is called, is 
 now before you, Fig. 29 (next page). It is composed of 
 two of Dove's sirens, c and c', one turned upside down. 
 You will recognize in the lower siren the instrument with 
 which you are already acquainted. The disks of the two 
 sirens have a common axis, so that when one disk rotates 
 the other rotates with it. As in the former case, the num- 
 ber of revolutions is recorded by clock-work (omitted in the 
 figure). When air is urged through the tube t' the upper 
 
 1 It is hardly necessary to remark that the quickest vibrations and short- 
 est waves correspond to the extreme violet, while the slowest vibrations and 
 longest waves correspond to the extreme red, of the spectrum. 
 
104: 
 
THE DOUBLE SIREN. 105 
 
 siren alone sounds ; when urged through t, the lower one 
 only sounds ; when it is urged simultaneously through t' 
 and t, both the sirens sound. With this instrument, 
 therefore, we are able to introduce much more varied com- 
 binations than with the former one. Helmholtz has also 
 contrived a means by which not only the disk of the upper 
 siren, but the box c' above the disk, can be caused to 
 rotate. This is effected by a toothed wheel and pinion, 
 turned by a handle. Underneath the handle is a dial with 
 an index, the use of which will be subsequently illus- 
 trated. 
 
 Let us direct our attention for the present to the upper 
 siren. By means of an India-rubber tube, the orifice t' is 
 connected with an acoustic bellows, and air is urged into 
 c'. Its disk turns round, and we obtain with it all the 
 results already obtained with Dove's siren. The pitch of 
 the note is uniform. Turning the handle above, so as to 
 cause the orifices of the cylinder c' to meet those of the 
 disk, the two sets of apertures pass each other more rapidly 
 than when the cylinder stood still. An instant rise of 
 pitch is the result. By reversing the motion, the orifices 
 are caused to pass each other more slowly than when c' is 
 motionless, and in this case you notice an instant fall of 
 pitch when the handle is turned. Thus, by imparting in 
 quick alternation a right-handed and left-handed motion to 
 the handle, we obtain successive rises and falls of pitch. 
 An extremely instructive effect of this kind may be ob- 
 served at any railway station on the passage of a rapid 
 train. During its approach the sonorous waves emitted by 
 the whistle are virtually shortened, a greater number of 
 them being crowded into the ear in a given time. During 
 its retreat we have a virtual lengthening of the sonorous 
 waves. The consequence is, that, when approaching, the 
 whistle sounds a higher note, and when retreating it sounds 
 a lower note, than if the train were still. A fall of pitch, 
 
106 SOUND. 
 
 therefore, is perceived as the train passes the station. 1 This 
 is the basis of Doppler's theory of the colored stars. He 
 supposes that all stars are white, but that some of them 
 are rapidly retreating from us, thereby lengthening their 
 luminiferous waves and becoming red. Others are rapidly 
 approaching us, thereby shortening their w r aves, and be- 
 coming green or blue. The ingenuity of this theory is 
 extreme, but its correctness is more than doubtful. 
 
 13. Transmission of Musical Sounds ~bij Liquids and 
 
 Solids. 
 
 We have thus far occupied ourselves with the trans- 
 mission of musical sounds through air. They are also 
 transmitted by liquids and solids. When a tuning-fork 
 screwed into a little wooden foot vibrates, nobody, except 
 the persons closest to it, hears its sound. On dipping the 
 foot into a glass of water a musical sound is audible : the 
 vibrations having been transmitted through the water to 
 the air. The tube M N, Fig. 30, three feet long, is set up- 
 right upon a wooden tray A B. The tube ends in a funnel 
 at the top, and is now filled with water to the brim. The 
 fork F is thrown into vibration, and on dipping its foot 
 into the funnel at the top of the tube, a musical sound 
 swells out. I must so far forestall matters as to remark 
 that in this experiment the tray is the real sounding body. 
 It has been thrown into vibration by the fork, but the 
 vibrations have been conveyed to the tray ~by the water. 
 Through the same medium vibrations are communicated 
 to the auditory nerve, the terminal filaments of which are 
 immersed in a liquid : substituting mercury for water, a 
 similar result is obtained. 
 
 1 Experiments on this subject were first made by M. Buys Ballot on the 
 Dutch railway, and subsequently by Mr. Scott Russell in this country. 
 Doppler's idea is now applied to determine, from changes of wave-length, 
 motions in the sun and fixed stars. 
 
MUSICAL SOUNDS THROUGH LIQUIDS. 
 
 107 
 
 FIG. 30. 
 
 The siren has received its name from its capacity to 
 under water. A vessel now in front of the table is 
 half filled with water, in which a siren is wholly immersed. 
 When a cock is turned the water from the pipes which 
 supply the house forces itself through the instrument. Its 
 disk is now rotating, and a sound of rapidly augmenting 
 pitch issues from the vessel. The pitch rises thus rapidly 
 because the heavy and powerfully pressed water soon drives 
 the disk up to its maximum speed of rotation. "When 
 the supply is les- 
 sened, the mo- 
 tion relaxes and 
 the pitch falls. 
 Thus, by alter- 
 nately opening 
 and closing the 
 cock, the song 
 of the siren is 
 caused to rise 
 and fall in a wild 
 and melancholy 
 manner. You 
 would not con- 
 sider such a 
 sound likely to 
 woo mariners to 
 their doom. 
 
 The transmis- 
 sion of musical 
 sounds through 
 solid bodies is also capable of easy and agreeable illustra- 
 tion. Before you is a wooden rod, thirty feet long, passing 
 from the table through a window in the ceiling, into the 
 open air above. The lower end of the rod rests upon a 
 wooden tray, to which the musical vibrations of a body ap- 
 
08 SOUND. 
 
 plied to the upper end of the rod are to be transferred. 
 An assistant is above, with a tuning-fork in his hand. He 
 strikes the fork against a pad ; it vibrates, but you hear 
 nothing. He now applies the stem of the fork to the end 
 of the rod, and instantly the wooden tray upon the table is 
 rendered musical. The pitch of the sound, moreover, is 
 exactly that of the tuning-fork ; the wood has been passive 
 as regards pitch, transmitting the precise vibrations im- 
 parted to it without any alteration. With another fork a 
 note of another pitch is obtained. Thus fifty forks might 
 be employed instead of two, and 300 feet of wood instead 
 of 30 ; the rod would transmit the precise vibrations im- 
 parted to it, and no other. 
 
 We are now prepared to appreciate an extremely beau- 
 tiful experiment, for which we are indebted to Sir Charles 
 Wheatstone. In a room underneath this, and separated 
 from it by two floors, is a piano. Through the two floors 
 passes a tin tube 2J- inches in diameter, and along the 
 axis of this tube passes a rod of deal, the end of which 
 emerges from the floor in front of the lecture-table. The 
 rod is clasped by India-rubber bands, which entirely close 
 the tin tube. The lower end of the rod rests upon the 
 sound-board of the piano, its upper end being exposed 
 before you. An artist is at this moment engaged at the 
 instrument, but you hear no sound. When, however, a 
 violin is placed upon the end of the rod, the instrument 
 becomes instantly musical, not, however, with the vibrations 
 of its own strings, but with those of the piano. When the 
 violin is removed, the sound ceases ; putting in its place a 
 guitar, the music revives. For the violin and guitar we 
 may substitute a plain wooden tray, which is also rendered 
 musical. Here, finally, is a harp, against the sound- 
 board of which the end of the deal rod is caused to press ; 
 every note of the piano is reproduced before you. On lift- 
 ing the harp so as to break the connection with the piano, 
 
MUSICAL SOUNDS THROUGH SOLIDS. 109 
 
 the sound vanishes ; but the moment the sound-board is 
 caused to press upon the rod the music is restored. The 
 sound of the piano so far resembles that of the harp that 
 it is hard to resist the impression that the music you hear 
 is that of the latter instrument. An uneducated person 
 might well believe that witchcraft or " spiritualism " is con- 
 cerned in the production of this music. 
 
 What a curious transference of action is here presented 
 to the mind ! At the command of the musician's will, the 
 fingers strike the keys ; the hammers strike the strings, by 
 which the rude mechanical shock is converted into tremors. 
 The vibrations are communicated to the sound-board of 
 the piano. Upon that board rests the end of the deal rod, 
 thinned off to a sharp edge to make it fit more easily be- 
 tween the wires. Through the edge, and afterward along 
 the rod, are poured with unfailing precision the entangled 
 pulsations produced by the shocks of those ten agile fin- 
 gers. To the sound-board of the harp before you, the rod 
 faithfully delivers up the vibrations of which it is the 
 vehicle. This second sound-board transfers the motion to 
 the air, carving it and chasing it into forms so transcen- 
 dently complicated that confusion alone could be antici- 
 pated from the shock and jostle of the sonorous waves. 
 But the marvelous human ear accepts every feature of the 
 motion, and all the strife and struggle and confusion melt 
 finally into music upon the brain. 1 
 
 1 An ordinary musical box may be substituted for the piano in this ex- 
 periment. 
 
110 SOUND. 
 
 SUMMAEY OF CHAPTEE II. 
 
 A MUSICAL sound is produced by sonorous shocks which 
 follow each other at regular intervals with a sufficient 
 rapidity of succession. 
 
 Noise is produced by an irregular succession of sonorous 
 shocks. 
 
 A musical sound may be produced by taps which rap- 
 idly and regularly succeed each other. The taps of a card 
 against the cogs of a rotating wheel are usually employed 
 to illustrate this point. 
 
 A musical sound may also be produced by a succession 
 of puffs. The siren is an instrument by which such puffs 
 are generated. 
 
 The pitch of a musical note depends solely on the 
 number of vibrations concerned in its production. The 
 more rapid the vibrations, the higher the pitch. 
 
 By means of the siren the rate of vibration of any 
 sounding body may be determined. It is only necessary 
 to render the sound of the siren and that of the body iden- 
 tical in pitch to maintain both sounds in unison for a cer- 
 tain time, and to ascertain, by means of the counter of the 
 siren, how many puffs have issued from the instrument in 
 that time. This number expresses the number of vibra- 
 tions executed by the sounding body. 
 
 When a body capable of emitting a musical sound a 
 tuning-fork, for example vibrates, it moulds the surround- 
 ing air into sonorous waves, each of which consists of a 
 condensation and a rarefaction. 
 
 The length of the sonorous wave is measured from 
 
SUMMARY. Hi 
 
 condensation to condensation, or from rarefaction to rare- 
 faction. 
 
 The wave-length is found by dividing the velocity of 
 sound per second by the number of vibrations executed by ]/ 
 the sounding body in a second. 
 
 Thus a tuning-fork which vibrates 256 times in a 
 second produces in air of 15 C., where the velocity is 
 1,120 feet a second, waves 4 feet 4 inches long. While 
 two other forks, vibrating respectively 320 and 384 times 
 a second, generate waves 3 feet 6 inches, and 2 feet 11 
 inches long. 
 
 A vibration, as defined in England and Germany, com- 
 prises a motion to and fro. It is a complete vibration. 
 In France, on the contrary, a vibration comprises a move- 
 ment to or fro. The French vibrations are with us semi- 
 vibrations. 
 
 The time required by a particle of air over which a 
 sonorous wave passes to execute a complete vibration is 
 that required by the wave to move through a distance 
 equal to its own length. 
 
 The higher the temperature of the air, the longer is 
 the sonorous wave corresponding to any particular rate of 
 vibration. Given the wave-length and the rate of vibra- 
 tion, we can readily deduce the temperature of the 
 air. 
 
 The human ear is limited in its range of hearing 
 musical sounds. If the vibrations number less than 16 a 
 second, we are conscious only of the separate shocks. If 
 they exceed 38,000 a second, the consciousness of sound v 
 ceases altogether. The range of the best ear covers about 
 1 1 octaves, but an auditory range limited to 6 or 7 octaves 
 is not uncommon. 
 
 The sounds available in music are produced by vibra- / 
 tions comprised between the limits of 40 and 4,000 a 
 second. They embrace Y octaves. 
 
112 SOUND. 
 
 The range of the ear far transcends that of the eye. 
 which hardly exceeds an octave. 
 
 By means of the Eustachian tube, which is opened in 
 the act of swallowing, the pressure of the air on both sides 
 of the tympanic membrane is equalized. 
 
 By either condensing or rarefying the air behind the 
 tympanic membrane, deafness to sounds of low pitch may 
 be produced. 
 
 On the approach of a railway train the pitch of the 
 whistle is higher, on the retreat of the train the pitch is 
 lower, than it would be if the train were at rest. 
 
 Musical sounds are transmitted by liquids and solids. 
 Such sounds may be transferred from one room to another ; 
 from the ground-floor to the garret of a house of many 
 stories, for example, the sound being unheard in the rooms 
 intervening between both, and rendered audible only 
 when the vibrations are communicated to a suitable sound- 
 board. 
 
CHAPTER III. 
 
 Vibration of Strings. How employed in Music. Influence of Sound-Boards. 
 Laws of Vibrating Strings. Combination of Direct and Reflected Pulses. 
 Stationary and Progressive Waves. Nodes and Ventral Segments. 
 Application of Results to the Vibrations of Musical Strings. Experiments 
 of Melde. Strings set in Vibration by Tuning-Forks. Laws of Vibration 
 thus demonstrated. Harmonic Tones of Strings. Definitions of Timbre 
 or Quality, or Overtones and Clang. Abolition of Special Harmonics. 
 Conditions which affect the Intensity of the Harmonic Tones. Optical 
 Examination of the Vibrations of a Piano- Wire. 
 
 1. Vibrations of Strings : Use of Sound-Boards. 
 
 WE have to begin our studies to-day with the vibra- 
 tions of strings or wires ; to learn how bodies of this form 
 are rendered available as sources of musical sounds, and 
 to investigate the laws of their vibrations. 
 
 To enable a musical string to vibrate transversely , or 
 at right angles to its length, it must be stretched between 
 two rigid points. Before you, Fig. 31 (next page), is an 
 instrument employed to stretch strings, and to render their 
 vibrations audible. From the pin j9, to which one end of 
 it is firmly attached, a string passes across the two bridges 
 B and B', being afterward carried over the wheel H, which 
 moves with- great freedom. The string is finally stretched 
 by a weight w, of 28 Ibs., attached to its extremity. The 
 bridges B and B', which constitute the real ends of the 
 string, are fastened on to the long wooden box M N. The 
 whole instrument is called a monochord, or sonometer. 
 
 Taking hold of the stretched string B B 7 at its middle 
 and plucking it aside, it springs back to its first position, 
 passes it, returns, and thus vibrates for a time to and fro 
 across its position of equilibrium. You hear a sound, but 
 
114 
 
 SOUND. 
 
 the sonorous waves which at present strike your ears do 
 not proceed immediately from the string. The amount 
 of wave-motion generated by so thin a body is too small 
 to be sensible at any distance. But the string is drawn 
 tightly over the two bridges B B' ; and when it vibrates, 
 its tremors are communicated through these bridges to the 
 
 FIG. 31. 
 
 entire mass of the box M N, and to the air within the box, 
 which thus become the real sounding bodies. 
 
 That the vibrations of the string alone are not sufficient 
 to produce the sound may be thus experimentally demon- 
 strated : A B, Fig. 32 (next page), is a piece of wood placed 
 across an iron bracket c. From each end of the piece of 
 wood depends a rope ending in a loop, while stretching 
 across from loop to loop is an iron bar m n. From the 
 middle of the iron bar hangs a steel wire s ', stretched by 
 a weight w, of 28 Ibs. By this arrangement the wire is 
 detached from all large surfaces to which it could impart 
 its vibrations. Plucking the wire s s', it vibrates vigor- 
 ously, but even those nearest to it do not hear any sound* 
 The agitation imparted to the air is too inconsiderable 
 to affect the auditory nerve at any distance. A second 
 
INFLUENCE OF SOUND-BOARDS. 
 
 115 
 
 FIG. 
 
 iffiiiir 
 c 
 
 wire t t', Fig. 33 (next page), of the same length, thick- 
 ness, and material as s s', has one of its ends attached to 
 the wooden tray A B. This wire also carries a weight w, 
 of 28 Ibs. Finally, passing 
 over the bridges B B' of the 
 sonometer, Fig. 31, is our 
 third wire, in every respect L 
 like the two former, and, 
 like them, stretched by a 
 weight w, of 28 Ibs. When 
 the wire t t', Fig. 33, is 
 caused to vibrate, you hear 
 its sound distinctly. Though 
 one end only of the wire is 
 connected with the tray A B, 
 the vibrations transmitted 
 to it are sufficient to con- 
 vert the tray into a sound- 
 ing body. Finally, when 
 the wire of the sonometer 
 M N, Fig. 31, is plucked, the 
 sound is loud and full, be- 
 cause the instrument is spe- 
 cially constructed to take 
 up the vibrations of the 
 wire. 
 
 The importance of em- 
 ploying proper sounding ap- 
 paratus in stringed instru- 
 ments is rendered manifest 
 by these experiments. It is 
 not the strings of a harp, or a lute, or a piano, or a violin, 
 that throw the air into sonorous vibrations. It is the large 
 surfaces with which the strings are associated, and the air 
 inclosed by these surfaces. The goodness of such instru- 
 
116 
 
 SOUND. 
 
 FIG. 38. 
 
 ments depends almost wholly upon the quality and dispo- 
 sition of their sound-boards. 1 
 
 Take the violin as an example. It is, or ought to be, 
 
 formed of wood 
 of the most per- 
 fect elasticity. 
 Imperfectly elas- 
 tic wood expends 
 the motion im- 
 parted to it in 
 the friction of its 
 own molecules ; 
 the motion is con- 
 verted into heat, 
 instead of sound. 
 The strings of the 
 violin pass from 
 the " tail-piece " 
 of the instrument 
 over the "bridge," 
 being thence car- 
 ried to the "pegs," 
 the turning of 
 which regulates 
 the tension of 
 the strings. The 
 bow is drawn 
 across at a point 
 about one-tenth 
 of the length of the string from the bridge. The two 
 
 1 To show the influence .of a large vibrating surface in communicating 
 sonorous motion to the air, Mr. Kilburn incloses a musical box within cases 
 of thick felt. Through the cases a wooden rod, which rests upon the box, 
 issues. When the box plays a tune, it is unheard as long as the rod only 
 emerges ; but when a thin disk of wood is fixed on the rod, the music be- 
 comes immediately audible. 
 
INFLUENCE OF SOUND-BOARDS. 117 
 
 " feet " of the bridge rest upon the most yielding portion 
 of the " belly " of the violin, that is, the portion that lies 
 between the two /"-shaped orifices. One foot is fixed over 
 a short rod, the " sound post," which runs from belly to 
 back through the interior of the violin. This foot of the 
 bridge is thereby rendered rigid, and it is mainly through 
 the other foot, which is not thus supported, that the vibra- 
 tions are conveyed to the wood of the instrument, and 
 thence to the air within and without. The sonorous qual- 
 ity of the wood of a violin is mellowed by age. The very 
 act of playing also has a beneficial influence, apparently 
 constraining the molecules of the wood, which in the first 
 instance might be refractory, to conform at last to the re- 
 quirements of the vibrating strings. 
 
 This is the place to make the promised reference (page 
 38) to Prof. Stokes' s explanation of the action of sound- 
 boards. Although the amplitude of the vibrating-board 
 may, be very small, still its larger area renders the abo- 
 lition of the condensations and rarefactions difficult. The 
 air cannot move away in front nor slip in behind be- 
 fore it is sensibly condensed and rarefied. Hence with 
 such vibrating bodies sound-waves may be generated, and 
 loud tones produced, while 
 the thin strings that set them 
 in vibration, acting alone, 
 are quite inaudible. 
 
 The increase of sound, 
 produced by the stoppage 
 of lateral motion, has been 
 experimentally illustrated 
 by Prof. Stokes. Let the 
 two black rectangles in Fig. 
 34 represent the section of a tuning-fork. After it has 
 been made to vibrate, place a sheet of paper, or the blade 
 of a broad knife, with its edge parallel to the axis of the 
 
118 SOUND. 
 
 fork, and as near to the fork as may be without touching. 
 If the obstacle be so placed that the section of it is A or 
 B no effect is produced ; but if it be placed at c, so as to 
 prevent the reciprocating to-and-fro movement of the air, 
 which tends to abolish the condensations and rarefactions, 
 the sound becomes much stronger. 
 
 2. Laws of Vibrating Strings. 
 
 Having thus learned how the vibrations of strings are 
 rendered available in music, we have next to investigate 
 the laws of such vibrations. I pluck at its middle point 
 the string B B', Fig. 31. The sound heard is the funda- 
 mental or lowest note of the string, to produce which it 
 swings, as a whole, to and fro. By placing a movable 
 bridge under the middle of the string, and pressing the 
 string against the bridge, it is divided into two equal 
 parts. Plucking either of those at its centre, a musical 
 note is obtained, which many of you recognize as the 
 octave of the fundamental note. In all cases, and with 
 all instruments, the octave of a note is produced by 
 doubling the number of its vibrations. It can, moreover, 
 be proved, both by theory and by the siren, that this half 
 string vibrates with exactly twice the rapidity of the whole. 
 In the same way it can be proved that one-third of the 
 string vibrates with three times the rapidity, producing a 
 note a fifth above the octave, while one-fourth of the 
 string vibrates with four times the rapidity, producing 
 the double octave of the whole string. In general terms, 
 the number of vibrations is inversely proportional to the 
 length of the string. 
 
 Again, the more tightly a string is stretched the more 
 rapid is its vibration. When this comparatively slack 
 string is caused to vibrate, you hear its low fundamental 
 note. By turning a peg, round which one end of it is 
 coiled, the string is tightened, and the pitch rendered 
 
LAWS OF VIBRATING STRINGS. 119 
 
 higher. Taking hold with my left hand of the weight w, 
 attached to the wire B B' of our sonometer, and plucking 
 the wire with the fingers of my right, I alternately press 
 upon the weight and lift it. The quick variations of ten- 
 sion are expressed by a varying wailing tone. Now, the 
 number of vibrations executed in the unit of time bears a 
 definite relation to the stretching force. Applying differ- 
 ent weights to the end of the wire B B', and determining in 
 each case the number of vibrations executed in a second, 
 we find the numbers thus obtained to be proportional to 
 the square roots of the stretching weights. A string, for 
 example, stretched by a weight of one pound, executes a 
 certain number of vibrations per second; if we wish to 
 double this number,, we must stretch it by a weight of four 
 pounds ; if we wish to treble the number, we must apply 
 a weight of nine pounds, and so on. 
 
 The vibrations of a string also depend upon its thick- 
 ness. Preserving the stretching weight, the length, and 
 the material of the string constant, the number of vibra- 
 tions varies inversely as the thickness of the string. If, 
 therefore, of two strings of the same material, equally 
 long and equally stretched, the one has twice the diam- 
 eter of the other, the thinner string will execute double 
 the number of vibrations of its fellow in the same time. 
 If one string be three times as thick as another, the latter 
 will execute three times the number of vibrations, and 
 so on. 
 
 Finally, the vibrations of a string depend upon the 
 density of the matter of which it is composed. A platinum 
 wire and an iron wire, for example, of the same length 
 and thickness, stretched by the same weight, will not vi- 
 brate with the same rapidity. For, w^hile the specific 
 gravity of iron, or in other words its density, is 7*8, that 
 of platinum is 21 '5. All other conditions remaining the 
 same, the number of vibrations is inversely proportional to 
 8 
 
120 SOUND. 
 
 the square root of the density of the string. If the density 
 of one string, therefore, be one-fourth that of another of 
 the same length, thickness, and tension, it will execute 
 its vibrations twice as rapidly ; if its density be one-ninth 
 that of the other, it will vibrate with three times the 
 rapidity, and so on. The two last laws, taken together, 
 may be expressed thus : The number of vibrations is i/ii^ 
 tersely proportional to the square root of the weight of 
 the string. 
 
 In the violin and other stringed instruments we avail 
 ourselves of thickness instead of length to obtain the 
 deeper tones. In the piano we not only augment the 
 thickness of the wires intended to produce the bass notes, 
 but we load them by coiling round them an extraneous 
 substance. They resemble horses heavily jockeyed, and 
 move more slowly on account of the greater weight im- 
 posed upon the force of tension. 
 
 3. Mechanical Illustrations of Vibrations. Progres- 
 sive and Stationary Waves. Ventral Segments, and 
 Nodes, 
 
 These, then, are the four laws which regulate the 
 transverse vibrations of strings. We now turn to certain 
 allied phenomena, which, though they involve mechanical 
 considerations, of a rather complicated kind, may be com- 
 pletely mastered by an average amount of attention. And 
 they must be mastered if we would thoroughly compre- 
 hend the philosophy of stringed instruments. 
 
 From the ceiling 0, Fig. 35, of this room hangs an India- 
 rubber tube twenty-eight feet long. The tube is filled 
 with sand to render its motions slow and more easily fol- 
 lowed by the eye. I take hold of its free end #, stretch the 
 tube a little, and by properly timing my impulses cause it 
 to swing to and fro as a whole, as shown in the figure. It 
 has its definite period of vibration dependent on its length, 
 
STATIONARY AND PROGRESSIVE WAVES. 
 
 121 
 
 FIG. 85. 
 
 FIG. 86. 
 
 weight, thickness, and tension, and my impulses must syn- 
 chronize with that period. 
 
 I now stop the motion, and by a sudden jerk raise a 
 hump upon the tube, which runs along it as a pulse toward 
 
 its fixed end ; here the hump 
 
 reverses itself, and runs back 
 
 to my hand. At the fixed end 
 
 of the tube, in obedience to 
 
 the law of reflection, the pulse 
 
 reversed both its position and 
 
 the direction of its motion. 
 
 Supposing <?, Fig. 36, to be 
 
 the fixed end of the tube, and 
 
 a the end held in the hand : if 
 
 the pulse on reaching c have 
 
 the position shown in (1), after 
 
 reflection it will have the posi- 
 tion shown in (2). The arrows 
 
 mark the direction of progres- 
 sion. The time required for 
 
 the pulse to pass from the 
 
 hand to the fixed end and 
 
 back is exactly that required 
 
 to accomplish one complete 
 
 vibration of the tube as a 
 
 whole. It is indeed the ad- 
 dition of such impulses which 
 
 causes the tube to continue 
 
 to vibrate as a whole. 
 
 If, instead of a single 
 
 jerk, a succession of jerks be 
 
 imparted, thereby sending a 
 series of pulses along the tube, every one of them will be 
 reflected above, and we have now to inquire how the 
 direct and reflected pulses behave toward each other. 
 
122 
 
 SOUND. 
 
 FIG. 87. 
 
 a 
 (2) 
 
 Let the time required by the pulse to pass from my 
 hand to the fixed end be one second ; at the end of half a 
 second it occupies the position a b (1), Fig. 37, its fore- 
 most point having reached the middle of the tube. At 
 the end of a whole second it would have the position b c 
 
 (2), its foremost point having 
 reached the fixed end c of the 
 tube. At the moment when re- 
 flection begins at c, let another 
 jerk be imparted at a. The 
 reflected pulse from c moving 
 with the same velocity as this 
 direct one from #, the foremost 
 points of both will arrive at the 
 centre b (3) at the same moment. 
 What must occur ? The hump 
 a b wishes to move on to c, and 
 to do so must move the point 
 ~b to the right. The hump c b 
 wishes to move toward #, and 
 to do so must move the point b 
 to the left. The point &, urged 
 by equal forces in two opposite 
 directions at the same time, will 
 not move in either direction. 
 Under these circumstances, the 
 two halves a , b c of the tube 
 will oscillate as if they were in- 
 dependent of each other (4). 
 Thus by the combination of 
 two progressive pulses, the one 
 direct and the other reflected, we produce two stationary 
 pulses on the tube a c. 
 
 The vibrating parts a I and b c are called ventral seg- 
 ments ; the point of no vibration b is called a node. 
 
 The term " pulse " is here used advisedly, instead of 
 
NODES AND VENTRAL SEGMENTS. 
 
 123 
 
 the more usual term wave. For a wave embraces two of 
 these pulses. It embraces both the hump and the de- 
 pression which follows the hump. The length of a wave, 
 therefore, is twice that of a ventral segment. 
 
 Supposing the jerks to be so timed as to cause each 
 hump to be one-third of the tube's length. At the end of 
 one-third of a second from starting the pulse will be in 
 the position a 1) (1), Fig. 38. In two-thirds of a second it 
 
 FIG. 88. 
 c 
 
 \ 
 
 a 
 (1) 
 
 a 
 (2) 
 
 a 
 (8) 
 
 a 
 (4) 
 
 a 
 (5) 
 
 r I 
 
 I V 
 
 a 
 (6) 
 
 will have reached the position I V (2), Fig. 38. At this 
 moment let a new pulse be started at a ; after the lapse of 
 
124: SOUND. 
 
 an entire second from the commencement we shall have 
 two humps upon the tube, one occupying the position 
 a b (3), the other the position 1)' c (3). It is here manifest 
 that the end of the reflected pulse from 0, and the end of 
 the direct one from , will reach the point V at the same 
 moment. We shall therefore have the state of things rep- 
 resented in (4), where b b f wishes to move upward, and 
 c V to move downward. The action of both upon the 
 point I) 1 being in opposite directions, that point will re- 
 main fixed. And from it, as if it were a fixed point, the 
 pulse 1) y will be reflected, while the segment ~b' c will 
 oscillate as an independent string. Supposing that at 
 the moment b b f (4) begins to be reflected at y we start 
 another pulse from a, it will reach b at the same moment 
 the pulse reflected from y reaches it. The pulses will 
 neutralize each other at b, and we shall have there a sec- 
 ond node. Thus, by properly timing our jerks, we divide 
 the rope into three ventral segments, separated from each 
 other by two nodal points. As long as the agitation con- 
 tinues the tube will vibrate as in (6). 
 
 There is no theoretic limit to the number of nodes 
 and ventral segments that may be thus produced. By the 
 quickening of the impulses, the tube is divided into four 
 ventral segments separated by three nodes ; quickening 
 still more we have five ventral segments and four nodes. 
 With this particular tube the hand may be caused to 
 vibrate sufficiently quick to produce ten ventral segments, 
 as shown in Fig. 38 (7). When the stretching force is 
 constant, the number of ventral segments is proportional 
 to the rapidity of the hand's vibration. To produce 
 2, 8, 4, 10 ventral segments requires twice, three times, 
 four times, ten times the rapidity of vibration necessary 
 to make the tube swing as a whole. When the vibration 
 is very rapid the ventral segments appear like a series 
 of shadowy spindles, separated from each other by dark 
 
STATIONARY WAVES. 125 
 
 motionless nodes. The experiment is a beautiful one, and 
 it is easily performed. 
 
 If , instead of moving the hand to and fro, it be caused 
 to describe a small circle, the ventral segments become 
 " surfaces of revolution." Instead of the hand, moreover, 
 we may employ a hook turned by a whirling-table. Before 
 you is a cord more rigid than the India-rubber tube, 25 
 feet long, with one of its ends attached to a freely-moving 
 swivel fixed in the ceiling of the room. By turning the 
 whirling-table to which the other end is attached, this 
 cord may be divided into as many as 20 ventral segments, 
 separated from each other by their appropriate nodes. In 
 another arrangement a string of catgut 12 feet long, 
 with silvered beads strung along it, is stretched horizon- 
 tally between a vertical wheel and a free swivel fixed in a 
 rigid stand. On turning the wheel, and properly regu- 
 lating both the tension and the rapidity of rotation, the 
 beaded cord may be caused to rotate as a whole, and to 
 divide itself successively into 2, 3, 4, or 5 ventral seg- 
 ments. When we envelop the cord in a luminous beam, 
 every spot of light on every bead describes a brilliant cir- 
 cle, and a very beautiful experiment is the result. 
 
 4:. Mechanical Illustrations of Damping Various 
 Points of Vibrating Cord. 
 
 The subject of stationary waves was first experimen- 
 tally treated by the Messrs. Weber, in their excellent re- 
 searches on wave-motion. It is a subject which will well 
 repay your attention by rendering many of the most diffi- 
 cult phenomena of musical strings perfectly intelligible. 
 It will make the connection of both classes of vibrations 
 more obvious if we vary our last experiments. Before you 
 is a piece of India-rubber tubing, 10 or 12 feet long, 
 stretched from c to a, Fig. 39, and made fast to two pins 
 at c and a. The tube is blackened, and behind it is 
 
126 
 
 SOUND. 
 
 placed a surface of white paper, to render its motions 
 more visible. Encircling the tube at its centre ~b (1) bj 
 the thumb and forefinger of my left hand, and taking 
 the middle of the lower half 1) a of the tube in my right, 
 I pluck it aside. Not only does the lower half swing, but 
 
 A 
 
 
 
 A 
 
 \ / 
 
 
 
 A 4 
 
 I 
 
 
 
 / \ 
 
 
 
 
 )i 
 
 \ 
 
 
 
 
 1 \ 
 
 -^f 
 
 f 
 
 1 
 
 
 | 
 
 -? 
 
 
 V 
 
 a 
 (*) 
 
 (5 
 
 / 
 
 ) ( 
 
 V 
 
 a 
 6) 
 
 the upper half also is thrown into vibration. Withdraw- 
 ing the hands wholly from the tube, its two halves a ~b 
 and b c continue to vibrate, being separated from each 
 other by a node b at the centre (2). 
 
 I now encircle the tube at a point b (3) one-third of 
 
THE NODES NOT POINTS OF ABSOLUTE REST. 127 
 
 its length from its lower end a, and, taking hold of a b at 
 its centre, pluck it aside ; the length 5 c above my hand 
 instantly divides into two vibrating segments. With- 
 drawing the hands wholly, you see the entire tube divided 
 into three ventral segments, separated from each other by 
 two motionless nodes, 5 and ~U (4). I pass on to the point 
 1} (5), which marks off one-fourth of the length of the 
 tube, encircle it, and pluck the shorter segment aside. 
 The longer segment above my hand divides itself imme- 
 diately into three vibrating parts. So that, on withdraw- 
 ing the hand, the whole tube appears before you divided 
 into four ventral segments, separated from each other by 
 three nodes 5 1)' W (6). In precisely the same way the 
 tube may be divided into five vibrating segments with 
 four nodes. 
 
 This sudden division of the long upper segment of the 
 tube, without any apparent cause, is very surprising ; but if 
 you grant me your attention for a moment, you will find 
 that these experiments are essentially similar to those 
 which illustrated the coalescence of direct and reflected 
 undulations. Reverting for a moment to the latter, you 
 observed that the to-and-fro motion of the hand through 
 the space of a single inch was sufficient to make the 
 middle points of the ventral segments vibrate through a 
 foot or eighteen inches. By being properly timed the 
 impulses accumulated, until the amplitude of the vibrat- 
 ing segments exceeded immensely that of the hand which 
 produced them. The hand, in fact, constituted a nodal 
 point, so small was its comparative motion. Indeed, it is 
 usual, and correct, to regard the ends of the tube also as 
 nodal points. 
 
 Consider now the case represented in (1), Fig. 39, where 
 the tube was encircled at its middle, the lower segment 
 a ~b being thrown into the vibration corresponding to its 
 length and tension. The circle formed by the finger and 
 
128 SOUND. 
 
 thumb permitted the tube to oscillate at the point b 
 through the space of an inch ; and the vibrations at that 
 point acted upon the upper half ~b c exactly as my hand 
 acted when it caused the tube suspended from the ceiling 
 to swing as a whole, as in Fig. 35. Instead of the timid 
 vibrations of the hand, we have now the timid vibrations of 
 the lower half of the tube ; and these, though narrowed to 
 an inch at the place clasped by the finger and thumb, soon 
 accumulate, and finally produce an amplitude, in the upper 
 half, far exceeding their own. The same reasoning applies 
 to all the other cases of subdivision. If, instead of encir- 
 cling a point by the finger and thumb, and plucking the 
 portion of the tube below it aside, that same point were 
 taken hold of by the hand and agitated in the period proper 
 to the lower segment of the tube, precisely the same effect 
 would be produced. We thus reduce both effects to one 
 and the same cause; namely, the combination of direct 
 and reflected undulations. 
 
 And here let me add that, when the tube was divided 
 by the timid impulses of the hand, not one of its nodes 
 was, strictly speaking, a point of no motion ; for were the 
 nodes not capable of vibrating through a very small ampli- 
 tude, the motion of the various segments of the tube could 
 not be maintained. 
 
 5. /Stationary Water-waves. 
 
 What is true of the undulations of an India-rubber 
 tube applies to all undulations whatsoever. Water-waves, 
 for example, obey the same laws, and the coalescence 
 of direct and reflected waves exhibits similar phenomena. 
 This long and narrow vessel with glass sides, Fig. 40, is a 
 copy of the wave-canal of the brothers Weber. It is filled 
 to the level A B with colored water. By tilting the end A 
 suddenly, a wave is generated, which moves on to B, and 
 is there reflected. By sending forth fresh waves at the 
 
STATIONARY WATER-WAVES. 129 
 
 proper intervals, the surface is divided into two stationary 
 undulations. Making the succession of impulses more 
 rapid we can subdivide the surface into three, four (shown 
 in the figure), or more stationary undulations, separated 
 from each other by nodes. The step of a water-carrier is 
 sometimes so timed as to throw the surface of the water in 
 his vessel into stationary waves, which may augment in 
 height until the water splashes over the brim. Practice 
 has taught the water-carrier what to do ; he changes his 
 step, alters the period of his impulses, and thus stops the 
 accumulation of the motion. 
 
 In traveling recently in the coupe of a French railway 
 carriage, I had occasion to place a bottle half filled with 
 water on one of the little coupe tables. It was interesting 
 
 FIG. 40. 
 
 to observe it. At times it would be quite still ; at times 
 it would oscillate violently. To the passenger within the 
 carriage there was no sensible change in the motion of the 
 train to which the difference could be ascribed. But in 
 the one case the tremor of the carriage contained no vibra- 
 tions synchronous with the oscillating period of the water, 
 while in the other case such vibrations were present. Out 
 of the confused assemblage of tremors the water selected 
 the particular constituent which belonged to itself, and 
 declared its presence when the traveler was utterly uncon- 
 scious of its introduction. 
 
130 SOUND 
 
 6. Application of Mechanical Illustrations to Musical 
 Strings. 
 
 From these comparatively gross, but by no means un 
 beautiful, mechanical vibrations, we pass to those of a 
 sounding string. In the experiments with our monochord, 
 when the wire was to be shortened, a movable bridge was 
 employed, against which the wire was pressed so as to 
 deprive the point resting on the bridge of all possibility 
 of motion. This strong pressure, however, is not neces- 
 sary. Placing the feather-end of a goose-quill lightly 
 against the middle of the string, and drawing a violin-bow 
 over one of its halves, the string yields the octave of the 
 note yielded by the whole string. The mere damping of 
 the string at the centre, by the light touch of the feather, 
 is sufficient to cause the string to divide into two vibrating 
 segments. JS"or is it necessary to hold the feather there 
 throughout the experiment : after having drawn the bow, 
 the feather may be removed ; the string will continue to 
 vibrate, emitting the same note as before. We have here 
 a case exactly analogous to that in which the central point 
 of our stretched India-rubber tube was damped, by encir- 
 cling it with the finger and thumb as in Fig. 39 (1). Not 
 only did the half plucked aside vibrate, but the other half 
 vibrated also. We can, in fact, reproduce, with the vi- 
 brating string, every effect obtained with the tube. This, 
 however, is a point of such importance as to demand full 
 experimental illustration. 
 
 To prove that when the centre is damped, and the bow 
 drawn across one of the halves of the string, the other 
 half vibrates, I place across the middle of the untouched 
 half a kittle rider of red paper. Damping the centre and 
 drawing the bow, the string shivers, and the rider is over- 
 thrown, Fig. 41. 
 
 When the string is damped at a point which cuts off 
 
DIVISION OF MUSICAL STRINGS. 
 
 131 
 
 one-third of its length, and the bow drawn across the 
 shorter section, not only is this section thereby thrown 
 into vibration, but the longer section divides itself into 
 two ventral segments with a node between them. This is 
 proved by placing small riders of red paper on the ventral 
 
 FIG. 41. 
 
 segments, and a rider of blue paper at the node. Passing 
 the bow across the short segment you observe a fluttering 
 of the red riders, and now they are completely tossed off, 
 while the blue rider which crosses the node is undisturbed, 
 Fig. 42. 
 
 Damping the string at the end of one-fourth of its 
 
 FIG. 42. 
 
 length, the bow is drawn across the shorter section ; the 
 remaining three-fourths divide themselves into three ven- 
 
132 
 
 SOUND. 
 
 tral segments, with two nodes between them. This is 
 proved by the unhorsing of the three riders placed astride 
 the ventral segments, the two at the nodes keeping their 
 places undisturbed, Fig. 43. 
 
 Finally, damping the string at the end of one-fifth of 
 
 PIG. 43. 
 
 its length, and arranging, as before, the red riders on the 
 ventral segments and the blue ones on the nodes, by a 
 single sweep of the bow the four red riders are unhorsed, 
 and the three blue ones left undisturbed, Fig. 44. In this 
 way we perform with a sounding string the same series of 
 
 experiments that were formerly executed with a stretched 
 India-rubber tube, the results in both cases being iden- 
 tical. 1 
 
 1 Chladni remarks (" Akustik," p. 65) that it is usual to ascribe to Sauveur 
 the discovery, in 1701, of the nodes of vibration corresponding to the higher 
 
MELDE'S EXPERIMENTS. 133 
 
 To make, if possible, this identity still more evident to 
 you, a stout steel wire 28 feet in length is stretched 
 behind the table from side to side of the room. I take 
 the central point of this wire between my finger and 
 thumb, and allow my assistant to pluck one-half of it 
 aside. It vibrates, and the vibrations transmitted to the 
 other half are sufficiently powerful to toss into the air a 
 large sheet of paper placed astride the wire. With this 
 long wire, and with riders not of one-eighth of a square 
 inch, but of 30, 40, or 50 square inches in area, we may 
 repeat all the experiments which you have witnessed with 
 the musical string. The sheets of paper placed across the 
 nodes remain always in their places, while those placed 
 astride the ventral segments are tossed simultaneously into 
 the air when the shorter -segment of the wire is set in vi- 
 bration. In this case, when close to it, you can actually 
 see the division of the wire. 
 
 7. Meldds Experiments. 
 
 It is now time to introduce to your notice some recent 
 experiments on vibrating strings, which appeal to the eye 
 with a beauty and a delicacy far surpassing anything 
 attainable with our monochord. To M. Melde, of Mar- 
 burg, we are indebted for this new method of exhibiting 
 the vibrations of strings. The scale of the experiments 
 will be here modified so as to suit our circumstances. 
 
 First, then, you observe here a large tuning-fork T, 
 Fig. 45, with a small screw fixed into the top of one of its 
 prongs, by which a silk string can be firmly attached to 
 the prong. From the fork the string passes round a dis- 
 tant peg P, by turning which it may be stretched to any 
 required extent. When the bow is drawn across the fork, 
 an irregular flutter of the string is the only result. On 
 
 tones of strings ; but that Noble and Pigott had made the discovery in Ox- 
 ford in 1676, and that Sauveur declined the honor of the discovery when he 
 found that others had made the observation before him. 
 
L34 SOUND. 
 
 tightening it, however, when at the proper tension it 
 expands into a beautiful gauzy spindle six feet long, more 
 than six inches across at its widest part, and shining with 
 a kind of pearly lustre. The stretching force at the pres- 
 ent moment is such that the string swings to and fro as a 
 whole, its vibrations being executed in a vertical plane. 
 
 Relaxing the string gradually, when the proper tension 
 lias been reached, it suddenly divides into two ventral 
 segments, separated from each other by a sharply-defined 
 and apparently motionless node. 
 
 While the fork continues vibrating, if the string be 
 
 FIG. 45. 
 
 relaxed still further, it divides into three vibrating parts. 
 Slackening it still more, it divides into four vibrating parts. 
 And thus we might continue to subdivide the string into 
 ten, or even twenty ventral segments, separated from each 
 other by the appropriate number of nodes. 
 
 When white-silk strings vibrate thus, the nodes appear 
 perfectly fixed, while the ventral segments form spindles 
 of the most delicate beauty. Every protuberance of the 
 twisted string, moreover, writes its motion in a more or 
 less luminous line on the surface of the aerial gauze. 
 The four nodes of vibration just illustrated are represented 
 in Fig. 46 (next page), 1, 2, 3, 4. 1 
 
 1 The first experiment really made in the lecture was with a bar of 
 steel 62 inches long, 1$ inch wide, and an inch thick, bent into the shape 
 
STRINGS EXCITED BY TUNING-FORKS. 135 
 
 When the synchronism between fork and string is 
 perfect, the vibrations of the string are steady and long- 
 continued. A slight departure from synchronism, how- 
 ever, introduces unsteadiness, and the ventral segments, 
 
 FIG. 46. 
 
 though they may show themselves for a time, quickly 
 disappear. 
 
 In the experiments just executed the fork vibrated in 
 the direction of the length of the string. Every forward 
 
 of a tuning-fork, with its prongs 2 inches apart, and supported on a heavy 
 stand. The cord attached to it was 9 feet long and a quarter of an inch 
 thick. The prongs were thrown into vibration by striking them briskly 
 with two pieces of lead covered with pads and held one in each hand. The 
 prongs vibrated transversely to the cord. The vibrations produced by a 
 single stroke were sufficient to carry the cord through several of its subdi- 
 visions and back to a single ventral segment. That is to say, by striking 
 the prongs and causing the cord to vibrate as a whole, it could, by relaxing 
 the tension, be caused to divide into two, three, or four vibrating segments ; 
 and then, by increasing the tension, to pass back through four, three, and 
 two divisions, to one, without renewing the agitation of the prongs. The 
 cord was of such a character that, instead of oscillating to and fro in the 
 same plane, each of its points described a circle. The ventral segments, 
 therefore, instead of being flat surfaces were surfaces of revolution, and 
 were equally well seen from all parts of the room. The tuning-forks 
 employed in the subsequent illustrations were prepared for me by that ex- 
 cellent acoustic mechanician, Konig, of Paris, being such as are usually 
 employed in the projection of Lissajou's experiments. 
 
136 SOUND. 
 
 stroke of the fork raised a protuberance, which ran to the 
 fixed end of the string, and was there reflected ; so that 
 when the longitudinal impulses were properly timed they 
 produced a transverse vibration. Let us consider this 
 further. One end of this heavy cord is attached to a 
 hook A, Fig. 47, fixed in the wall. Laying hold of the 
 other end I stretch the cord horizontally, and then move 
 my hand to and fro in the direction of the cord. It swings 
 as a whole, and you may notice that always, when the cord 
 is at the limit of its swing, the hand is in its most forward 
 position. If it vibrate in a vertical plane, the hand, in 
 order to time the impulses properly, must be at its for- 
 ward limit at the moment the cord reaches the upper 
 
 FIG. 47. 
 
 boundary, and also at the moment it reaches the lower 
 boundary of its excursion. A little reflection will make it 
 plain that, in order to accomplish this, the hand must 
 execute a complete vibration while the cord executes a 
 semi-vibration ; in other words, the vibrations of the hand 
 must be twice as rapid as those of the cord. 
 
 Precisely the same is true of our tuning-fork. When 
 the fork vibrates in the direction of the string, the number 
 of vibrations which it executes in a certain time is twice 
 the number executed by the string itself. And if, while 
 arranged thus, a fork and string vibrate with sufficient 
 rapidity to produce musical notes, the note of the fork 
 will be an octave above that of the string. 
 
 But if, instead of the hand being moved to and fro in 
 the direction of this heavy cord, it is moved at right angles 
 
STRINGS EXCITED BY TUNING-FORKS. 
 
 137 
 
 to that direction, then every upward movement of the 
 hand coincides with an upward movement of the cord ; 
 every downward movement of the hand with a downward 
 movement of the cord. In fact, the vibrations of hand 
 and string, in this case, synchronize perfectly ; and if the 
 hand could emit a musical note, the cord would emit a 
 note of the same pitch. The same holds good when a vi- 
 brating fork is substituted for the vibrating hand. 
 
 Hence, if the string vibrate as a whole when the vibra- 
 tions of the fork are along it, it will divide into two ven- 
 tral segments when the vibrations are across it ; or, more 
 generally expressed, preserving the tension constant, what- 
 ever be the number of ventral segments produced by the 
 fork when its vibrations are in the direction of the string, 
 twice that number will be produced when the vibrations 
 are transverse to the string. The string A B, for example, 
 Figs. 48 and 49, passing over a pulley B, is stretched by a 
 definite weight (not shown in the figure). "When the tun- 
 ing-fork vibrates along it, as in Fig. 48, the string divides 
 
 Fie. 43 
 
 into two equal ventral segments. When the fork is turned 
 so that it shall vibrate at right angles to the string, the 
 number of ventral segments is four, Fig. 49, or double the 
 
 FIG. 49. 
 
 f ormer number. Attaching two strings of the same length 
 
138 SOUND. 
 
 to the same fork, the one parallel and the other perpendic- 
 ular to the direction of vibration, and stretching both with 
 equal weights, when the fork is caused to vibrate, one of 
 them divides itself into twice the number of ventral seg- 
 ments exhibited by the other. 
 
 A number of exquisite effects may be obtained with 
 these vibrating cords. The path described by any point 
 of any one of them may be studied, after the manner of 
 Dr. Young, by illuminating that point, and watching the 
 line of light which it describes. This is well illustrated by 
 a flat burnished silver wire, twisted so as to form a spiral 
 surface, from which, at regular intervals, the light flashes 
 when the wire is illuminated. When the vibration is 
 steady, the luminous spots describe straight lines of sunlike 
 brilliancy. On slackening the wire, but not so much as 
 to produce its next higher subdivision, upon the larger 
 motion of the wire are superposed a host of minor motions, 
 the combination of all producing scrolls of marvelous 
 complication and of indescribable splendor. 
 
 In reflecting on the best means of rendering these 
 effects visible, the thought occurred to me of employing a 
 fine platinum wire heated to redness by an electric current 
 Such a wire now stretches from a tuning-fork over a bridge 
 of copper, and then passes round a peg. The copper 
 bridge on the one hand and the tuning-fork on the other 
 are the poles of a voltaic battery, from which a current 
 passes through the wire and causes it to glow. On draw- 
 ing the bow across the fork, the wire vibrates as a whole ; 
 its two ends are brilliant, while its middle is dark, being 
 chilled by its rapid passage through the air. Thus you 
 have a shading off of incandescence from the ends to the 
 centre of the wire. On relaxing the tension, the wire 
 divides itself into two ventral segments ; on relaxing still 
 further, we obtain three ; still further, and the wire divides 
 into four ventral segments, separated from each other by 
 
NEW DETERMINATION OF LAWS OF VIBRATION. 139 
 
 three brilliant nodes. Bight and left from every node the 
 incandescence shades away until it disappears. You notice 
 also, when the wire settles into steady vibration, that the 
 nodes shine out with greater brilliancy than that possessed 
 by the wire before the vibration commenced. The reason 
 is this. Electricity passes more freely along a cold wire 
 than along a hot one. When, therefore, the vibrating 
 segments are chilled by their swift passage through the 
 air, their conductivity is improved, more electricity passes 
 through the vibrating than through the motionless wire, 
 and hence the augmented glow of the nodes. If, previous 
 to the agitation of the fork, the wire be at a bright-red 
 heat, when it vibrates its nodes may be raised to the tem- 
 perature of fusion. 
 
 8. New Mode of determining the Laws of Vibration. 
 
 We may extend the experiments of M. Melde to the 
 establishment of all the laws of vibrating strings. Here 
 are four tuning-forks, which we may call a, 5, c, d. whose 
 rates of vibration are to each other, as the numbers 1, 2, 4, 8. 
 To the largest fork is attached a string, a, stretched by a 
 weight, which causes it to vibrate as a whole. Keeping 
 the stretching weight the same, I determine the lengths of 
 the same string, which, when attached to the other three 
 forks, 5, c, d, swing as a whole. The lengths in the four 
 respective cases are as the numbers 8, 4, 2, 1. 
 
 From this follows the first law of vibration, already es- 
 tablished (p. 12) by another method, viz. : the length of 
 the string is inversely proportional to the rapidity of vi- 
 bration? 
 
 In this case the longest string vibrates as a whole when 
 
 1 A string steeped in a solution of the sulphate of quinine, and illuminated 
 by the violet rays of the electric lamp, exhibits brilliant fluorescence. When 
 the fork to which it is attached vibrates, the string divides itself into a series 
 of spindles, and separated from each other by more intensely luminous nodes, 
 emitting a light of the most delicate greenish-blue. 
 
140 SOUND. 
 
 attached to the fork a. I now transfer the string to J, still 
 keeping it stretched by the same weight. It vibrates when 
 b vibrates ; but how ? By dividing into two equal ventral 
 segments. In this way alone can it accommodate itself to 
 the swifter vibrating period of &. Attached to o, the 
 same string separates into four, while when attached to d, 
 it divides into eight ventral segments. The number of 
 the ventral segments is proportional to the rapidity of vi- 
 bration. It is evident that we have here, in a more deli- 
 cate form, a result which we have already established in 
 the case of our India-rubber tube set in motion by the hand. 
 It is also plain that this result might be deduced theoret- 
 ically from our first law. 
 
 We may extend the experiment. Here are two tuning- 
 forks separated from each other by the musical interval 
 called a fifth. Attaching a string to one of the forks, I 
 stretch the string until it divides into two ventral segments : 
 attached to the other fork, and stretched by the same 
 weight, it divides instantly into three segments when the 
 fork is set in vibration. Now, to form the interval of a 
 fifth, the vibrations of the one fork must be to those of the 
 other in the ratio of 2:3. The division of the string, 
 therefore, declares the interval. In the same way the divis- 
 ion of the string in relation to all other musical intervals 
 may be illustrated. 1 
 
 Again. Here are two tuning-forks, a and 5, one of 
 which (a) vibrates twice as rapidly as the other. A string 
 of silk is attached to , and stretched until it synchronizes 
 with the fork, and vibrates as a whole. Here is a second 
 string of the same length, formed by laying four strands 
 of the first one side by side. I attach this compound 
 thread to 5, and, keeping the tension the same as in the 
 last experiment, set ~b in vibration. The compound thread 
 
 1 The subject of musical intervals will be treated in a subsequent lect- 
 ure. 
 
LAWS OF VIBRATION. 141 
 
 synchronizes with J, and swings as a whole. Hence, as 
 the fork I vibrates with half the rapidity of #, by quad- 
 rupling the weight of the string we halved its rapidity of 
 vibration. In the same simple way it might be proved 
 that by augmenting the weight of the string nine times 
 we reduce the number of its vibrations to one-third. We 
 thus demonstrate the law : 
 
 The rapidity of vibration is inversely proportional to 
 the square root of the weight of the string. 
 
 An instructive confirmation of this result is thus ob- 
 tained : Attached to this tuning-fork is a silk string six 
 feet long. Two feet of the string are composed of four 
 strands of the single thread, placed side by side ; the re- 
 maining four feet are a single thread. A stretching force 
 is applied, which causes the string to divide into two ven- 
 tral segments. But how does it divide ? Not at its 
 centre, as is the case when the string is of uniform thick- 
 ness throughout, but at the precise point where the thick 
 string terminates. This thick segment, two feet long, is 
 now vibrating at the same rate as the thin segment four 
 feet long, a result which follows by direct deduction from 
 the two laws already established. 
 
 Here again are two strings of the same length and 
 thickness. One of them is attached to the fork #, the 
 other to the fork 5, which vibrates with twice the rapidity 
 of a. Stretched by a weight of 20 grains, the string 
 attached to ~b vibrates as a whole. Substituting b for #, a 
 weight of SO grains causes the string to vibrate as a 
 whole. Hence, to double the rapidity of vibration, we 
 must quadruple the stretching weight. In the same way 
 it might be proved that to treble the rapidity of vibra- 
 tion we should have to make the stretching weight nine- 
 fold. Hence our third law : 
 
 The rapidity of vibration is proportional to the square 
 root of the tension. 
 
142 
 
 SOUND. 
 
 Let us vary this experiment. This silk cord is carried 
 from the tuning-fork over the pulley, and stretched by a 
 weight of 80 grains. The string vibrates as a whole as 
 at A, Fig. 50. By diminishing the weight -the string is 
 
 20 grains. 
 
 B 
 
 9 grains. 
 
 C 
 
 5 grains. 
 
 relaxed, and finally divides sharply into two ventral seg- 
 ments, as at B, Fig. 50. What is now the stretching 
 weight? 20 grains, or one-fourth uf the first. With a 
 stretching weight of almost exactly 9 grains it divides into 
 three segments, as at c ; while with a stretching weight 
 of 5 grains it divides into four segments, as at D. Thus, 
 
TIMBKE: KLANGFARBE : CLANG-TINT. 
 
 then, a tension of one-fourth doubles, a tension of one- 
 ninth trebles, and a tension of one-sixteenth quadruples 
 the number of ventral segments. In general terms, the 
 number of segments is inversely proportional to the square 
 root of the tension. This result may be deduced by 
 reasoning from our first and third laws, and its realization 
 here confirms their correctness. 
 
 Thus, by a series of reasonings and experiments totally 
 different from those formerly employed, we arrive at 
 the self -same laws. In science, different lines of reason- 
 ing often converge upon the same truth ; and if we only 
 follow them faithfully, we are sure to reach that truth at 
 last. We may emerge, and often do emerge, from our 
 reasoning with a contradiction in our hands ; but on re- 
 tracing our steps, we infallibly find the cause of the con- 
 tradiction to be due, not to any lack of constancy in Nature, 
 but of accuracy in man. It is the millions of experiences 
 of this kind which science furnishes that give us our 
 present faith in the stability of Nature. 
 
 HARMONIC SOUNDS OR OVERTONES. 
 
 9. Timbre; Klangfarbe Clang -tint. 
 
 We now approach a portion of our subject which will 
 subsequently prove to be of the very highest importance. 
 It has been shown by the most varied experiments 
 that a stretched string can either vibrate as a whole, or 
 divide itself into a number of equal parts, each of which 
 vibrates as an independent string. Now it is not possible 
 to sound the string as a whole without at the same time 
 causing, to a greater or less extent, its subdivision ; that 
 is to say, superposed upon the vibrations of the whole 
 string we have always, in a greater or less degree, the 
 vibrations of its aliquot parts. The higher notes produced 
 7 
 
144 SOUND. 
 
 by these latter vibrations are called the harmonics of the 
 string. And so it is with other sounding bodies ; we have 
 in all cases a coexistence of vibrations. Higher tones 
 mingle with the fundamental one, and it is their inter- 
 mixture which determines what, for want of a better 
 term, we call the quality of the sound. The French call 
 it timbre, and the Germans call it Rlangfarbe* It is this 
 union of high and low tones that enables us to distinguish 
 one musical instrument from another. A clarionet and a 
 violin, for example, though tuned to the same fundamental 
 note, are not confounded ; the auxiliary tones of the one 
 are different from those of the other, and these latter tones, 
 uniting themselves to the fundamental tones of the two 
 instruments, destroy the identity of the sounds. 
 
 All bodies and instruments, then, employed for pro- 
 ducing musical sounds emit, besides their fundamental 
 tones, others due to higher orders of vibration. The Ger- 
 mans embrace all such sounds under the general term 
 Obertone. I think it will be an advantage if we in Eng- 
 land adopt the term overtones as the equivalent of the 
 term employed in Germany. One has occasion to envy 
 the power of the German language to adapt itself to 
 requirements of this nature. The term Klangfarbe, for 
 example, employed by Helmholtz is exceedingly expressive, 
 and we need its equivalent also. Color depends upon 
 rapidity of vibration, blue light bearing to red the same 
 relation that a high tone does to a low one. A simple 
 color has but one rate of vibration, and it may be regarded 
 as the analogue of a simple tone in music. A tone, then, 
 may be defined as the product of a vibration which cannot 
 be decomposed into more simple ones. A compound 
 color, on the contrary, is produced by the admixture of 
 two or more simple ones, and an assemblage of tones, such 
 
 1 " This quality of sound, sometimes called its register, color, or timbre." 
 (Thomas Young, " Essay on Music.") 
 
RELATION OF POINT PLUCKED TO OVERTONES. 145 
 
 as we obtain when the fundamental tone and the harmonics 
 of a string sound together, is called by the Germans a 
 Klang. May we not employ the English word dang to 
 denote the same thing, and thus give the term a precise 
 scientific meaning akin to its popular one ? And may we 
 not, like Helmholtz, add the word color or tint, to denote 
 the character of the clang, using the term clang-tint as the 
 equivalent of Klangfarbe ? 
 
 With your permission I shall henceforth employ these 
 terms ; and now it becomes our duty to look a little 
 more closely than we have hitherto done into the sub- 
 division of a string into its harmonic segments. Our 
 monochord with its stretched wire is before you. The 
 scale of the instrument is divided into 100 equal parts. 
 At the middle point of the wire stands the number 50 ; at 
 a point almost exactly one-third of its length from its 
 end stands the number 33 ; w r hile at distances equal to 
 one-fourth and one-fifth of its length from its end stand 
 the numbers 25 and 20 respectively. These numbers 
 are sufficient for our present purpose. When the wire 
 is plucked at 50 you hear its clang, rather hollow and 
 dull. When plucked at 33, the clang is different. When 
 plucked at 25, the clang is different from either of the 
 former. As we retreat from the centre of the string, the 
 clang-tint becomes more " brilliant," the sound more brisk 
 and sharp. What is the reason of these differences in the 
 sound of the same wire ? 
 
 The celebrated Thomas Young, once professor in this 
 Institution, enables us to solve the question. He proved 
 that when any point of a string is plucked, all the higher 
 tones which require that point for a node vanish from the 
 clang. Let me illustrate this experimentally. I pluck 
 the point 50, and permit the string to sound. It may be 
 proved that the first overtone, which corresponds to a di- 
 vision of the string into two vibrating parts, is now absent 
 
146 SOUND. 
 
 from the clang. If it were present, the damping of the 
 point 50 would not interfere with it, for this point would 
 be its node. But on damping the point 50 the fundamen- 
 tal tone is quenched, and no octave of that tone is heard. 
 Along with the octave its whole progeny of overtones, 
 with rates of vibration four times, six times, eight times 
 all even numbers of times the rate of the fundamental 
 tone, disappear from the clang. All these tones require 
 that a node should exist at the centre, where, according 
 to the principle of Young, it cannot now be formed. 
 Let us pluck some other point, say 25, and damp 50 as 
 before. The fundamental tone is now gone, but its oc- 
 tave, clear and full, rings in your ears. The point 50 in 
 this case not being the one plucked, a node can form 
 there ; it has formed, and the two halves of the string 
 continue to vibrate after the vibrations of the string as a 
 whole have been extinguished. Plucking the point 33, 
 the second harmonic or overtone is absent from the clang. 
 This is proved by damping the point 33. If the second 
 harmonic were on the string this would not affect it, for 
 33 is its node. The fundamental is quenched, but no tone 
 corresponding to a division of the string into three vibrat- 
 ing parts is now heard. The tone is not heard because it 
 was never there. 
 
 All the overtones which depend on this division, those 
 with six times, nine times, twelve times the rate of 
 vibration of the fundamental one, are also withdrawn from 
 the clang. Let us now pluck 20, damping 33 as before. 
 The second harmonic is not extinguished, but continues 
 to sound clearly and fully after the extinction of the fun- 
 damental tone. In this case the point 33 not being that 
 plucked, a node can form there, and the string can divide 
 itself into three parts accordingly. In like manner, if 25 
 be plucked and then damped, the third harmonic is not 
 heard ; but when a point between 25 and the end of the 
 
MINGLING OF OVERTONES WITH FUNDAMENTAL. 147 
 
 wire is plucked, and the point 25 damped, the third har- 
 monic is plainly heard. And thus we might proceed, the 
 general rule enunciated by Young, and illustrated by these 
 experiments, being, that when any point of a string is 
 plucked or struck, or, as Helmholtz adds, agitated with 
 a bow, the harmonic which requires that point for a node 
 vanishes from the general clang of the string. 
 
 10. Mingling of Overtones with fundamental. 
 The ^Eolian Harp. 
 
 You are now in a condition to estimate the influence 
 which these higher vibrations must have upon the quality 
 of the tone emitted by the string. The sounds which ring 
 in your ears so plainly after the fundamental tone is 
 quenched mingled with that note before it was extin- 
 guished. It seems strange that tones of such power could 
 be so masked by the fundamental one that even the disci- 
 plined ear of a musician is unable to separate the one from 
 the other. But Helmholtz has shown that this is due to 
 want of practice and attention. The musician's faculties 
 were never exercised in this direction. There are numer- 
 ous effects which the musician can distinguish, because 
 his art demands the habit of distinguishing them. But it 
 is no necessity of his art to resolve the clang of an instru- 
 ment into its constituent tones. By attention, however, 
 even the unaided ear can accomplish this, particularly if 
 the mind be informed beforehand what the ear has to bend 
 itself to find. 
 
 And this reminds me of an occurrence which took place 
 in this room at the beginning of my acquaintance with 
 Faraday. I wished to show him a peculiar action of an 
 electro-magnet upon a crystal. Everything was arranged, 
 when just before the magnet was excited he laid his hand 
 upon my arm and asked, " What am I to look for ? " Amid 
 the assemblage of impressions connected with an experi- 
 
14:8 SOUND. 
 
 ment, even this prince of experimenters felt the advantage 
 of having his attention directed to the special point to be 
 illustrated. Such help is the more needed when we at- 
 tempt to resolve into its constituent parts an effect so 
 intimately blended as the composite tones of a clang. 
 When we desire to isolate a particular tone, one way of 
 helping the attention is to sound that tone feebly on a 
 string of the proper length. Thus prepared, the ear 
 glides more readily from the single tone to that of the 
 same pitch in a composite clang, and detaches it more 
 readily from its companions. In the experiments executed 
 a moment ago, where our aim in each respective case was 
 to bring out the higher tone of the string in all its power, 
 we entirely extinguished its fundamental tone. It may, 
 however, be enfeebled without being destroyed. I pluck 
 this string at 33, and lay the feather lightly for a moment 
 on the string at 50. The fundamental tone is thereby so 
 much lowered that its octave can make itself plainly heard. 
 By again touching the string at 50, the fundamental tone 
 is lowered still more ; so that now its first harmonic is 
 more powerful than itself. You hear the sound of both, 
 and you might have heard them in the first instance by a 
 sufficient stretch of attention. 
 
 The harmonics of a string may be augmented or sub- 
 dued within wide limits. They may, as we have seen, be 
 masked by the fundamental tone, and they may also effect- 
 ually mask it. A stroke with a hard body is favorable, 
 while a stroke with a soft body is unfavorable to their 
 development. They depend, moreover, on the promptness 
 with which the body striking the string retreats after 
 striking. Thus they are influenced by the weight and 
 elasticity of the hammers in the pianoforte. They also de- 
 pend upon the place at which the shock is imparted. When, 
 for example, a string is struck in the centre, the harmonics 
 are less powerful than when it is 'truck near one end. 
 
THE CLANG OF PIANO-WIRES. 149 
 
 Helmholtz, who is equally eminent as a mathematician 
 and as an experimental philosopher, has calculated the 
 theoretic intensity of the harmonics developed in various 
 ways ; that is to say, the actual vis viva or energy of the 
 vibration, irrespective of its effects upon the ear. A single 
 example given by him will suffice to illustrate this subject. 
 Calling the intensity of the fundamental tone, in each case, 
 100, that of the second harmonic, when the string was 
 simply pulled aside at a point ^-th of its length from its 
 end and then liberated, was found to be 56-1, or a little 
 better than one-half. When the string was struck with 
 the hammer of a pianoforte, whose contact with the string 
 endured for fths of the period of vibration of the funda- 
 mental tone, the intensity of the same tone was 9. In this 
 case the second harmonic was nearly quenched. When, 
 however, the duration of contact was diminished to -^ths 
 of the period of the fundamental, the intensity of the har- 
 monic rose to 357; while, when the string was sharply 
 struck with a very hard hammer, the intensity mounted to 
 505, or to more than quintuple that of the fundamental 
 tone. 1 Pianoforte manufacturers have found that the most 
 pleasing tone is excited by the middle strings of their in- 
 struments, when the point against which the hammer 
 strikes is from ij-th to -Jth of the length of the wire from 
 its extremity. 
 
 Why should this be the case ? Helmholtz has given 
 the answer. Up to the tones which require these points 
 as nodes the overtones all form cords with the funda- 
 mental ; but the sixth and eighth overtones of the wire do 
 not enter into such chords ; they are dissonant tones, and 
 hence the desirability of doing away with them. This is 
 accomplished by making the point at which a node is re- 
 quired that on which the hammer falls. The possibility 
 of the tone forming is thereby shut out, and its injurious 
 effect is avoided. 
 
 1 "Lehre von den Tonempfindungen," p. 135. 
 
L50 SOUND. 
 
 The strings of the ^Eolian harp are divided into har- 
 monic parts by a current of air passing over them. The 
 instrument is usually placed in a window between the sash 
 and frame, so as to leave no way open to the entrance of 
 the air except over the strings. Sir Charles Wheatstone 
 recommends the stretching of a first violin-string at the 
 bottom of a door which does not closely fit. When the 
 door is shut, the current of air entering beneath sets the 
 string in vibration, and when a fire is in the room, the vi- 
 brations are so intense that a great variety of sounds are 
 simultaneously produced. 1 A gentleman in Basle once 
 constructed with iron wires a large instrument which he 
 called the weather-harp or giant-harp, and which, accord 
 ing to its maker, sounded as the weather changed. Its 
 sounds were also said to be evoked by changes of terres- 
 trial magnetism. Chladni pointed out the error of these 
 notions, and reduced the action of the instrument to that 
 of the wind upon its strings. 
 
 11. Young's Optical Illustrations. 
 
 Finally, with regard to the vibrations of a wire, the 
 experiments of Dr. Young, who was the first to employ 
 optical methods in such experiments, must be mentioned. 
 He allowed a sheet of sunlight to cross a pianoforte-wire, 
 and obtained thus a brilliant dot. Striking the wire he 
 caused it to vibrate, the dot described a luminous line like 
 that produced by the whirling of a burning coal in the air, 
 and the form of this line revealed the character of the vi- 
 bration. It was rendered manifest by these experiments 
 that the oscillations of the wire were not confined to a 
 single plane, but that it described in its vibrations curves 
 of greater or less complexity. Superposed upon the vi- 
 
 1 The action of such a string is substantially the same as that of the 
 siren. The string renders intermittent the current of air. Its action also 
 resembles that of a reed. See Lecture V. 
 
YOUNG'S OPTICAL ILLUSTRATIONS. 
 
 151 
 
 bration of the whole string were partial vibrations, which 
 revealed themselves as loops and sinuosities. Some of the 
 lines observed by Dr. Young are given in Fig. 51. Every 
 
 FIG. 51. 
 
 one of these figures corresponds to a distinct impression 
 made by the wire upon the surrounding air. The form of 
 the sonorous wave is affected by these superposed vibra- 
 tions, and thus they influence the clang-tint or quality of 
 the sound. 
 
152 SOUND 
 
 SUMMAKY OF CHAPTER III. 
 
 THE amount of motion communicated by a \ibrating 
 J string to the air is too small to be perceived as sound, 
 even at a small distance from the string. 
 
 When a broad surface vibrates in air, condensations 
 and rarefactions are more readily formed than when the 
 vibrating body is of small dimensions like a string. 
 Hence, when strings are employed as sources of musical 
 sounds, they are associated with surfaces of larger area 
 which take up their vibrations, and transfer them to the 
 surrounding air. 
 
 Thus the tone of a harp, a piano, a guitar, or a violin, 
 depends mainly upon the sound-board of the instrument. 
 
 The following four laws regulate the vibrations of 
 strings : The rate of vibrations is inversely proportional to 
 the length ; it is inversely proportional to the diameter ; it 
 is directly proportional to the square root of the stretching 
 weight or tension ; and it is inversely proportional to the 
 square root of the density of the string. 
 
 When strings of different diameters and densities are 
 compared, the law is, that the rate of vibration is in- 
 versely proportional to the square root of the weight of 
 the string. 
 
 When a stretched rope, or an India-rubber tube filled 
 with sand, with one of its ends attached to a fixed object, 
 receives a jerk at the other end, the protuberance raised 
 upon the tube runs along it as a pulse to the fixed end, 
 and, being there reflected, returns to the hand by which 
 the jerk was imparted. 
 
SUMMARY. 153 
 
 The time required for the pulse to travel from the 
 hand to the fixed end of the tube and back is that re- 
 quired by the whole tube to execute a complete vibration. 
 
 When a series of pulses are sent in succession along 
 the tube, the direct and reflected pulses meet, and by their 
 coalescence divide the tube into a series of vibrating parts, 
 called ventral segments, which are separated from each 
 other by points of apparent rest called nodes. 
 
 The number of ventral segments is directly propor- 
 tional to the rate of vibration at the free end of the tube. 
 
 The hand which produces these vibrations may move 
 through less than an inch of space ; while by the accumu- 
 lation of its impulses the amplitude of the ventral seg- 
 ments may amount to several inches, or even to several 
 feet. 
 
 If an India-rubber tube, fixed at both ends, be encir- 
 cled at its centre by the finger and thumb, when either of 
 its halves is pulled aside and liberated, both halves are 
 thrown into a state of vibration. 
 
 If the tube be encircled at a point one-third, one- 
 fourth, or one-fifth of its length from one of its ends, on 
 pulling the shorter segment aside and liberating it, the 
 longer segment divides itself into two, three, or four vibrat- 
 ing parts, separated from each other by nodes. 
 
 The number of vibrating segments depends upon the 
 rate of vibration at the point encircled by the finger and 
 thumb. 
 
 Here also the amplitude of vibration at the place en- 
 circled by the finger and thumb may not be more than a 
 fraction of an inch, while the amplitude of the ventral 
 segments may amount to several inches. 
 
 A musical string damped by a feather at a point one- 
 half, one-third, one-fourth, one-fifth, etc., of its length 
 from one of its ends, and having its shorter segment agi- 
 tated, divides itself exactly like the India-rubber tube. 
 
154 SOUND. 
 
 Its division may be rendered apparent by placing little 
 paper riders across it. Those placed at the ventral seg- 
 ments are thrown off, while those placed at the nodes 
 retain their places. 
 
 The notes corresponding to the division of a string 
 into its aliquot parts are called the harmonics of the 
 string. 
 
 When a string vibrates as a whole, it usually divides at 
 the same time into its aliquot parts. Smaller vibrations 
 are superposed upon the larger, the tones corresponding to 
 those smaller vibrations, and which we have agreed to call 
 overtones, mingling at the same time with the funda- 
 mental tone of the string. 
 
 The addition of these overtones to the fundamental 
 tone determines the timbre or quality of the sound, or, as 
 we have agreed to call it, the clang-tint. 
 
 It is the addition of such overtones to fundamental 
 tones of the same pitch which enables us to distinguish 
 the sound of a clarionet from that of a flute, and the 
 sound of a violin from both. Could the pure fundamental 
 tones of these instruments be detached, they would be 
 undistinguishable from each other ; but the different ad- 
 mixture of overtones in the different instruments renders 
 their clang-tints diverse, and therefore distinguishable. 
 
 Instead of the heavy India-rubber tube in the experi- 
 ment above referred to, we may employ light silk strings, 
 and, instead of the vibrating hand, we may employ vibrat- 
 ing tuning-forks, and cause the strings to swing as a whole, 
 or to divide themselves into any number of ventral seg- 
 ments. Effects of great beauty are thus obtained, and by 
 experiments of this character all the laws of vibrating 
 strings may be demonstrated. 
 
 "When a stretched string is plucked aside or agitated 
 by a bow, all the overtones which require the agitated 
 point for a node vanish from the clang: of the string. 
 
SUMMARY. 155 
 
 The point struck by the hammer of the piano is from 
 one-seventh to one-ninth of the length of the string from 
 its end : by striking this point, the notes which require it 
 as a node cannot be produced, a source of dissonance being 
 thus avoided. 
 
CHAPTER IY. 
 
 Fibrations of a Rod fixed at Both Ends : its Subdivisions and Corresponding 
 Overtones. Vibrations of a Rod fixed at One End. The Kaleidophone. 
 The Iron Fiddle and Musical Box. Vibrations of a Rod free at Both Ends. 
 The Claque-bois and Glass Harmonica. Vibrations of a Tuning-Fork : its 
 Subdivision and Overtones. Vibrations of Square Plates. Chladni's Dis- 
 coveries. Wheatstone's Analysis of the Vibrations of Plates. Chladni's 
 Figures. Vibrations of Disks and Bells. Experiments of Faraday and 
 Strehlke. 
 
 1. Transverse Vibrations of a Rod fixed at Both Ends. 
 OUR last chapter was devoted to the transverse vibrations 
 of strings. This one I propose devoting to the trans- 
 verse vibrations of rods, plates, and bells, commencing 
 with the case of a rod fixed at both ends. Its modes of 
 vibration are exactly those of a string. It vibrates as a 
 whole, and can also divide itself into two, three, four, or 
 more vibrating parts. But, for a reason to be immediately 
 assigned, the laws which regulate the pitch of the succes- 
 sive notes are entirely different in the two cases. Thus, 
 when a string divides into two equal parts, each of its 
 halves vibrates with twice the rapidity of the whole; 
 while, in the case of the rod, each of its halves vibrates 
 with nearly three times the rapidity of the whole. With 
 greater strictness, the ratio of the two rates of vibration is 
 as 9 is to 25, or as the square of 3 to the square of 5. In 
 Fig. 52, a a' , c c', l> V , d d ', are sketched the first four 
 modes of vibration of a rod fixed at both ends : the succes- 
 sive rates of vibration in the four cases bear to each other 
 the following relation : 
 
 Number of nodes .0 1 2 8 
 
 Number of vibrations .9 25 49 81 
 
TRANSVERSE VIBRATIONS OF RODS FIXED AT ONE END. 157 
 
 the last row of figures being the squares of the odd num- 
 bers 3, 5, 7, 9. 
 
 In the case of a string, the vibrations are maintained 
 by a tension externally applied ; in the case of a rod, the 
 vibrations are maintained by the elasticity of the rod 
 itself. The modes of division are in both cases the same, 
 
 FIG 52. 
 
 f 
 
 but the forces brought into play are different, and hence 
 also the successive rates of vibration. 
 
 2. Transverse Vibrations of a Rod fixed at One End. 
 
 Let us now pass on to the case of a rod fixed at one end 
 and free at the other. Here also it is the elasticity of the 
 material, and not any external tension, that sustains the 
 vibrations. Approaching, as usual, sonorous vibrations 
 through more grossly mechanical ones, I fix this long rod 
 of iron, n o, Fig. 53, in a vice, draw it aside, and liberate 
 it. To make its vibrations more evident, its shadow is 
 thrown upon a screen. The rod oscillates as a whole to 
 and fro, between the points p p f . But it is capable of 
 other modes of vibration. Damping it at the point a, by 
 holding it gently there between the finger and thumb, 
 and striking it sharply between a and 0, the rod divides 
 into two vibrating parts, separated by a node as shown in 
 Fig. 54. You see upon the screen a shadowy spindle be- 
 tween a and the vice below, and a shadowy fan above #, 
 with a black node between both. The division may be 
 effected without damping #, by merely imparting a suffi- 
 ciently sharp shock to the rod between a and o. In this 
 case, however, besides oscillating in parts, the rod oscil 
 
158 
 
 SOUND. 
 
 lates as a whole, the partial oscillations being superposed 
 upon the large one. 
 
 You notice, moreover, that the amplitude of the par- 
 tial oscillations depends upon the promptness of the stroke. 
 When the stroke is sluggish, the partial division is but 
 feebly pronounced, the whole oscillation being most 
 marked. But when the shock is sharp and prompt, the 
 whole oscillation is feeble, and the partial oscillations are 
 
 FIG. 53. 
 * 
 
 FIG. 54. 
 
 executed with vigor. If the vibrations of this rod were 
 rapid enough to produce a musical sound, the oscillation 
 of the rod as a whole would correspond to its fundamental 
 tone, while the division of the rod into two vibrating parts 
 would correspond to the first of its overtones. If, more- 
 over, the rod vibrated as a whole and as a divided rod at 
 the same time, the fundamental tone and the overtone 
 
CHLADNI'S TONOMETER. 159 
 
 would be heard simultaneously. By damping the proper 
 point and imparting the proper shock, we can still further 
 subdivide the rod, as shown in Fig. 55. 
 
 3. Chladni's^ Tonometer : the Iron Fiddle, Musical Box, 
 and the Kaleidophone. 
 
 And now let us shorten our rod, so as to bring its vibra- 
 tions into proper relation to our ears. When it is about 
 four inches long, it emits a low musical sound. When 
 further shortened, the tone is higher ; and, by continuing 
 to shorten the rod, the speed of vibration is augmented, 
 until finally the sound becomes painfully acute. These 
 musical vibrations differ only in rapidity from the grosser 
 oscillations which a moment ago appealed to the eye. 
 
 The increase in the rate of vibrations here observed is 
 ruled by a definite law; the number of vibrations exe- 
 cuted at a given time is inversely proportional to the 
 square of the length of the vibrating rod. You hear the 
 sound of this strip of brass, two inches long, as the fiddle- 
 bow is passed over its end. Making the length of the 
 strip one inch, the sound is the double octave of the last 
 one ; the rate of vibration is augmented four times. Thus, 
 by doubling the length of the vibrating strip, we reduce 
 its rate of vibration to one-fourth ; by trebling the length, 
 we reduce the rate of vibration to one-ninth ; by quad- 
 rupling the length, we reduce the vibrations to one- 
 sixteenth, and so on. It is plain that, by proceeding in 
 this way, we should finally reach a length where the vibra- 
 tions would be sufficiently slow to be counted. Or, it is 
 plain that, beginning with a long strip whose vibrations 
 could be counted, we might, by shortening, not only make 
 the strip sound, but also determine the rates of vibration 
 corresponding to its different tones. Supposing we start 
 with a strip 36 inches long, which vibrates once in a 
 second, the strip reduced to 12 inches would, according to 
 
160 SOUND. 
 
 the above law, execute 9 vibrations a second : reduced to 
 6 inches, it would execute 36, to 3 inches, 144 ; while, if 
 reduced to 1 inch in length, it would execute 1,296 vibra- 
 tions in a second. It is easy to fill the spaces between the 
 lengths here given, and thus to determine the rate of vibra- 
 tion corresponding to any particular tone. This method 
 was proposed and carried out by Chladni. 
 
 A musical instrument may be formed of short rods. 
 Into this common wooden tray a number of pieces of 
 stout iron wire of different lengths are fixed, being ranged 
 in a semicircle. When the fiddle-bow is passed over the 
 series, we obtain a succession of very pleasing notes. A 
 competent performer could certainly extract very tolerable 
 music from a sufficient number of these iron pins. The 
 iron fiddle (molon de fer) is thus formed. The notes of 
 the ordinary musical box are also produced by the vibra- 
 tions of tongues of metal fixed at one end. Pins are fixed 
 in a revolving cylinder, the free ends of the tongues are 
 lifted by these pins and then suddenly let go. The 
 tongues vibrate, their length and strength being so ar- 
 ranged as to produce in each particular case the proper 
 rapidity of vibration. 
 
 Sir Charles Wheatstone has devised a simple and ingen- 
 ious optical method for the study of vibrating rods fixed 
 at one end. Attaching light glass beads, silvered within, 
 to the end of a metal rod, and allowing the light of a lamp 
 or candle to fall upon the bead, he obtained a small spot 
 intensely illuminated. When the rod vibrated, this spot 
 described a brilliant line which showed the character of 
 the vibration. A knitting-needle, fixed in a vice with a 
 small bead stuck on to it by marine glue, answers perfectly 
 as an illustration. In Wheatstone's more complete instru- 
 ment, which he calls a kaleidophone, the vibrating rods are 
 firmly screwed into a massive stand. Extremely beautiful 
 figures are obtained by this simple contrivance, some of 
 
THE KALEIDOPHONE. 
 
 which may now be projected on a magnified scale upon 
 the screen before you. 
 
 Fixing the rod horizontally in the vice, a condensed 
 beam is permitted to fall upon the silvered bead, a spot of 
 suulike brilliancy being thus obtained. Placing a lens in 
 front of the bead, a bright image of the spot is thrown 
 upon the screen, the needle is then drawn aside, and 
 suddenly liberated. The spot describes a ribbon of light, 
 at first straight, but speedily opening out into an ellipse, 
 passing into a circle, and then again through a second 
 ellipse back to a straight line. This is due to the fact that 
 a rod held thus in a vice vibrates not only in the direction 
 in which it is drawn aside, but also at right angles to this 
 direction. The curve is due to the combination of two 
 rectangular vibrations. 1 "While the rod is thus swinging as 
 a whole, it may also divide itself into vibrating parts. By 
 properly drawing a violin-bow across the needle, this ser- 
 rated circle, Fig. 56, is obtained, a number of small undu- 
 lations being superposed upon the large 
 one. You moreover hear a musical tone, 
 which you did not hear when the rod 
 vibrated as a whole only ; its oscilla- 
 tions, in fact, were then too slow to 
 excite such a tone. The vibrations 
 which produce these sinuosities, and 
 which correspond to the first division 
 of the rod, are executed with about 6J times the rapid 
 ity of the vibrations of the rod swinging as a whole. 
 Again I draw the bow ; the note rises in pitch, the ser- 
 rations run more closely together, forming on the screen 
 a luminous ripple more minute and, if possible, more 
 
 . l Chladni also observed this compounding of vibrations, and executed 
 a series of experiments, which, in their developed form, are those of the 
 kaleidophone. The composition of vibrations will be studied at some length 
 in a subsequent lecture. 
 
162 
 
 SOUND. 
 
 FIG. 5T. 
 
 beautiful than the last one, Fig. 57. Here we have the 
 second division of the rod, the sinuosities of which corre- 
 spond to 17|-| times its rate of vibra- 
 tion as a whole. Thus every change in 
 the sound of the rod is accompanied 
 by a change of the figure upon the 
 screen. 
 
 The rate of vibration of the rod as a 
 whole is to the rate corresponding to 
 its first division nearly as the square 
 of 2 is to the square of 5, or as 4 : 25. From the first 
 division onward the rates of vibration are approximately 
 proportional to the squares of the series of odd numbers 
 3, 5, 7, 9, 11, etc. Supposing the vibrations of the rod as 
 a whole to number 36, then the vibrations corresponding 
 to this and to its successive divisions would be expressed 
 approximately by the following series of numbers : 
 
 36, 225, 625, 1225, 2025, etc. 
 In Fig. 58, a, 5, <?, d, e, are shown the modes of division 
 
 Fia. 58. 
 
 \ 
 
 corresponding to this series of numbers. You will not 
 fail to observe that these overtones of a vibrating rod rise 
 far more rapidly in pitch than the harmonics of a string. 
 Other forms of vibration may be obtained bv smartly 
 
FIGURES OF THE KALEIDOPHONE. 
 
 163 
 
 striking the rod with the finger near its fixed end. In fact, 
 an almost infinite variety of luminous scrolls can be thus 
 produced, the beauty of which may be inferred from the 
 subjoined figures first obtained by Sir C. Wheatstone. They 
 may be produced by illuminating the bead with sunlight, 
 or with the light of a lamp or candle. The scrolls, more- 
 
 FIG. 59. 
 
 
 
 over, may be doubled by employing two candles instead 
 of one. Two spots of light then appear, each of which 
 
164: SOUND. 
 
 describes its own luminous line when the knitting-needle 
 is set in vibration. In a subsequent lecture we shall be- 
 come acquainted with "Wheatstone's application of his 
 method to the study of rectangular vibrations. 
 
 4. Transverse Vibrations of a Rod free at Both Ends. 
 The Claque^bois and Glass Harmonica. 
 
 From a rod or bar fixed at one end, we will now pass 
 to rods or bars free at both ends ; for such an arrangement 
 has also been employed in music. By a method afterward 
 to be described, Chladni, the father of modern acoustics, 
 determined experimentally the modes of vibration pos- 
 sible to such bars. The simplest mode of division in this 
 case occurs when the rod is divided by two nodes into 
 three vibrating parts. This division is easily illustrated 
 by a flexible box ruler, six feet long. Holding it at about 
 twelve inches from its two ends between the forefinger 
 and thumb of each hand, and shaking it, or causing its 
 centre to be struck, it vibrates, the middle segment form- 
 ing a shadowy spindle, and the two ends forming fans. 
 The shadow of the ruler on the screen renders the mode 
 of vibration very evident. In this case the distance of 
 each node from the end of the ruler is about one-fourth 
 
 FIG. 60. 
 
 of the distance between the two nodes. In its second 
 mode of vibration the rod or ruler is divided into four 
 vibrating parts by three nodes. In Fig. 60, 1 and 2, 
 
THE CLAQUE-BOIS. 165 
 
 these respective modes of division are shown. Looking 
 at the edge of the ruler 1, the dotted lines cutting a a', 
 b V, show the manner in which the segments bend up and 
 down when the first division occurs, while c c ', d d', show 
 the mode of vibration corresponding to the second division. 
 The deepest tone of a rod free at both ends is higher than 
 the deepest tone of a rod fixed at one end in the propor- 
 tion of 4 : 25. Beginning with the first two nodes, the rates 
 of vibration of the free bar rise in the following propor- 
 tion: 
 
 Number of nodes . . 2, 3, 4, 6, 6, 7. 
 
 Numbers to the squares of which the ) 
 pitch is approximately proportional \ 3 ' 5 ' 7 ' 9 ' U 13 ' 
 
 Here, also, we have a similarly rapid rise of pitch to that 
 noticed in the last two cases. 
 
 For musical purposes the first division only of a free 
 rod has been employed. When bars of wood of different 
 lengths, widths, and depths, are strung along a cord which 
 passes through the nodes, we have the daqu&bois of the 
 French, an instrument now before you, A B, Fig. 61. Sup 
 
 FIG 61. 
 
 porting the cord at one end by a hook Jc and holding it at 
 the other in the left hand, I run the hammer h along the 
 
166 
 
 SOUND. 
 
 series of bars, and produce an agreeable succession of musi- 
 cal tones. Instead of using the cord, the bars may rest at 
 their nodes on cylinders of twisted straw ; hence the name 
 " straw - fiddle," sometimes applied to this instrument. 
 Chladni informs us that it is introduced as a play of bells 
 (Glockenspiel) into Mozart's opera of "Die Zauberflote." 
 If, instead of bars of wood, we employ strips of glass, 
 we have the glass harmonica. 
 
 5. Vibrations of a Tuning-fork. 
 
 From the vibrations of a bar free at both ends, it is 
 easy to pass to the vibrations of a tuning-fork, as analyzed 
 by Chladni. Supposing a #, Fig. 62, to represent a straight 
 
 steel bar, with the nodal points corresponding to its first 
 mode of division marked by the transverse dots. Let the 
 bar be bent to the form ~b I ; the two nodal points still re- 
 main, but they have approached nearer to each other. The 
 tone of the bent bar is also somewhat lower than that of 
 the straight one. Passing through various stages of bend- 
 ing, c c, d d, we at length convert the bar into a tuning- 
 fork e e, with parallel prongs ; it still retains its two nodal 
 points, which, however, are much closer together than 
 when the bar was straight. 
 
 When such a fork sounds its deepest note, its free ends 
 oscillate as in Fig. 63, where the prongs vibrate between 
 
NODES AND OVERTONES OF TUNING-FORK. 167 
 
 the limits J and n, and f and m, and where p and q are 
 the nodes. There is no division of a tuning-fork corre- 
 sponding to the division of a straight bar by three nodes. 
 In its second mode of division, which corresponds to the 
 first overtone of the fork, we have a node on each prong, 
 and two at the bottom. The principle of Young, referred 
 to at p. 145, extends also to tuning-forks. To free the 
 fundamental tone from an overtone, you draw your bow 
 across the fork at the place where the node is required to 
 form the latter. In the third mode of division there are 
 two nodes on each prong and one at the bottom. In the 
 fourth division there are two nodes on each prong and 
 two at the bottom ; while in the fifth division there are 
 three nodes on each prong and one at the bottom. The 
 first overtone of the fork requires, according to Chladni, 6J 
 times the number of vibrations of the fundamental tone. 
 
 It is easy to elicit the overtones of tuning-forks. Here, 
 for example, is our old series, vibrating respectively 256, 
 320, 384, and 512 times in a second. In passing from 
 the fundamental tone to the first overtone of each, you 
 notice that the intervil is vastly greater than that between 
 the fundamental tone and the first overtone of a stretched 
 string. From the numbers just mentioned we pass at 
 once to 1,600, 2.000, 2,400, and 3,200 vibrations a second. 
 Chladni's numbers, however, though approximately correct, 
 are not always rigidly verified by experiment. A pair of 
 forks, for example, may have their fundamental tones in 
 perfect unison and their overtones discordant. Two such 
 forks are now before you. When the fundamental tones 
 of both are sounded, the unison is perfect ; but when the 
 first overtones of both are sounded, they are not in unison. 
 You hear rapid " beats," which grate upon the ear. By 
 loading one of the forks with wax, the two overtones may 
 be brought into unison ; but now the fundamental tones 
 produce loud beats when sounded together. This could 
 
 8 
 
168 SOUND. 
 
 not occur if the first overtone of each fork was produced 
 by a number of vibrations exactly 6J times the rate of its 
 fundamental. In a series of forks examined by Helmholtz, 
 the number of vibrations of the first overtone varied from 
 5*6 to 6*6 times that of the fundamental. 
 
 Starting from the first overtone, and including it, the 
 rates of vibration of the whole series of overtones are as 
 the squares of the numbers 3, 5, Y, 9, etc. That is to say, 
 in the time required by the first overtone to execute 9 
 vibrations, the second executes 25, the third 49, the fourth 
 81, and so on. Thus the overtones of the fork rise with 
 far greater rapidity than those of a string. They also 
 vanish more speedily, and hence adulterate to a less extent 
 the fundamental tone by their admixture. 
 
 6. ChladnVs Figures,. 
 
 The device of Chladni for rendering these sonorous 
 vibrations visible has been of immense importance to the 
 science of acoustics. Lichtenberg had made the experi- 
 ment of scattering an electrified powder over an electrified 
 resin-cake, the arrangement of the powder revealing the 
 electric condition of the surface. This experiment sug- 
 gested to Chladni the idea of rendering sonorous vibrations 
 visible by means of sand strewed upon the surface of the 
 vibrating body. Chladni's own account of his discovery is 
 of sufficient interest to justify its introduction here : 
 
 " As an admirer of music, the elements of which I had 
 begun to learn rather late, that is, in my nineteenth yea*r, 
 I noticed that the science of acoustics was more neglected 
 than most other portions of physics. This excited in me 
 the desire to make good the defect, and by new discovery 
 to render some service to this part of science. In 1785 I 
 had observed that a plate of glass or metal gave different 
 sounds when it was struck at different places, but I could 
 nowhere find any reformation regarding the corresponding 
 

 London. Longmans &. C 
 
NODAL LINES RENDERED VISIBLE. 169 
 
 modes of vibration. At this time there appeared in the 
 journals some notices of an instrument made in Italy by 
 the Abbe Mazzochi, consisting of bells, to which one or 
 two violin-bows were applied. This suggested to me the 
 idea of employing a violin-bow to examine the vibrations 
 of different sonorous bodies. When I applied the bow to 
 a round plate of glass fixed at its middle it gave different 
 sounds, which, compared with each other, were (as regards 
 the number of their vibrations) equal to the squares of 2, 
 3, 4, 5, etc. ; but the nature of the motions to which these 
 sounds corresponded, and the means of producing each of 
 them at will, were yet unknown to me. The experiments 
 on the electric figures formed on a plate of resin, dis- 
 covered and published by Lichtenberg, in the memoirs of 
 the Royal Society of Gottingen, made me presume that 
 the different vibratory motions of a sonorous plate might 
 also present different appearances, if a little sand or some 
 other similar substance were spread over the surface. On 
 employing this means, the first figure that presented itself 
 to my eyes upon the circular plate already mentioned 
 resembled a star with ten or twelve rays, and the very 
 acute sound, in the series alluded to, was that which 
 agreed with the square of the number of diametrical lines." 
 
 7. Vibrations of Square Plates : Nodal Lines. 
 
 I will now illustrate the experiments of Chladni, com- 
 mencing with a square plate of glass held by a suitable 
 clamp at its centre. The plate might be held with the 
 finger and thumb, if they could only reach far enough. 
 Scattering fine sand over the plate, the middle point of 
 one of its edges is damped by touching it with the finger- 
 nail, and a bow is drawn across the edge of the plate, near 
 one of its corners. The sand is tossed away from certain 
 parts of the surface, and collects along two nodal lines 
 which divide the large square into four smaller ones, as in 
 
170 
 
 SOUND. 
 
 Fig. 64:. This division of the plate corresponds to its 
 deepest tone. 
 
 The signs -f- and employed in these figures denote 
 
 FIG. 64. 
 
 FIG. 65. 
 
 FIG. 66. 
 
 that the two squares on which they occur are always mov- 
 fng in opposite directions. When the squares marked -|- 
 are above the average level of the plate those marked 
 are below it ; and when those marked are above the 
 average level those marked -|- are below it. The nodal 
 lines mark the boundaries of these opposing motions. 
 They are the places of transition from the one motion to 
 the other, and are therefore unaffected by either. 
 
 Scattering sand once more over its surface, I damp one 
 of the corners of the plate, and excite it by drawing the 
 bow across the middle of one of its sides. The sand 
 dances over the surface, and finally ranges itself in two 
 sharply-defined ridges along its diagonals, Fig. 65. The 
 note here produced is a fifth above the last. Again damp- 
 ing two other points, and drawing the bow across the 
 centre of the opposite side of the plate, we obtain a far 
 shriller note than in either of the former cases, and the 
 manner in which the plate vibrates to produce this note is 
 represented in Fig. 66. 
 
 Thui far plates of glass have been employed held by a 
 clamp at the centre. Plates of metal are still more suitable 
 for such experiments. Here is a plate of brass, 12 inches 
 square, and supported on a suitable stand. Damping it 
 
VIBRATIONS OF SQUARE PLATES. 171 
 
 with the finger and thumb of my left hand at two points 
 of its edge, and drawing the bow with my right across a 
 vibrating portion of the opposite edge, the complicated 
 pattern represented in Fig. 67 is obtained. 
 
 Fio. 6T. 
 
 The beautiful series of patterns shown on page 172 
 were obtained by Chladni, by damping and exciting square 
 plates in different ways. It is not only interesting but 
 startling to see the suddenness with which these sharply- 
 defined figures are formed by the sweep of the bow of a 
 skillful experimenter. 
 
 8. WTieatstone* s Analysis of the Vibrations of 
 Square Plates. 
 
 And now let us look a little more closely into the 
 mechanism of these vibrations. The manner in which a 
 bar free at both ends divides itself when it vibrates trans- 
 versely has been already explained. Rectangular pieces 
 of glass or of sheet metal the glass strips of the har- 
 monica, for example also obey the laws of free rods and 
 bars. In Fig. 69 is drawn a rectangle &, with the nodes 
 corresponding to its first division marked upon it, and 
 underneath it is placed a figure showing the manner in 
 
VIBRATIONS OF SQUARE PLATES. 173 
 
 which the rectangle, looked at edgeways, bends up and 
 down when it is set in vibration. 1 For the sake of plain- 
 ness the b\ending is greatly exagger- FIG. eo. 
 ated. The figures 5 and c indicate 
 that the vibrating parts of the plate 
 alternately rise above and fall below 
 the average level of the plate. At ;; ; 
 
 one moment, for example, the centre c :: ^ -^ 
 
 of the plate is above the level and 
 its ends below it, as at 5 / while at the next moment its 
 centre is below and its two ends above the average level, 
 as at c. The vibrations of the plate consist in the quick 
 successive assumption of these two positions. Similai 
 remarks apply to all other modes of division. 
 
 ISfow suppose the rectangle gradually to widen, till it 
 becomes a square. There then would be no reason why 
 the nodal lines should form parallel to one pair of sides 
 rather than to the other. Let us now examine what would 
 be the effect of the coalescence of two such systems of vi- 
 brations. 
 
 To keep your conceptions clear, take two squares of 
 glass and draw upon each of them the nodal lines belong- 
 ing to a rectangle. Draw the lines on one plate in white, 
 and on the other in black ; this will help you to keep the 
 plates distinct in your mind as you look at them. ~Now 
 lay one square upon the other so that their nodal lines 
 shall coincide, and then realize with perfect mental clear- 
 ness both plates in a state of vibration. Let us assume, 
 in the first instance, that the vibrations of the two plates 
 are concurrent ; that the middle segment and the end seg- 
 ments of each rise and fall together ; and now suppose the 
 
 1 I copy this figure from Sir C. Wheatstone's memoir ; the nodes, 
 however, ought to be nearer the ends, and the free terminal portions of 
 the dotted lines ought not to be bent upward or downward. The nodal 
 lines in the next two figures are also drawn too far from the edge of the 
 plates. 
 
174: SOUND. 
 
 vibrations of. one plate transferred to the other. What 
 would be the result? Evidently vibrations of a double 
 amplitude on the part of the plate which has received this 
 accession. But suppose the vibrations of the two plates, 
 instead of being concurrent, to be in exact opposition tc 
 each other that when the middle segment of the one rises 
 the middle segment of the other falls what would be the 
 consequence of adding them together ? Evidently a neu- 
 tralization of all vibration. 
 
 Instead of placing the plates so that their nodal lines 
 coincide, set these lines at right angles to each other. 
 That is to say, push A over A', Fig. 70. In these figures the 
 
 letter p means positive, indicating, in the section where it 
 occurs, a motion of the plate upward ; while N means nega- 
 tive, indicating, where it occurs, a motion downward. You 
 have now before you a kind of check pattern, as shown in 
 the third square, consisting of a square s in the middle, a 
 smaller square ~b at each corner, and four rectangles at the 
 middle portions of the four sides. Let the plates vibrate, 
 and let the vibrations of their corresponding sections be 
 concurrent, as indicated by the letters P and N ; and then 
 suppose the vibrations of one of them transferred to the 
 other. What must result? A moment's reflection will 
 show you that the big middle square s will vibrate with 
 augmented energy ; the same is true of the four smaller 
 squares 5, J, 5, &, at the four corners; but you will at 
 
ANALYSIS OF VIBRATIONS. 175 
 
 once convince yourselves that the vibrations in the four 
 rectangles are in opposition, and that where their ampli- 
 tudes are equal they will destroy each other. The middle 
 point of each side of the plate of glass would, therefore, be 
 a point of rest ; the points where the nodal lines of the' 
 two plates cross each other would also be points of rest. 
 Draw a line through every three of these points and you 
 will obtain a second square inscribed in the first. The 
 sides of this square are lines of no motion. 
 
 We have thus far been theorizing. Let us now clip 
 a square plate of glass at a point near the centre of one 
 of its edges, and draw the bow across the adjacent corner 
 of the plate. When the glass is homogeneous, a close 
 approximation to this inscribed square is obtained. The 
 reason is that when the plate is agitated in this manner 
 the two sets of vibrations which we have been considering 
 actually coexist in the plate, and produce the figure due to 
 their combination. 
 
 Again, place the squares of glass one upon the other 
 exactly as in the last case ; but now, instead of supposing 
 them to concur in their vibrations, let their corresponding 
 sections oppose each other : that is, let A cover A', Fig. 71. 
 
 FIG. 71. 
 
 Then it is manifest that on superposing the vibrations the 
 middle point of our middle square must be a point of rest ; 
 for here the vibrations are equal and opposite. The inter 
 sections of the nodal lines are also points of rest, and 
 
176 SOUND. 
 
 so also is every corner of the plate itself, for here the 
 added vibrations are also equal and opposite. We have 
 thus fixed four points of rest on each diagonal of the 
 square. Draw the diagonals, and they will represent the 
 nodal lines consequent on the superposition of the two vi- 
 brations. 
 
 These two systems actually coexist in the same plate 
 when the centre is clamped and one of the corners touched, 
 while the fiddle-bow is drawn across the middle of one of 
 the sides. In this case the sand which marks the lines of 
 rest arranges itself along the diagonals. This, in its sim- 
 plest possible form, is Sir C. Wheatstone's analysis of these 
 superposed vibrations. 
 
 9. Vibrations of Circular Plates. 
 
 Passing from square plates to round ones, we also 
 obtain various beautiful effects. This disk of brass is sup- 
 ported horizontally upon an upright stand : it is black- 
 ened, and fine white sand is scattered lightly over it. The 
 disk is capable of dividing itself in various ways, and of 
 emitting notes of various pitch. I sound the lowest funda- 
 mental note of the disk by touching its edge at a certain 
 point, and drawing the bow across the edge at a point 
 45 degrees distant from the damped one. You hear the 
 note and you see the sand. It quits the four quadrants 
 of the disk, and ranges itself along two of the diameters, 
 Fig. 72, A (next page). When a disk divides itself thus 
 into four vibrating segments, it sounds its deepest note. I 
 stop the vibration, clear the disk, and once more scatter 
 sand over it. Damping its edge, and drawing the bow 
 across it at a point 30 degrees distant from the damped 
 one, the sand immediately arranges itself in a star. We 
 have here six vibrating segments, separated from each 
 other by their appropriate nodal lines, Fig. 72, B. Again 
 I damp a point, and agitate another nearer to the damped 
 
VIBRATIONS OF CIRCULAR PLATES. 
 
 177 
 
 one than in the last instance ; the disk divides itself into 
 eight vibrating segments with lines of sand between them, 
 Fig. 72, c. In this way the disk may be subdivided into 
 ten, twelve, fourteen, sixteen sectors, the number of sectors 
 being always an even one. As the division becomes more 
 
 minute the vibrations become more rapid, and the pitch 
 consequently more high. The note emitted by the sixteen 
 segments into which the disk is now divided is so acute as 
 to be almost painful to the ear. Here you have Chladni's 
 first discovery. You can understand his emotion on wit- 
 nessing this wonderful effect, " which no mortal had pre- 
 viously seen." By rendering the centre of the disk free, 
 and damping appropriate points of the surface, nodal cir- 
 cles and other curved lines may be obtained. 
 
 The rate of vibration of a disk is directly proportional 
 to its thickness, and inversely proportional to the square 
 of its diameter. Of these three disks two have the same 
 diameter, but one is twice as thick as the other ; two of 
 them are of the same thickness, but one has half the 
 diameter of the other. According to the law just enun- 
 ciated, the rules of vibration of the disks are as the num- 
 bers 1, 2, 4. When they are sounded in succession, the 
 musical ears present can testify that they really stand to 
 each other in the relation of a note, its octave, and its 
 double octave. 
 
178 
 
 SOUND. 
 
 10. Strehlke and Faraday^s Experiments : Deportment 
 of Light Powders. 
 
 The actual movement of the sand toward the nodal 
 lines may be studied by clogging the sand with a semi-fluid 
 substance. When gum is employed to retard the motion 
 of the particles, the curves which they individually de- 
 scribe are very clearly drawn upon the plates. M. Strehlke 
 has sketched these appearances, and from him the patterns 
 A, B, c, Fig. Y3, are borrowed. 
 
 FIG. 73. 
 
 An effect of vibrating plates which long perplexed 
 experimenters is here to be noticed. When with the sand 
 strewed over a plate a little fine dust is mingled, say the 
 fine seed of lycopodium, this light substance, instead of 
 collecting along the nodal lines, forms little heaps at the 
 places of most violent motion. It is heaped at the four 
 corners of the plate, Fig. 74, at the four sides of the plate, 
 
 FIG. 74. 
 
 FIG. 75. 
 
 Fia. 76. 
 
 Fig. 75, and lodged between the nodal lines of the plate, 
 
VIBRATIONS OF BELLS. 179 
 
 Fig. 76. These three figures represent the three states of 
 vibration illustrated in Figs. 64, 65, and 66. The dust 
 chooses in all cases the place of greatest agitation. Vari- 
 ous explanations of this effect had been given, but it was 
 reserved for Faraday to assign its extremely simple cause. 
 The light powder is entangled by the little whirlwinds of 
 air produced by the vibrations of the plate: it cannot 
 escape from the little cyclones, though the heavier sand 
 particles are readily driven through them. When, there- 
 fore, the motion ceases, the light powder settles down at 
 the places where the vibration was a maximum. In vacuo 
 no such effect is observed: here all powders, light and 
 heavy, move to the nodal lines. 
 
 11. Vibration of Bells : Means of rendering 
 them visible. 
 
 The vibrating segments and nodes of a bell are similar 
 to those of a disk. When a bell sounds its deepest note, 
 the coalescence of its pulses causes it to divide into four 
 vibrating segments, separated from each other by four 
 nodal lines, which run up from the sound-bow to the 
 crown of the bell. The place where the hammer strikes is 
 always the middle of a vibrating segment ; the point dia- 
 metrically opposite is also the middle of such a segment. 
 Ninety degrees from these points, we have also vibrating 
 segments, while at 45 degrees right and left of them we 
 come upon the nodal lines. Supposing the strong, dark 
 circle in Fig. 77 (next page) to represent the circumference 
 of the bell in a state of quiescence, then when the ham- 
 mer falls on any one of the segments #, <?, b, or d, the sound- 
 bow passes periodically through the changes indicated by 
 the dotted lines. At one moment it is an oval, with a b 
 for its longest diameter ; at the next moment it is an oval, 
 with c d for its longest diameter. The changes from one 
 oval to the other constitute, in fact, the vibrations of 
 
[80 SOUND. 
 
 the bell. The four points n, n, n, n, where the two ovals 
 intersect each other, are the nodes. As in the case of 
 a disk, the number of vibra- 
 tions executed by a bell in a 
 given time varies directly as 
 the thickness, and inversely as 
 the square of the bell's diam- 
 eter. 
 
 Like a disk, also, a bell can 
 divide itself into any even num- 
 ber of vibrating segments, but 
 not into au odd number. By ~~d~ 
 
 damping proper points in suc- 
 cession tli bell can be caused to divide into 6, 8, 10, and 12 
 vibrating parts. Beginning with the fundamental note, the 
 number of vibrations corresponding to the respective divis- 
 ions of a bell, as of a disk, is as follows : 
 
 Number of divisions 4, 6, 8, 10, 12. 
 
 Numbers the squares of which express the ) 
 
 rates of vibration . . . . [ 2 3) 4 > 5 ' 6 * 
 
 Thus, if the vibrations of the fundamental tone be 40, that 
 of the next higher tone will be 90, the next 160, the next 
 250, the next 360, and so on. If the bell be thin, the 
 tendency to subdivision is so great, that it is almost impos- 
 sible to bring out the pure fundamental tone without the 
 admixture of the higher ones. 
 
 I will now repeat before you a homely, but an instruc- 
 tive experiment. This common jug, when a fiddle-bow is 
 drawn across its edge, divides into four vibrating segments 
 exactly like a bell. The jug is provided with a handle ; 
 and you are to notice the influence of this handle upon the 
 tone. When the fiddle-bow is drawn across the edge at a 
 point diametrically opposite to the handle, a certain note is 
 heard. When it is drawn at a point 90 from the handle, 
 the same note is heard. In both these cases the handle 
 
SONOROUS RIPPLES. 
 
 occupies the middle of a vibrating segment, loading that 
 segment by its weight. But I now draw the bow at an an- 
 gular distance of 45 from the handle ; the note is sensibly 
 higher than before. The handle in this experiment occupies 
 a node ; it no longer loads a vibrating segment, and hence 
 the elastic force, having to cope with less weight, produces 
 a more rapid vibration. Chladni executed with a teacup 
 the experiment here made with a jug. Now bells often 
 exhibit round their sound-bows an absence of uniform thick- 
 ness, tantamount to the want of symmetry in the case of our 
 jug ; and we shall learn subsequently that the intermittent 
 sound of many bells, noticed more particularly when their 
 tones are dying out, is produced by the combination of two 
 distinct rates of vibration, which have this absence of uni- 
 formity for their origin. 
 
 There are no points of absolute rest in a vibrating bell, 
 for the nodes of the higher tones are not those of the fun-' 
 damental one. But it is easy to show that the various 
 parts of the sound-bow, when the fundamental tone is pre- 
 dominant, vibrate with very different degrees of intensity. 
 Suspending a little ball of sealing-wax a, Fig. 78 (next 
 page), by a string, and allowing it to rest gently against 
 the interior surface of an inverted bell, it is tossed to and 
 fro when the bell is thrown into vibration. But the rat- 
 tling of the sealing-wax ball is far more violent when it 
 rests against the vibrating segments than when it rests 
 against the nodes. Permitting the ivory bob of a short 
 pendulum to rest in succession against a vibrating segment 
 and against a node of the " Great Bell " of Westminster, I 
 found that in the former position it was driven away five 
 inches, in the latter only two inches and three-quarters, 
 when the hammer fell upon the bell. 
 
 Could the " Great Bell " be turned upside down and 
 filled with water, on striking it the vibrations would 
 express themselves in beautiful ripples upon the liquid 
 
182 
 
 SOUND. 
 
 surface. Similar ripples may be obtained with smaller 
 bells, or even with finger and claret glasses, but they would 
 be too minute for our present purpose. Filling a large 
 hemispherical glass with water, and passing the fiddle-bow 
 across its edge, large crispations immediately cover its 
 surface. When the bow is vigorously drawn, the water 
 rises in spray from the four vibrating segments. Pro- 
 jecting, by means of a lens, a magnified image of the 
 
 FIG. 78. 
 
 illuminated water-surface upon the screen, I pass the bow 
 gently across the edge of the glass, or rub the finger gently 
 along the edge. You hear this low sound, and at the same 
 time observe the ripples breaking, as it were, in visible 
 music over the four sectors of the figure. 
 
 You know the experiment of Leidenfrost which proves 
 that, if water be poured into a red-hot silver basin, it rolls 
 about upon its own vapor. The same effect is produced 
 if we drop a volatile liquid, like ether, on the surface of 
 warm water. And, if a bell-glass be filled with ether or 
 
FARADAY'S AND MELDE'S FIGURES. 
 
 183 
 
 with alcohol, a sharp sweep of the bow over the edge of 
 the glass detaches the liquid spherules, which, when they 
 fall back, do not mix with the liquid, but are driven over 
 the surface on wheels of vapor to the nodal lines. The 
 warming of the liquid, as might be expected, improves the 
 effect. M. Melde, to whom we are indebted for this beau- 
 tiful experiment, has given the drawings, Figs. 79 and 80, 
 
 FIG. T9. 
 
 FIG. 80. 
 
 representing what occurs when the surface is divided into 
 four and into six vibrating parts. With a thin wine-glass 
 and strong brandy the effect may also be obtained. 1 
 
 The glass and the liquid within it vibrate here together, 
 and everything that interferes with the perfect continuity 
 of the entire mass disturbs the sonorous effect. A crack 
 in the glass passing from the edge downward extinguishes 
 its sounding power. A rupture in the continuity of the 
 liquid has the same effect. When a glass containing a 
 solution of carbonate of soda is struck with a bit of wood, 
 you hear a clear musical sound. But when a little tar- 
 taric acid is added to the liquid, it foams, and a dry, un- 
 
 1 Under the shoulder of the Wetterhorn I found in 1867 a pool of clear 
 water into which a driblet fell from a brow of overhanging limestone rock. 
 The rebounding water-drops, when they fell back, rolled in myriads over the 
 surface. Almost any fountain, the spray of which falls into a basin, will ex- 
 hibit the same effect. 
 
184 
 
 SOUND. 
 
 musical collision takes the place of the musical sound. As 
 the foam disappears, the sonorous power returns, and now 
 that the liquid is once more clear, you hear the musical 
 ring as before. 
 
 The ripples of the tide leave their impressions upon 
 FIG. si. the sand over which they pass. 
 
 The ripples produced by so- 
 norous vibrations have been 
 proved by Faraday competent 
 to do the same. Attaching a 
 plate of glass to a long flexible 
 board, and pouring a thin layer 
 of water over the surface of 
 the glass, on causing the board 
 to vibrate, its tremors chase the 
 water into a beautiful mosaic 
 of ripples. A thin stratum of sand strewed upon the plate 
 is acted upon by the water, and carved into patterns, of 
 wliich Fig. 81 is a reduced specimen. 
 
SUMMARY. J85 
 
 StJMMAKY OF CHAPTEE IV. 
 
 A BOD fixed at both ends and caused to vibrate trans- 
 versely divides itself in the same manner as a string vibrat- 
 ing transversely. 
 
 But the succession of its overtones is not the same as 
 those of a string, for while the series of tones emitted by 
 the string is expressed by the natural numbers, 1, 2, 3, 4, 5, 
 etc., the series of tones emitted by the rod is expressed by 
 the squares of the odd numbers, 3, 5, 7, 9, etc. 
 
 A rod fixed at one end can also vibrate as a whole, or 
 can divide itself into vibrating segments separated from 
 each other by nodes. 
 
 In this case the rate of vibration of the fundamental 
 tone is to that of the first overtone as 4 : 25, or as the 
 square of 2 to the square of 5. From the first division on- 
 ward the rates of vibration are proportional to the squares 
 of the odd numbers, 3, 5, 7, 9, etc. 
 
 With rods of different lengths the rate of vibration is 
 inversely proportional to the square of the length of the 
 rod. 
 
 Attaching a glass bead silvered within to the free end 
 of the rod, and illuminating the bead, the spot of light re- 
 flected from it describes curves of various forms when the 
 rod vibrates. The kaleidophone of Wheatstone is thus 
 constructed. 
 
 The iron fiddle and the musical box are instruments 
 whose tones are produced by rods, or tongues, fixed at one 
 end and free at the other. 
 
 A rod free at both ends can also be rendered a source 
 
186 SOUND. 
 
 of sonorous vibrations. In its simplest mode of division 
 it has two nodes, the subsequent overtones correspond to 
 divisions by 3, 4, 5, etc., nodes. Beginning with its first 
 mode of division, the tones of such a rod are represented 
 by the squares of the odd numbers 3, 5, 7, 9, etc. 
 
 The claque-bois, straw-fiddle, and glass harmonica are 
 instruments whose tones are those of rods or bars free at 
 both ends, and supported at their nodes. 
 
 When a straight bar, free at both ends, is gradually 
 bent at its centre, the two nodes corresponding to its fun- 
 damental tone gradually approach each other. It finally 
 assumes the shape of a tuning-fork which, when it sounds 
 its fundamental note, is divided by two nodes near the base 
 of its two prongs into three vibrating parts. 
 
 There is no division of a tuning-fork by three nodes. 
 
 In its second mode of division, which corresponds to 
 the first overtone of the fork, there is a node on each prong 
 and two others at the bottom of the fork. 
 
 The fundamental tone of the fork is to its first overtone 
 approximately as the square of 2 is to the square of 5. 
 The vibrations of the first overtone are, therefore, about 6J 
 times as rapid as those of the fundamental. From the first 
 overtone onward the successive rates of vibration are as the 
 squares of the odd numbers 3, 5, 7, 9, etc. 
 
 We are indebted to Chladni for the experimental in- 
 vestigation of all these points. He was enabled to con- 
 duct his inquiries by means of the discovery that, when 
 sand is scattered over a vibrating surface, it is driven from 
 the vibrating portions of the surface, and collects along the 
 nodal lines. 
 
 Chladni embraced in his investigations plates of various 
 forms. A square plate, for example, clamped at the 
 centre, and caused to emit its fundamental tone, divides 
 itself into four smaller squares by lines parallel to its 
 sides. 
 
SUMMARY. 187 
 
 The same plate can divide itself into four triangular 
 vibrating parts, the nodal lines coinciding with the diag- 
 onals. The note produced in this case is a fifth above 
 the fundamental note of the plate. 
 
 The plate may be further subdivided, sand-figures of 
 extreme beauty being produced ; the notes rise in pitch as 
 the subdivision of the plate becomes more minute. 
 
 These figures may be deduced from the coalescence of 
 different systems of vibration. 
 
 When a circular plate clamped at its centre sounds its 
 fundamental tone, it divides into four vibrating parts, 
 separated by four radial nodal lines. 
 
 The next note of the plate corresponds to a division 
 into six vibrating sectors, the next note to a division into 
 eight sectors; such a plate can divide into any even 
 number of vibrating sectors, the sand-figures assuming 
 beautiful stellar forms. 
 
 The rates of vibration corresponding to the divisions 
 of a disk are represented by the squares of the numbers 
 2, 3, 4, 5, 6, etc. In other words, the rates of vibration 
 are proportional to the squares of the numbers represent- 
 ing the sectors into which the disk is divided. 
 
 When a bell sounds its deepest note it is divided intc 
 four vibrating parts separated from each other by nodal 
 lines, which run upward from the sound-bow and cross 
 each other at the crown. 
 
 It is capable of the same subdivisions as a disk ; the 
 succession of its tones being also the same. 
 
 The rate of vibration of a disk or bell is directly pro- 
 portional to the thickness and inversely proportional to 
 the square of the diameter. 
 
CHAPTEE V. 
 
 Longitudinal Vibrations of a Wire. Relative Velocities of Sound in Brass 
 and Iron. Longitudinal Vibrations of Rods fixed at One End. Of Rods 
 free at Both Ends. Divisions and Overtones of Rods vibrating longitu- 
 dinally. Examination of Vibrating Bars by Polarized Light. Deter- 
 mination of Velocity of Sound in Solids. Resonance. Vibrations of 
 Stopped Pipes : their Divisions and Overtones. Relation of the Tones 
 of Stopped Pipes to those of Open Pipes. Condition of Column of Air 
 within a Sounding Organ-Pipe. Reeds and Reed-Pip.es. The Voice. 
 Overtones of the Vocal Chords. The Vowel Sounds. Kundt's Experi- 
 ments. New Methods of determining the Velocity of Sound. 
 
 1. Longitudinal Vibrations of Wires and Rods : Con- 
 version of Longitudinal into Transverse Vibrations. 
 
 WE have thus far occupied ourselves exclusively with 
 transversal vibrations ; that is to say, vibrations executed 
 at right angles to the lengths of the strings, rods, plates, 
 and bells subjected to examination. A string is also 
 capable of vibrating in the direction of its length, but 
 here the power which enables it to vibrate is not a ten- 
 sion applied externally, but the elastic force of its own 
 molecules. Now this molecular elasticity is much greater 
 than any that we can ordinarily develop by stretching the 
 string, and the consequence is that the sounds produced 
 by the longitudinal vibrations of a string are, as a gen- 
 eral rule, much more acute than those produced by its 
 transverse vibrations. These longitudinal vibrations may 
 be excited by the oblique passage of a fiddle-bow; but 
 they are more easily produced by passing briskly along 
 the string a bit of cloth or leather on which powdered 
 
LONGITUDINAL VIBRATIONS OF WIRES. 189 
 
 resin has been strewed. The resined fingers answer the 
 same purpose. 
 
 When the wire of our monochord is plucked aside, you 
 hear the sound produced by its transverse vibrations. 
 When resined leather is rubbed along the wire, a note 
 much more piercing than the last is heard. This is due 
 to the longitudinal vibrations of the wire. Behind the 
 table is stretched a stout iron wire, 23 feet long. One end 
 of it is firmly attached to an immovable wooden tray, 
 the other end is coiled round a pin fixed firmly into one 
 of our benches. With a key this pin can be turned, and 
 the wire stretched so as to facilitate the passage of the 
 rubber. Clasping the wire with the resined leather, and 
 passing the hand to and fro along it, a rich, loud musical 
 sound is heard. Halving the wire at its centre, and 
 rubbing one of its halves, the note heard ib ^he octave of 
 the last: the vibrations are twice as rapid. When the 
 wire is clipped at one-third of its length and the shorter 
 segment rubbed, the note is a fifth above the octave. 
 Taking one-fourth of its length and rubbing as before, the 
 note yielded is the double octave of that of the whole wire, 
 being produced by four times the number of vibrations. 
 Thus, in longitudinal as well as in transverse vibrations, 
 the number of vibrations executed in a given time is 
 inversely proportional to the length of the wire. 
 
 And notice the surprising power of these sounds when 
 the wire is rubbed vigorously. With a shorter length, 
 the note is so acute, and at the same time so powerful, as 
 to be hardly bearable. It is not the wire itself which 
 produces this intense sound ; it is the wooden tray at its 
 end to which its vibrations are communicated. And, the 
 vibrations of the wire being longitudinal, those of the 
 tray, which is at right angles to the wire, must be trans- 
 versal. We have here, indeed, an instructive example of 
 the conversion of longitudinal into transverse vibrations. 
 
190 SOUND. 
 
 2. Longitudinal Pulses in Iron and Brass : their Rela- 
 tive Velocities determined. 
 
 Causing the wire to vibrate again longitudinally 
 through its entire length, my assistant shall at the same 
 time turn the key at the end, thus changing the tension. 
 You notice no variation of the note. The longitudinal 
 vibrations of the wire, unlike the transverse ones, are in- 
 dependent of the tension. Beside the iron wire is stretched 
 a second, of brags, of the same length and thickness. I 
 rub them both. Their tones are not the same ; that of 
 the iron wire is considerably the higher of the two. Why ? 
 Simply because the velocity of the sound-pulse is greater 
 in iron than in brass. The pulses in this case pass to and 
 fro from end to end of the wire. At one moment the wire 
 pushes the tray at its end; at the next moment it pulls 
 the tray, this pushing and pulling being due to the 
 passage of the pulse to and fro along the whole wire. The 
 time required for a pulse to run from one end to the other 
 and 'back is that of a complete vibration. In that time 
 the wire imparts one push and one pull to the wooden 
 tray at its end ; the wooden tray imparts one complete 
 vibration to the air, and the air bends once in and once 
 out the tympanic membrane. It is manifest that the 
 rapidity of vibration, or, in other words, the pitch of the 
 note, depends upon the velocity with which the sound- 
 pulse is transmitted through the wire. 
 
 And now the solution of a beautiful problem falls of 
 itself into our hands. By shortening the brass wire we 
 cause it to emit a note of the same pitch as that emitted 
 by the other. You hear both notes now sounding in 
 unison, and the reason is that the sound-pulse travels 
 through these 23 feet of iron wire, and through these 
 15 feet 6 inches of brass wire, in the same time. These 
 lengths are in the ratio of 11 : 17, and these two numbers 
 
LONGITUDINAL VIBRATIONS OF WIRES. 
 
 express the relative velocities of sound in brass and iron. 
 In fact, the former velocity is 11,000 feet, and the latter 
 17,000 feet a second. The same method is of course ap- 
 plicable to many other metals. 
 
 When a wire or string, vibrating longitudinally, emits 
 its lowest note, there is no node whatever upon it ; the 
 pulse, as just stated, runs to and fro along the whole 
 length. But, like a string vibrating transversly, it can 
 also subdivide itself into ventral segments separated by 
 nodes. By damping the centre of the wire we make that 
 point a node. The pulses here run from both ends, meet 
 in the centre, recoil from each other, and return to the 
 ends, where they are reflected as before. The note pro- 
 duced is the octave of the fundamental note. The next 
 higher note corresponds to the division of the wire into 
 three vibrating segments, separated from each other by 
 two nodes. The first of these three modes of vibration is 
 shown in Fig. 82, a and 5 / the second at c and d / the 
 
 < * 
 
 Fra. 
 
 82. 
 tgr-* 
 
 
 
 cu 
 
 !/ V -< 
 
 I 
 
 b 
 
 i 
 - 
 
 ! 
 c 
 
 I 
 
 
 
 d 
 
 i 
 tgui v 
 
 1 j e : 
 
 
 \ j s \ 
 
 
 
 third at e and/*/ the nodes being marked by dotted trans- 
 verse lines, and the arrows in each case pointing out the 
 direction in which the pulse moves. The rates of vibra- 
 tion follow the order of the numbers, 1, 2, 3, 4, 5, etc., 
 just as in the case of a wire vibrating transversely. 
 
 A rod or "bar of wood or metal, with its two ends fixed, 
 and vibrating longitudinally, divides itself in the same 
 manner as the wire. The succession of tones is also the 
 same in both cases. 
 9 
 
192 
 
 SOUND. 
 
 3. Longitudinal Vibrations of Rods fixed at One End : 
 Musical Instruments formed on this Principle. 
 
 Rods and bars with one end fixed are also capable of 
 vibrating longitudinally. A smooth wooden or metal rod, 
 for example, with one of its ends fixed in a vice, yields a 
 musical note, when the resined fingers are passed along it. 
 "When such a note yields its lowest note, it simply elon- 
 gates and shortens in quick alternation; there is, then, 
 no node upon the rod. The pitch of the note is inversely 
 proportional to the length of the rod. This follows neces- 
 sarily from the fact that the time of a complete vibration 
 is the time required for the sonorous pulse to run twice to 
 and fro over the rod. The first overtone of a rod, fixed at 
 one end, corresponds to its division by a node at a point 
 one-third of its length from its free end. Its second over- 
 tone corresponds to a division by two nodes, the highest 
 of which is at a point one-fifth of the length of the rod 
 from its free end, the remainder of the rod being divided 
 into two equal parts by the second node. In Fig. 83, a and 
 
 J, G and d, e and /*, are 
 
 clinxr-n tin 
 
 FIG. 88. 
 
 1 1 
 
 shown the conditions of 
 the rod answering to its 
 first three modes of vibra- 
 tion : the nodes, as before, 
 are marked by dotted 
 lines, the arrows in the 
 respective cases mark- 
 ing the direction of the 
 a o o a e f 
 
 pulses. 
 
 The order of the tones of a rod fixed at one end and 
 vibrating longitudinally is that of the odd numbers 1, 3, 
 5, 7, etc. It is easy to see that this must be the case. 
 For the time of vibration of c or d is that of the segment 
 above the dotted line : and the length of this segment 
 
LONGITUDINAL VIBRATIONS OF FIXED RODS. 
 
 193 
 
 Fia. 84. 
 
 being only one-third that of the whole rod, its vibrations 
 must be three times as rapid. The time of vibration in 
 e or f is also that of its 
 highest segment, and as 
 this segment is one-fifth 
 of the length of the 
 whole rod, its vibrations 
 must be five times as 
 rapid. Thus the' order 
 of the tones must be 
 that of the odd numbers. 
 Before you, Fig. 84, 
 is a musical instrument, 
 the sounds of which are 
 due to the longitudinal 
 vibrations of a number 
 of deal rods of different 
 lengths. Passing the res- 
 ined fingers over the rods 
 in succession, a series of 
 notes of varying pitch is 
 obtained. An expert per- 
 former might render the 
 tones of this instrument very pleasant to you. 
 
 4:. Vibrations of Rods free at Both Ends. 
 
 Rods with ~both ends free are also capable of vibrating 
 longitudinally, and producing musical tones. The investi- 
 gation of this subject will lead us to exceedingly important 
 results. Clasping a long glass tube exactly at its centre, 
 and passing a wetted cloth over one of its halves, a clear 
 musical sound is the result. A solid glass rod of the same 
 length would yield the same note. In this case the centre 
 of the tube is a node, and the two halves elongate and 
 shorten in quick alternation. M. Konig, of Paris, has pro- 
 
 i 
 
194 SOUND. 
 
 vided us with an instrument which will illustrate this 
 action. A rod of brass, a &, Fig. 85, is held at its centre 
 bj the clamp s, while an ivory ball, suspended by two 
 strings from the points, m and n, of a wooden frame, is 
 caused to rest against the end, &, of the brass rod. Draw- 
 ing gently a bit of resined leather over the rod near <z, it 
 is thrown into longitudinal vibration. The centre, s, is a 
 node ; but the uneasiness of the ivOry ball shows you that 
 the end, 5, is in a state of tremor. 1 apply the rubber 
 still more briskly. The ball, 5, rattles, and now the vi- 
 
 FIG. 85. 
 
 bration is so intense, that the ball is rejected with vio- 
 lence whenever it comes into contact with the end of the 
 rod. 
 
 5. Fracture of Glass Tube "by Sonorous 
 Vibrations. 
 
 When the wetted cloth is passed over the surface of 
 a glass tube the film of liquid left behind by the cloth 
 is seen forming narrow tremulous rings all along the rod. 
 Now this shivering of the liquid is due to the shivering of 
 the glass underneath it, and it is possible so to augment 
 the intensity of the vibration that the glass shall actually 
 go to pieces. Savart was the first to show this. Twice 
 
LONGITUDINAL VIBRATIONS OF FREE RODS. 
 
 195 
 
 in this place I have repeated this experiment, sacrificing 
 in each case a fine glass tube 6 feet long and 2 inches in 
 diameter. Seizing the tube at its centre c, Fig. 86, I 
 swept my hand vigorously to and fro along c D, until 
 FIG. 86. finally the half most 
 
 ID distant from my hand 
 
 was shivered into an- 
 nular fragments. On 
 examining these it was 
 found that, narrow as 
 they were, many of 
 them were marked by 
 circular cracks indi- 
 cating a still more 
 minute subdivision. 
 
 In this case also 
 the rapidity of vibra- 
 tion is inversely pro- 
 portional to the length 
 of the rod. A rod 
 of half the length vi- 
 brates longitudinally 
 & with double the ra- 
 
 ,^ pidity, a rod of one- 
 
 third the length with 
 
 treble the rapidity, and 
 so on. The time of 
 2 & complete vibration 
 
 ^ being that required 
 
 ^ by the pulse to travel 
 
 to and fro over the 
 rod, and that time 
 being directly propor- 
 tional to the length of the rod, the rapidity of vibration 
 must, of necessity, be in the inverse proportion. 
 
196 SOUND. 
 
 This division of a rod by a single node at its centre 
 corresponds to the deepest tone produced by its longi- 
 tudinal vibration. But, as in all other cases hitherto 
 examined, such rods can subdivide themselves further. 
 Holding the long glass rod a e. Fig. 87, at a point &, mid- 
 way between its centre and one of its ends, and rubbing 
 its short section, a b, with a wet cloth, the point 5 be- 
 comes a node, a second node, d, being formed at the same 
 distance from the opposite end of the rod. Thus we have 
 the rod divided into three vibrating parts, consisting of 
 one whole ventral segment, 5 d, and two half ones, a ~b 
 and d e. The sound corresponding to this division of the 
 rod is the octave of its fundamental note. 
 
 You have now a means of checking me. For, if the 
 second mode of division just described produces the octave 
 of the fundamental note, and if a rod of half the length 
 produces the same octave, then the whole rod held at a 
 point one-fourth of its length from one of its ends ought 
 to emit the same note as the half rod held in the middle. 
 When both notes are sounded together they are heard to 
 be identical in pitch. 
 
 Fig. 88, a and &, o and d, e and ./, shows the three first 
 
 FIG. 
 
 divisions of a rod free at both ends and vibrating longitu- 
 dinally. The nodes, as before, are marked by transverse 
 dots, the direction of the pulses being shown by arrows. 
 The order of the tones is that of the numbers 1, 2, 3, 
 4, etc. 
 
EXAMINATION BY POLARIZED LIGHT. 
 
 197 
 
 6. Action of Sonorous Vibrations on Polarized Light. 
 
 "When a tube or rod vibrating longitudinally yields its 
 fundamantal tone, its two ends are in a state of free vibra- 
 tion, the glass there suffering neither strain nor pressure. 
 The case at the centre is exactly the reverse ; here there 
 is no vibration, but a quick alternation of tension and 
 compression. When the sonorous pulses meet at the centre 
 they squeeze the glass ; when they recoil they strain it. 
 Thus while at the ends we have the maximum of vibration, 
 but no change of density r , at the centre we have the maxi- 
 mum changes of density, hut no vibration. 
 
 We have now cleared the way for the introduction of a 
 very beautiful experiment made many years ago by Biot, 
 but never, to my knowledge, repeated on the scale here 
 presented to you. The beam from our electric lamp, L, 
 Fig. 89, being sent through a prism, B, of bi-refracting 
 
 Fie. 89. 
 
 spar, a beam of polarized light is obtained. This beam 
 impinges on a second prism of spar, n, but, though both 
 prisms are perfectly transparent, the light which has passed 
 
198 SOUND. 
 
 through the first cannot get through the second. By 
 introducing a piece of glass between the two prisms, and 
 subjecting the glass to either strain or pressure, the light 
 is enabled to pass through the entire system. 
 
 I now introduce between the prisms B and n a rec- 
 tangle, s s', of plate glass, 6 feet long, 2 inches wide, and 
 ^ of an inch thick, which is to be thrown into longitudinal 
 vibration. The beam from L passes through the glass at 
 a point near its centre, which is held in a vice, c, so that 
 when a wet cloth is passed over one of the halves, c , of 
 the strip, the centre will be a node. During its longitu- 
 dinal vibration the glass near the centre is, as already 
 explained, alternately strained and compressed ; and this 
 successive strain and pressure so changes the condition 
 of the light as to enable it to pass through the second 
 prism. The screen is now dark ; but on passing the 
 wetted cloth briskly over the glass a brilliant disk of light, 
 three feet in diameter, flashes out upon the screen. The 
 vibration quickly subsides, and the luminous disk as quick- 
 ly disappears, to be, however, revived at will by the pas- 
 sage of the wetted cloth along the glass. 
 
 The light of this disk appears to be continuous, but it 
 is really intermittent, for it is only when the glass is under 
 strain or pressure that the light can get through. In 
 passing from strain to pressure, and from pressure to 
 strain, the glass is for a moment in its natural state, which, 
 if it continued, would leave the screen dark. But the 
 impressions of brightness, due to the strains and pressures, 
 remain far longer upon the retina than is necessary to 
 abolish the intervals of darkness ; hence the screen ap- 
 pears illuminated by a continuous light. When the glass 
 rectangle is shifted so as to cause the beam of polarized 
 light to pass through it close to its end, s, the longitudinal 
 vibrations of the glass have no effect whatever upon the 
 polarized beam. 
 
VIBRATIONS OF WOODEN RODS. 199 
 
 Thus, by means of this subtile investigator, we demon- 
 strate that, while the centre of the glass, where the vibra- 
 tion is nil, is subjected to quick alternations of strain and 
 pressure, the ends of the rectangle, where the vibration is 
 a maximum, suffer neither. 1 
 
 7. Vibrations of Rods of Wood : Determination of 
 Relative Velocities in Different Woods. 
 
 Rods of wood and metal also yield musical tones when 
 they vibrate longitudinally. Here, however, the rubber 
 employed is not a wet cloth, but a piece of leather covered 
 with powdered resin. The resined fingers also elicit the 
 music of the rods. The modes of vibration here are those 
 already indicated, the pitch, however, varying with the 
 velocity of the sonorous pulse in the respective substances. 
 "When two rods of the same length, the one of deal, the 
 other of Spanish mahogany, are sounded together, the 
 pitch of the one is much lower than that of the other. 
 Why ? Simply because the sonorous pulses pass more slow- 
 ly through the mahogany than through the deal. Can we 
 find the relative velocity of sound through both ? With 
 the greatest ease. We have only to carefully shorten the 
 mahogany rod till it yields the same note as the deal one. 
 The notes, rendered approximate by the first trials, are 
 now identical. Through this rod of mahogany 4: feet long, 
 and through this rod of deal 6 feet long, the sound-pulse 
 passes in the same time, and these numbers express the 
 relative velocities of sound through the two substances. 
 
 Modes of investigation, which could only be hinted at 
 in our earlier lectures, are now falling naturally into our 
 hands. When in the first lecture the velocity of sound 
 in air was spoken of, many possible methods of determin- 
 ing this velocity must have occurred to your minds, because 
 here we have miles of space to operate upon. Its velocity 
 
 1 This experiment succeeds almost equally well with a glass tube. 
 
200 SOUND. 
 
 through wood or metal, where such distances are out of 
 the question, is determined in the simple manner just in- 
 dicated. From the notes which they emit when suitably 
 prepared, we may infer with certainty the relative veloci- 
 ties of sound through different solid substances ; and de- 
 termining the ratio of the velocity in any one of them to 
 its velocity in air, we are able to draw up a table of abso- 
 lute velocities. But how is air to be introduced into the 
 series ? "We shall soon be able to answer this question, 
 approaching it, however, through a number of phenomena 
 with which, at first sight, it appears to have no connec- 
 tion. 
 
 EESONANCE. 
 
 8. Experiments with Resonant Jars. Analysis and 
 Explanation. 
 
 The series of tuning-forks now before you have had 
 their rates of vibration determined by the siren. One, 
 you will remember, vibrates 256 times in a second, the 
 length of its sonorous wave being 4 feet 4 inches. It is 
 detached from its case, so that when struck against a pad 
 you hardly hear it. "When held over this glass jar, A B, 
 Fig. 90, 18 inches deep, you still fail to hear the sound of 
 the fork. Preserving the fork in its position, I pour water 
 with the least possible noise into the jar. The column of 
 air underneath the fork shortens, the sound augments in 
 intensity, and when the water has reached a certain level 
 it bursts forth with extraordinary power. A greater quan- 
 tity of water causes the sound to sink, and become finally 
 inaudible, as at first. Ey pouring the water carefully out 
 a point is reached where the reinforcement of the sound 
 
CONDITIONS OF RESONANCE. 
 
 201 
 
 again occurs. Experimenting thus, we learn that there is 
 
 one particular length FIG. 90. 
 
 of the column of air 
 
 which, when the fork 
 
 is placed above it, 
 
 produces a maximum 
 
 augmentation of the 
 
 sound. This reenf orce- 
 
 ment of the sound is 
 
 named resonance. 
 
 Operating in the 
 same way with all the 
 forks in succession, a 
 column of air is found 
 for each, which yields 
 a maximum resonance. 
 These columns become 
 shorter as the rapidity 
 of vibration increases. 
 In Fig. 91 the series of jars is represented, the number of 
 vibrations to which each re- FIG. 91. 
 
 sounds being placed above it. 
 
 "What is the physical 
 meaning of this very won- 
 derful effect ? To solve this 
 question we must revive our 
 knowledge of the relation 
 of the motion of the fork 
 itself to the motion of the 
 sonorous wave produced by 
 the fork. S upposing a prong 
 of this fork, which executes 256 vibrations in a second, 
 to vibrate between the points a and 5, Fig. 92, in its 
 motion from a to 5 the fork generates half a sonorous 
 wave, and as the length of the whole wave emitted by 
 
 256 
 
 320 
 
 384 
 
 512 
 
202 
 
 SOUND. 
 
 this fork is 4 feet 4 inches, at the moment the prong 
 reaches 5 the foremost point of the sonorous wave will be 
 at c, 2 feet 2 inches distant from the fork. The motion 
 of the wave, then, is vastly greater than that of the fork. 
 
 FIG. 92. 
 
 -26 inches 
 
 FIG. 93. 
 
 V 
 
 In fact, the distance a o is, in this case, not more than one 
 twentieth of an inch, while the wave has passed over a 
 distance of 26 inches. With forks of lower pitch the 
 difference would be still greater. 
 
 Our next question is, what is the length of the column 
 of air which resounds to this fork ? By measurement with 
 a two-foot rule it is found to be 13 inches. But the length 
 of the wave emitted by the fork is 52 inches ; hence the 
 length of the column of air which 
 resounds to the fork is equal to one- 
 fourth of the length of the sound- 
 wave produced by the fork. This 
 rule is general, and might be illus- 
 trated by any other of the forks 
 instead of this one. 
 
 Let the prong, vibrating between 
 the limits a and 5, be placed over its 
 resonant jar, A B, Fig. 93. In the time 
 required by the prong to move from 
 a to 5, the condensation it produces 
 runs down to the bottom of the jar, 
 is there reflected, and, as the distance to the bottom and 
 
 a 
 
 Z> 
 
ANALYSIS AND EXPLANATION. 203 
 
 back is 26 inches, the reflected wave will reach the fork 
 at the moment when it is on the point of returning from 
 I to a. The rarefaction of the wave is produced by the 
 retreat of the prong from ~b to a. This rarefaction will 
 also run to the bottom of the jar and back, overtaking the 
 prong just as it reaches the limit, #, of its excursion. It 
 is plain from this analysis that the vibrations of the fork 
 are perfectly synchronous with the vibrations of the aerial 
 column A B ; and in virtue of this synchronism the motion 
 accumulates in the jar, spreads abroad in the room, and 
 produces this vast augmentation of the sound. 
 
 When we substitute for the air in one of these jars a 
 gas of different elasticity, we find the length of the re- 
 sounding column to be different. The velocity of sound 
 through coal-gas is to its velocity in air about as 8:5. 
 Hence, to synchronize with our fork, a jar filled with coal- 
 gas must be deeper than one filled with air. I turn this 
 jar, 18 inches long, upside down, and hold close to its 
 open mouth our agitated tuning-fork. It is scarcely audi- 
 ble. The jar, with air in it, is 5 inches too deep for this 
 fork. Let coal-gas now enter the jar. As it ascends the 
 note at a certain point swells out, proving that for the 
 more elastic gas a depth of 18 inches is not too great. In 
 fact, it is not great enough ; for if too much gas be allowed 
 to enter the jar the resonance is weakened. By suddenly 
 turning the jar upright, still holding the fork close to its 
 mouth, the gas escapes, and at the point of proper admixt- 
 ure of gas and air the note swells out again. 1 
 
 9. Reenforcement of Bell ly Resonance. 
 
 This fine, sonorous bell, Fig. 94, is thrown into intense 
 vibration by the passage of a resined bow across its edge. 
 You hear its sound, pure, but not very forcible. When, 
 
 1 This experiment is more easily executed with hydrogen than with 
 coal-gas. 
 
204 SOUND. 
 
 however, the open mouth of this large tube, which is 
 closed at one end, is brought close to one of the vibrating 
 segments of the bell, the tone swells into a musical roar. 
 
 FIG. 94. 
 
 As the tube is alternately withdrawn and advanced, the 
 sound sinks and swells in this extraordinary manner. 
 
 The second tube, open at both ends, is capable of being 
 lengthened and shortened by a telescopic slider. "When 
 brought near the vibrating bell, the resonance is feeble. 
 On lengthening the tube by drawing out the slider at a 
 certain point, the tone swells out as before. If the tube 
 be made longer, the resonance is again enfeebled. Note 
 the fact, which shall be explained presently, that the open 
 tube which gives the maximum resonance is exactly twice 
 the length of the closed one. For these fine experiments 
 we are indebted to Savart. 
 
 10. Expenditure of Motion in Resonance. 
 
 With the India-rubber tube employed in our third 
 chapter it was found necessary to time the impulses prop- 
 erly, so as to produce the various ventral segments. I 
 could then feel that the muscular work performed, when 
 the impulses were properly timed, was greater than when 
 
EXPENDITURE OF MOTION IN EESONANCE. 205 
 
 they were irregular. The same truth may be illustrated 
 by a claret-glass half filled with water. Endeavor to 
 move your hand to and fro, in accordance with the oscil- 
 lating period of the water: when you have thoroughly 
 established synchronism, the work thrown upon the hand 
 apparently augments the weight of the water. So like- 
 wise with our tuning-fork ; when its impulses are timed 
 to the vibrations of the column of air contained in this 
 jar, its work is greater than when they are not so timed. 
 As a consequence of this the tuning-fork comes sooner to 
 rest when it is placed over the jar than when it is permit- 
 ted to vibrate either in free air, or over a jar of a depth 
 unsuited to its periods of vibration. 1 
 
 Reflecting on what we have now learned, you would 
 have little difficulty in solving the following beautiful 
 problem : You are provided with a tuning-fork and a 
 siren, and are required by means of these two instruments 
 to determine the velocity of sound in air. To solve this 
 problem, you lack, if anything, the mere power of manip- 
 ulation which practice imparts. You would first deter- 
 mine, by means of the siren, the number of vibrations 
 executed by the tuning-fork in a second ; you would then 
 determine the length of the column of air which resounds 
 to the fork. This length multiplied by 4 would give you, 
 approximately, the wave-length of the fork, and the wave- 
 length multiplied by the number of vibrations in a second 
 would give you the velocity in a second. Without quitting 
 your private room, therefore, you could solve this impor- 
 tant problem. We will go on, if you please, in this fashion, 
 making our footing sure as we advance. 
 
 1 Only an extremely small fraction of the fork's motion is, however, 
 converted into sound. The remainder is expended in overcoming the in- 
 ternal friction of its own particles. In other words, nearly the whole of 
 the motion is converted into heat. 
 
206 SOUND. 
 
 11. Resonators of Ilelmholtz. 
 
 Helmholtz has availed himself of the principle of reso- 
 nance in analyzing composite sounds. He employs little 
 hollow spheres, called resonators, one of which is shown 
 in Tig. 94:#. The small projection 5, which has an orifice, 
 
 FIG. 94a. 
 
 is placed in the ear, while the sound-waves enter the hol- 
 low sphere through the wide aperture at a. Reenforced 
 by the resonance of such a cavity, and rendered thereby 
 more powerful than its companions, a particular note of a 
 composite clang may be in a measure isolated and studied 
 alone. 
 
 ORGAN-PIPES. ^ 
 
 12. Principles of Resonance applied to Organ-Pipes. 
 
 Thus disciplined we are prepared to consider the sub- 
 ject of organ-pipes, which is one of great importance. 
 Before me on the table are two resonant jars, and in my 
 right hand and my left are held two tuning-forks. I agi- 
 tate both, and hold them over this jar. One of them only 
 is heard. Held over the other jar, the other fork alone 
 is heard. Each jar selects that fork whose periods of 
 
VIBRATING COLUMNS OF AIR. 
 
 207 
 
 Fro. 95. 
 
 vibration synchronize with its own. And instead of two 
 forks suppose several of them to be held over the jar ; 
 from the confused assemblage of pulses thus generated, 
 the jar would select and reenforce that one which corre- 
 sponds to its own period of vibration. 
 
 "When I blow across the open mouth of the jar ; or, 
 better still, for the jar is too wide for this experiment, when 
 I blow across the open end of a glass tube, t u, Fig. 95, of 
 the same length as the jar, a fluttering of the air is thereby 
 produced, an assemblage of pulses at the open mouth of the 
 tube being generated. And what is the con- 
 sequence ? The tube selects that pulse of the 
 flutter which is in synchronism with itself, 
 and raises it to a musical sound. The sound, 
 you perceive, is precisely that obtained when 
 the proper tuning-fork is placed over the tube. 
 The column of air within the tube has, in 
 this case, virtually created its own tuning- 
 fork ; for by the reaction of its pulses upon 
 the sheet of air issuing from the lips it has 
 compelled that sheet to vibrate in synchronism 
 with itself, and made it thus act the part of 
 the tuning-fork. 
 
 Selecting for each of the other tuning- 
 forks a resonant tube, in every case, on blow- 
 ing across the open end of the tube, a tone is 
 produced identical in pitch with that obtained through 
 resonance. 
 
 When different tubes are compared, the rate of vibra- 
 tion is found to be inversely proportional to the length of 
 the tube. These three tubes are 24. 12, and 6 inches long, 
 respectively. I blow gently across the 24-inch tube, and 
 bring out its fundamental note ; similarly treated, the 12- 
 inch tube yields the octave of the note of the 24-inch. In 
 like manner the 6-inch tube yields the octave of the 12-inch. 
 
208 SOUND. 
 
 It is plain that this must be the case ; for, the rate of 
 vibration depending on the distance which the pulse has 
 to travel to complete a vibration, if in one case this dis- 
 tance be twice what it is in another, the rate of vibration 
 must be twice as slow. In general terms, the rate of vi- 
 bration is inversely proportional to the length of the tube 
 through which the pulse passes. 
 
 13. Vibrations of Stopped Pipes : Modes of Division : 
 Overtones. 
 
 But that the current of air should be thus able to ac- 
 commodate itself to the requirements of the tube, it must 
 enjoy a certain amount of flexibility. A little reflection 
 will show you that the power of the reflected pulse over 
 the current must depend to some extent on the force ot 
 the current. A stronger current, like a more powerfully 
 stretched string, requires a great force to deflect it, and 
 when deflected vibrates more quickly. Accordingly, to 
 obtain the fundamental note of this 24-inch tube, we must 
 blow very gently across its open end ; a rich, full, and for- 
 cible musical tone is then produced. With a little stronger 
 blast the sound approaches a mere rustle ; blowing stronger 
 still, a tone is obtained of much higher pitch than the 
 fundamental one. This is the first overtone of the tube, 
 to produce which the column of air within it has divided 
 itself into two vibrating parts, with a node between them. 
 With a still stronger blast a still higher note is obtained. 
 The tube is now divided into three vibrating parts, sepa- 
 rated from each other by two nodes. Once more I blow 
 with sudden strength ; a higher note than any before ob- 
 tained is the consequence. 
 
 In Fig. 96 are represented the divisions of the column 
 of air corresponding to the first three notes of a tube 
 stopped at one end. At a and 5, which correspond to the 
 fundamental note, the column is undivided ; the bottom of 
 
STOPPED PIPES. 
 
 209 
 
 FIG. 06. 
 
 the tube is the only node, and the pulse simply moves up 
 .and down from top to bottom, as denoted by the arrows. 
 In c and d, w r hich correspond to the first overtone of the 
 tube, we have one nodal surface shown by dots at a?, 
 against which the pulses abut, and from which they are 
 reflected as from a fixed surface. This nodal surface is 
 situated at one -third of 
 the length of the tube 
 from its open end. In 
 e and/*, which correspond 
 to the second overtone, 
 we have two nodal sur- 
 faces, the upper one, a/, 
 of which is at one-fifth of 
 the length of the tube 
 
 from its open end, the a c f 
 
 remaining four-fifths being divided into two equal parts 
 by the second nodal surface. The arrows, as before, mark 
 the directions of the pulses. 
 
 We have now to inquire into the relation of these 
 successive notes to each other. The space from node to 
 node has been called all through " a ventral segment ; " 
 hence the space between the middle of a ventral segment 
 and a node is a semi-ventral segment. You will readily 
 bear in mind the law that the number of vibrations 
 is directly proportional to the number of semi-ventral 
 segments into which the column of air within the tube is 
 divided. Thus, when the fundamental note is sounded, we 
 has^e but a single semi-ventral segment, as at a and 5. The 
 bottom here is a node, and the open end of the tube, where 
 the air is agitated, is the middle of a ventral segment. 
 The mode of division represented in c and d yields three 
 semi-ventral segments ; in e and f we have five. The vi- 
 brations, therefore, corresponding to this series of notes, 
 augment in the proportion of the series of odd numbers^ 
 
210 SOUND. 
 
 1 : 3 : 5. And could we obtain still higher notes, their 
 relative rates of vibration would contimie to be represented 
 by the odd numbers, 7, 9, 11, 13, etc., etc. 
 
 It is evident that this must he the law of succession. 
 For the time of vibration in c or d is that of a stopped 
 tube of the length x y ; but this length is one-third of the 
 length of the whole tube, consequently its vibrations must 
 be three times as rapid. The time of vibration in e or/* is 
 that of a stopped tube of the length x f y', and inasmuch as 
 this length is one-fifth that of the whole tube, its vibra- 
 tions must be five times as rapid. We thus obtain the 
 succession 1, 3, 5, and if we pushed matters further 
 we should obtain the continuation of the series of odd 
 numbers. 
 
 And here it is once more in your power to subject my 
 statements to an experimental test. Here are two tubes, 
 one of which is three times the length of the other. I 
 sound the fundamental note of the longest tube, and then 
 the next note above the fundamental. The vibrations of 
 these two notes are stated to be in the ratio of 1 : 3. This 
 latter note, therefore, ought to be of precisely the same 
 pitch as the fundamental note of the shorter of the two 
 tubes. "When both tubes are sounded their notes are 
 identical. 
 
 It is only necessary to place a seriqs of such tubes of 
 different lengths thus together to form that ancient instru- 
 ment, Pan's pipes, p p', Fig. 97 (next page), with which 
 we are so well acquainted. 
 
 The successive divisions, and the relation of the over- 
 tones of a rod fixed at one end (described in p. 93), are 
 plainly identical with those of a column of air in a tube 
 stopped at one end, which we have been here considering. 
 
OPEN PIPES. 211 
 
 14. Vibrations of Open Pipes : Modes of Division : 
 Overtones. 
 
 From tubes closed at one end, and which, for the sake 
 of brevity, may be called stopped tubes, we now pass to 
 tubes open at both ends, which we shall call open tubes. 
 Comparing, in the first instance, a stopped tube with an 
 open one of the same length, we find the note of the latter 
 an octave higher than that of the former. This result is 
 general. To make an open tube yield the same note as a 
 closed one, it must be twice the length of the latter. And, 
 since the length of a closed tube sounding its fundamental 
 note is one-fourth of the FIG. or. 
 
 length of its sonorous wave, 
 the length of an open tube 
 is one-half that of the sono- 
 rous wave that it produces. 
 
 It is not easy to obtain 
 a sustained musical note by 
 blowing across the end of 
 an open glass tube; but a 
 mere puff of breath across the end reveals the pitch to the 
 disciplined ear. In each case it is that of a closed tube 
 half the length of the open one. 
 
 There are various ways of agitating the air at the ends 
 of pipes and tubes, so as to throw the air-columns within 
 them into vibration. In organ-pipes this is done by blow- 
 ing a thin sheet of air against a sharp edge. You will 
 have no difficulty in understanding the construction of an 
 open organ-pipe, from this model, Fig. 98, one side of 
 which has been removed so that you may see its inner 
 parts. Through the tube t the air passes from the wind- 
 chest into the chamber, o, which is closed at the top, save a 
 narrow slit, e d, through which the compressed air of the 
 chamber issues. This thin air-current breaks against the 
 
212 
 
 SOUND. 
 
 FIG. 98. 
 
 sharp edge, a 5, and there pro- 
 duces a fluttering noise, and the 
 proper pulse of this flutter is 
 converted by the resonance of 
 the pipe above into a musical 
 sound. The open space be- 
 tween the edge, a 5, and the slit 
 below it is called the embou- 
 chure. Fig. 99 represents a 
 stopped pipe of the same length 
 as that shown in Fig. 98, and 
 hence producing a note an oc- 
 tave lower. 
 
 Instead of a fluttering sheet 
 of air, a tuning-fork whose rate 
 of vibration synchronizes with 
 that of the organ-pipe may^be 
 placed at the embouchure, as at 
 A B, Fig. 100. The pipe will 
 resound. Here, for example, 
 are four open pipes of different 
 lengths, and four tuning-forks 
 of different rates of vibration. 
 Striking the most slowly vi- 
 brating fork, and bringing it 
 near the embouchure of the 
 longest pipe, the pipe speaks 
 powerfully. When blown into, 
 the same pipe yields a tone 
 identical with that of the tun- 
 ing-fork. Going through all 
 the pipes in succession, we find 
 in each case that the note ob- 
 tained by blowing into the pipe 
 is exactly that produced when 
 
 99. 
 
 B^=3j 
 ih '- \ 
 
RESONANCE APPLIED TO ORGAN-PIPES. 
 
 213 
 
 the proper tuning-fork is placed at the embouchure. Con- 
 ceive now the four forks placed together near the same 
 embouchure ; we should have pulses of four different 
 periods there excited ; but out of the four the pipe would 
 select only one. And if four hundred vibrating forks 
 could be placed there instead of four, the pipe would still 
 make the proper selection. This it also does when for 
 the pulses of tuning-forks we substitute the assemblage of 
 pulses created by the current 
 of air when it strikes against 
 the sharp upper edge of the 
 embouchure. 
 
 The heavy vibrating mass 
 of the tuning-fork is prac- 
 tically uninfluenced by the 
 motion of the air within 
 the pipe. But this is not 
 the case when air itself is 
 the vibrating body. Here, as 
 before explained, the pipe 
 creates, as it were, its own 
 tuning-fork, by compelling 
 the fluttering stream at its 
 embouchure to vibrate in 
 periods answering to its own. 
 
 The condition of the air within an open organ-pipe, 
 when its fundamental note is sounded, is that of a rod 
 free at both ends, held at its centre, and caused to vibrate 
 longitudinally. The two ends are places of vibration, the 
 centre is a node. Is there any way of feeling the vibrat- 
 ing air-column so as to determine its nodes and its 
 places of vibration ? The late excellent William Hopkins 
 has taught us the following mode of solving this problem : 
 Over a little hoop is stretched a thin membrane, forming 
 a little tambourine. The front of this organ -pipe, p p'. 
 
SOUN T D. 
 
 Fig. 101, is of glass, through, which you can see the posi- 
 tion of any body within it. By means of a string, the little 
 tambourine, m, can be raised or lowered at pleasure 
 through the entire length of the pipe. When held above 
 the upper end of the pipe, you hear the loud buzzing of 
 the membrane. When lowered into the pipe, it continues 
 to buzz for a time ; the sound becoming gradually feebler, 
 FHJ 101 an( ^ fi na lty ceasing totally. It is now in 
 
 the middle of the pipe, where it cannot 
 vibrate, because the air around it is at 
 rest. On lowering it still further, the 
 buzzing sound instantly recommences, and 
 continues down to the bottom of the 
 pipe. Thus, as the membrane is raised 
 and lowered in quick succession, during 
 every descent and ascent, we have two 
 periods of sound separated from each 
 other by one of silence. If sand were 
 strewed upon the membrane, it would 
 dance above and below, but it would be 
 quiescent at the centre. We thus prove 
 experimentally that, when an organ-pipe 
 sounds its fundamental note, it divides it- 
 self into two semi-ventral segments sepa- 
 rated by a node. 
 
 What is the condition of the air at 
 this node? Again, that of the middle of 
 a rod, free at both ends, and yielding the 
 fundamental note of its longitudinal vi- 
 bration. The pulses reflected from both 
 ends of the rod, or of the column of air, 
 meet in the middle, and produce compression ; they then 
 retreat and produce rarefaction. Thus, while there is no 
 vibration in the centre of an organ-pipe, the air there under- 
 goes the greatest changes of density. At the two ends of 
 
NODES OF ORGAN -PIPES. 215 
 
 the pipe, on the other hand, the air-particles merely swing 
 up and down without sensible compression or rarefaction. 
 
 If the sounding pipe were pierced at the centre, and 
 the orifice stopped by a membrane, the air, when condensed, 
 would press the membrane outward, and, when rarefied, 
 the external air would press the membrane inward. The 
 membrane would therefore vibrate in unison with the 
 column of air. The organ-pipe, Fig. 102, is so arranged 
 that a small jet of gas, , can be lighted opposite the centre 
 of the pipe, and there acted upon by the vibrations of a 
 membrane. Two other gas-jets, a and c, are placed nearly 
 midway between the centre and the two ends of the pipe. 
 The three burners, #, &, <?, are fed in the following manner : 
 
 FIG. 102. 
 
 through the tube, t, the gas enters the hollow chamber, 
 e d, from which issue three little bent tubes, shown in the 
 figure, each communicating with a capsule closed under- 
 neath by the membrane. This is in direct contact with 
 the air of the organ-pipe. From the three capsules issue 
 the three little burners, with their flames, #, 5, c. 
 
 Blowing into the pipe so as to sound its fundamental 
 note, the three flames are agitated, but the central one 
 is most so. Lowering the flames so as to render them 
 very small, and blowing again, the central flame, 5, is ex- 
 tinguished, while the others remain lighted. The experi- 
 ment may be performed half a dozen times in succession ; 
 the sounding of the fundamental note always quenches the 
 middle flame. 
 10 
 
216 SOUND. 
 
 By blowing more sharply into the pipe, it is caused 
 to yield its first overtone. The middle node no longer 
 exists. The centre of the pipe is now a place of maximum 
 vibration, while two nodes are formed midway between the 
 centre and the two ends. But if this be the case, and if 
 the flame opposite the node be always blown out, then, 
 when the first overtone of this pipe is sounded, the two 
 flames a and c ought to be extinguished, while the central 
 flame remains lighted. This is the case. When the first 
 harmonic is sounded the two nodal flames are infallibly ex- 
 tinguished, while the flame 5 in the middle of the ventral 
 segment is not sensibly disturbed. 
 
 There is no theoretic limit to the subdivision of an 
 organ-pipe, either stopped or open. In stopped pipes we 
 begin with 1 semi-ventral segment, and pass on to 3, 5, 7, 
 etc., semi-ventral segments, the number of vibrations of 
 the successive notes augmenting in the same ratio. In 
 open pipes we begin with 2 semi-ventral segments, and 
 pass on to 4, 6, 8, 10, etc., the number of vibrations of 
 the successive notes augmenting in the same ratio ; that 
 is to say, in the ratio 1:2:3:4:5, etc. When, therefore, 
 we pass from the fundamental tone to the first overtone 
 in an open pipe, we obtain the octave of the fundamental. 
 When we make the same passage in a stopped pipe, we 
 obtain a note a fifth above the octave. No intermediate 
 modes of vibration are in either case possible. If the 
 fundamental tone of a stopped pipe be produced by 100 
 vibrations a second, the first overtone will be produced 
 by 300 vibrations, the second by 500, and so on. Such 
 a pipe, for example, cannot execute 200 or 400 vibrations 
 in a second. In like manner the open pipe, whose funda- 
 mental note is produced by 100 vibrations a second, cannot 
 vibrate 150 times in a second, but passes, at a jump, to 
 200, 300, 400, and so on. 
 
 In open pipes, as in stopped ones, the number of vibra- 
 
FIG. 103. 
 
 P t 
 
 UNIVERSITY OF CALIFORI 
 DEPARTMENT OF CIVIL ENGI NEE 
 BERKELEY, CALIFORNIA 
 
 DIVISIONS OF OPEN PIPE. 217 
 
 tions executed in the unit of time is inversely proportional 
 to the length of the pipe. This follows from the fact, 
 already dwelt upon so often, that the time of a vibration is 
 determined by the distance which the sonorous pulse has 
 to travel to complete a vibration. 
 
 In Fig. 103, a and 5 (at the bottom) represent the 
 division of an open pipe corresponding to its fundamental 
 tone ; c and d represent the division corresponding to its 
 first, e and f the di- 
 vision corresponding 
 to its second over- 
 tone, the dots mark- 
 ing the nodes. The 
 distance m n is one- 
 half, op is one-fourth, 
 and s t is one-sixth 
 of the whole length 
 of the pipe. But the 
 pitch of a is that of 
 a stopped pipe equal 
 in length to in n 
 the pitch of c is that 
 of a stopped pipe of 
 the length o p ; while 
 
 the pitch of e is that of a stopped pipe of the length s t. 
 Hence, as these lengths are in the ratio of i : i : ^, or as 
 1 : -| : -J-, the rates of vibration must be as the reciprocals 
 of these, or as 3 : 2 : 1. From the mere inspection, there- 
 fore, of the respective modes of vibration, we can draw the 
 inference that the succession of tones of an open pipe must 
 correspond to the series of natural numbers. 
 
 The pipe a. Fig. 103, has been purposely drawn twice 
 the length of a, Fig. 93 (p. 202). It is perfectly mani- 
 fest that to complete a vibration the pulse has to pass 
 over the same distance in both pipes, and hence that the 
 
218 SOUND. 
 
 pitch of the two pipes must be the same. The open pipe, 
 a n, consists virtually of two stopped ones, with the cen- 
 tral nodal surface at m as their common base. This shows 
 the relation of a stopped pipe to an open one to be that 
 which experiment establishes. 
 
 15. Velocity of Sound in Gases, Liquids, and Solids, 
 determined ly Musical Vibrations. 
 
 We have already learned that the relative velocities of 
 sound in different solid bodies may be determined from 
 the notes which they emit when thrown into longitu- 
 dinal vibration. It was remarked at the time that to 
 draw up a table of absolute velocities we only required 
 the accurate comparison of the velocity in any one of 
 those solids with the velocity in air. We are now in a 
 condition to supply this comparison. For we have learned 
 that the vibrations of the air in an organ-pipe open at 
 both ends are executed precisely as those of a rod free at 
 both ends. Any difference of rapidity, therefore, between 
 the vibrations of a rod and of an open organ-pipe of the 
 same length must be due solely to the different velocities 
 with which the sonorous pulses are propagated through 
 them. Take therefore an organ-pipe of a certain length, 
 emitting a note of a certain pitch, and find the length of 
 a rod* of pine which yields the same note. This length 
 would be ten times that of the organ-pipe, which would 
 prove the velocity of sound in pine to be ten times its 
 velocity in air. But the absolute velocity in air is 1,090 
 feet a second ; hence the absolute velocity in pine is 
 10,900 feet a second, which is that given in our first 
 chapter (p. YO). To the celebrated Chladni we are in- 
 debted for this beautiful niode of determining the velocity 
 of sound in solid bodies. 
 
 We had also in our first lecture a table of the velocities 
 of sound in other gases than air. I am persuaded that 
 
VELOCITY OF SOUND. 219 
 
 you could tell me, after due reflection, how this table was 
 constructed. It would only be necessary to find a series 
 of organ-pipes which, when filled with the different gases, 
 yield the same note ; the lengths of these pipes would 
 give the relative velocities of sound through the gases. 
 Thus we should find the length of a pipe filled with 
 hydrogen to be four times that of a pipe filled with 
 oxygen, yielding the same note, and this would prove the 
 velocity of sound in the former to be four times its velo- 
 city in the latter. 
 
 But we had also a table of velocities through various 
 liquids. How was it constructed ? By forcing the liquids 
 through properly constructed organ-pipes, and comparing 
 their musical tones. Thus, in water it requires a pipe a 
 little better than four feet long to produce the note of an 
 air-pipe one foot long ; and this proves the velocity of 
 sound in water to be somewhat more than four times its 
 velocity in air. My object here is to give you a clear 
 notion of the way in which scientific knowledge enables 
 us to cope with these apparently insurmountable problems. 
 It is not necessary to go into the niceties of these measure- 
 ments. You will, however, readily comprehend that all 
 the experiments with gases might be made with the same 
 organ-pipe, the velocity of sound in each respective gas 
 being immediately deduced from the pitch of its note. 
 With a pipe of constant length the pitch, or, in other 
 words, the number of vibrations, would be directly pro- 
 portional to the velocity. Thus, comparing oxygen with 
 hydrogen, we should find the note of the latter to be the 
 double octave of that of the former, whence we should 
 infer the velocity of sound in hydrogen to be four times 
 its velocity in oxygen. The same remark applies to ex- 
 periments with liquids. Here also the same pipe may be 
 employed throughout, the velocities being inferred from 
 the notes produced by the respective liquids. 
 
220 SOUND. 
 
 In fact, the length of an open pipe being, as already 
 explained, one-half the length of its sonorous wave, it is 
 only necessary to determine, by means of the siren, the 
 number of vibrations executed by the pipe in a second, 
 and to multiply this number by twice the length of the 
 pipe, in order to obtain the velocity of sound in the gas or 
 liquid within the pipe. Thus, an open pipe 26 inches 
 long and filled with air executes 256 vibrations in a second. 
 The length of its sonorous wave is twice 26 inches, or 4J 
 feet : multiplying 256 by 4| we obtain 1,120 feet per sec- 
 ond as the velocity of sound through air of this tempera- 
 ture. Were the tube filled with carbonic-acid gas, its 
 vibrations would be slower : were it filled with hydrogen, 
 its vibrations would be quicker ; and applying the same 
 principle, we should find the velocity of sound in both 
 these gases. 
 
 So likewise the length of a solid rod free at both ends, 
 and sounding its fundamental note, is half that of the so- 
 norous wave in the substance of the solid. Hence we have 
 only to determine the rate of vibration of such a rod, and 
 multiply it by twice the length of the rod, to obtain the 
 velocity of sound in the substance of the rod. You can 
 hardly fail to be impressed by the power which physi- 
 cal science has given us over these problems ; nor will 
 you refuse your admiration to that famous old investi- 
 gator, Chladni, who taught us how to master them ex~ 
 perimentally. 
 
 KEEDS AND EEED-PIPES. 
 
 The construction of the siren and our experiments 
 with that instrument are, no doubt, fresh in your recol- 
 lection. Its musical sounds are produced by the cutting 
 up into puffs of a series of air-currents. The same pur- 
 pose is effected by a vibrating reed, as employed in the 
 
KEEDS. 
 
 221 
 
 accordion, the concertina, and the harmonica. In these 
 instruments it is not the vibrations of the reed itself 
 which, imparted to the air, and transmitted through it to 
 our organs of hearing, produce the music ; the function of 
 the reed is constructive, not generative / it moulds into a 
 series of discontinuous puffs that which without it would 
 be a continuous current of air. 
 
 Reeds, if associated with organ-pipes, sometimes com- 
 mand, and are sometimes commanded by, the vibrations 
 of the column of air. When they are stiff they rule the 
 column ; when they are flexible the column rules them. 
 In the former case, to derive any advantage from the air- 
 column, its length ought to be so regulated that either its 
 fundamental tone or one of its overtones shall correspond 
 to the rate of vibration of the reed. The metal reed 
 commonly employed in organ-pipes is shown in Fig. 104, A 
 
 FIG. 104. 
 
 and B, both in perspective and in section. It consists of a 
 long and flexible strip of metal, v v, placed in a rectangu- 
 lar orifice, through which the current of air enters the 
 pipe. The manner in which the reed and pipe are associ- 
 ated is shown in Fig. 105. The front, I c, of the space 
 containing the flexible tongue is of glass, so that you may 
 see the tongue within it. A conical pipe, A B, surmounts 
 the reed. 1 The wire w i, shown pressing against the reed, 
 
 1 The clear illustrations of organ-pipes and reeds introduced here, and 
 at p. 213, have been substantially copied from the excellent work of Helm- 
 
222 
 
 SOUND. 
 
 is employed to lengthen or shorten it, and thus to vary with- 
 in certain limits its rate of vibration. At one time in the 
 practice of music the reed closed the aperture by simply 
 FIG 105 falling against its sides ; every stroke of 
 
 the reed produced a tap, and these linked 
 themselves together to an unpleasant, 
 screaming sound, which materially in- 
 jured that of the associated organ-pipe. 
 This was mitigated, but not removed, by 
 permitting the reed to strike against >soft 
 leather ; but the reed now employed is 
 the free reed, which vibrates to and fro 
 between the sides of the aperture, al- 
 most, but not quite, filling it. In this 
 way the unpleasantness referred to is 
 avoided. "When reed and pipe synchro- 
 nize perfectly, the sound is most pure and 
 forcible; a certain latitude, however, 
 is possible on both sides of perfect syn- 
 chronism. But if the discordance be 
 pushed too far, the pipe ceases to be of 
 any use. We then obtain the sound due 
 to the vibrations of the reed alone. 
 
 Flexible wooden reeds, which can 
 accommodate themselves to the require- 
 ments of the pipes above them, are also 
 employed in organ-pipes. Perhaps the 
 simplest illustration of the action of the 
 reed commanded by its aerial column is 
 furnished by a common wheaten straw. 
 At about an inch from a knot, at ?', I bury 
 my penknife in this straw, s r', Fig. 106, to a depth of about 
 one-fourth of the straw's diameter, and, turning the blade 
 flat, pass it upward toward the knot, thus raising a strip 
 
 holtz. Pipes opening with hinges, so as to show their inner parts, were shown 
 in the lecture. 
 
REED-PIPES. 223 
 
 of t'/ie straw nearly an inch in length. This strip, r /, is 
 to be our reed, and the straw itself is to be our pipe. It 
 is now eight inches long. When blown into, it emits this 
 decidedly musical sound. When cut so as to make its 
 length six inches, the pitch is higher; with a length of 
 four inches, the pitch is higher still; and with a length 
 of two inches, the sound is very shrill indeed. In these 
 experiments the reed was compelled to accommodate it- 
 self throughout to the requirements of the vibrating 
 column of air. 
 
 The clarionet is a reed-pipe. It has a single broad 
 tongue, with which a long, cylindrical tube is associated. 
 The reed-end of the instrument is grasped by the lips, and 
 by their pressure the slit between the reed and its frame 
 is narrowed to the required extent. The overtones of a 
 clarionet are different from those of a flute. A flute is an 
 
 FIG. 106. 
 -r r' 
 
 open pipe, a clarionet a stopped one, the end at which the 
 reed is placed answering to the closed end of the pipe. 
 The tones of a flute follow the order of the natural num- 
 bers, 1, 2, 3, 4, etc., or of the even numbers, 2, 4, 6, 8, 
 etc. ; while the tones of a clarionet follow the order of the 
 odd numbers, 1, 3, 5, 7, etc. The intermediate notes 
 are supplied by opening the lateral orifices of the instru- 
 ment. Sir C. Wheatstone was the first to make known 
 this difference between the flute and clarionet, and his 
 results agree with the more thorough investigations of 
 Helmholtz. In the hautboy and bassoon we have two 
 reeds inclined to each other at a sharp angle, with a slit 
 between them, through which the air is urged. The pipe 
 of the hautboy is conical, and its overtones are those of an 
 open pipe different, therefore, from those of a clarionet. 
 
224 SOUND. 
 
 The pulpy end of a straw of green corn may be split by 
 squeezing it, so as to form a double reed of this kind, and 
 such a straw yields a musical tone. In the horn, trumpet, 
 and serpent, the performer's lips play the part of the reed. 
 These instruments are formed of long, conical tubes, and 
 their overtones are those of an open organ-pipe. The 
 music of the older instruments of this class was limited to 
 their overtones, the particular tone elicited depending on 
 the force of the blast and the tension of the lips. It is 
 now usual to fill the gaps between the successive overtones 
 by means of keys, which enable the performer to vary the 
 length of the vibrating column of air. 
 
 16. The Voice. 
 
 The most perfect of reed instruments is the organ of 
 voice. The vocal organ in man is placed at the top of the 
 trachea or windpipe, the head of which is adjusted for the 
 attachment of certain elastic bands which almost close the 
 aperture. When the air is forced from the lungs through 
 the slit which separates these vocal chords, they are 
 thrown into vibration ; by varying their tension, the rate 
 of vibration is varied, and the sound changed in pitch. 
 The vibrations of the vocal chords are practically unaffect- 
 ed by the resonance of the mouth, though we shall after- 
 ward learn that this resonance, by reenforcing one or the 
 other of the tones of the vocal chords, influences in a 
 striking manner the quality of the voice. The sweetness 
 and smoothness of the voice depend on the perfect closure 
 of the slit of the glottis at regular intervals during the 
 vibration. 
 
 The vocal chords may be illuminated and viewed in a 
 mirror, placed suitably at the back of the mouth. Varied 
 experiments of this kind have been executed by Sig. 
 Garcia. 1 I once sought to project the larynx of M. 
 
 1 1 owe it to this eminent artist to direct attention to his experiments 
 
THE VOICE. 225 
 
 Czermak upon a screen in this room, but with only partial 
 
 success. The organ may, however, be viewed directly in 
 
 the laryngoscope; its motions, in singing, speaking, and 
 
 coughing, being strikingly visible. It is represented at 
 
 rest in Fig. 107. The roughness of the voice in colds is 
 
 due, according to Helmholtz, to mucous flocculi, which 
 
 get into the slit of the glottis, and which are seen by 
 
 means of the laryngoscope. The squeaking falsetto voice, 
 
 with which some persons are afflicted, Helmholtz thinks, 
 
 may be produced by the drawing aside of the mucous 
 
 layer which ordinarily lies under 
 
 and loads the vocal chords. Their 
 
 edges thus become sharper and 
 
 their weight less; while, their 
 
 elasticity remaining the same, 
 
 they are shaken into more rapid 
 
 tremors. The promptness and 
 
 accuracy with which the vocal 
 
 chords can change their tension, 
 
 their form, and the width of the 
 
 slit between them, to which must 
 
 be added the elective resonance 
 
 of the cavity of the mouth, render the voice the most 
 
 perfect of musical instruments. 
 
 The celebrated comparative anatomist, John Miiller, 
 imitated the action of the vocal chords by means of bands 
 of India-rubber. He closed the open end of a glass tube 
 by two strips of this substance, leaving a slit between 
 them. On urging air through the slit, the bands were 
 thrown into vibration, and a musical tone produced. 
 Helmholtz recommends the form shown in Fig. 108, where 
 the tube, instead of ending in a section at right angles 
 to its axis, terminates in two oblique sections, over which 
 
 communicated to the Royal Society in May, 1855, and recorded in the 
 Philosophical Magazine for 1855, vol. x., p. 218. 
 
226 SOUND. 
 
 the bands of India-rubber are drawn. The easiest mode 
 of obtaining sounds from reeds of this character is to 
 
 roll round the end of a glass 
 tube a strip of thin India-rubber, 
 leaving about an inch of the 
 substance projecting beyond the 
 end of the tube. Taking two 
 opposite portions of the project- 
 ing rubber in the fingers, and 
 stretching it, a slit is formed, 
 the blowing through which pro- 
 duces a musical sound, which varies in pitch, as the sides 
 of the slit vary in tension. 
 
 17. Vowel Sounds. 
 
 The formation of the vowel sounds of the human voice 
 excited long ago philosophic inquiry. We can distinguish 
 one vowel sound from another, while assigning to both 
 the same pitch and intensity. What, then, is the quality 
 which renders the distinction possible ? In the year 1779 
 this was made a prize question by the Academy of St. 
 Petersburg, and Kratzenstein gained the prize for the 
 successful manner in which he imitated the vowel sounds 
 by mechanical arrangements. At the same time Yon 
 Kempelen, of Vienna, made similar and more elaborate 
 experiments. The question was subsequently taken lip 
 by Mr. Willis, who succeeded beyond all his predecessors 
 in the experimental treatment of the subject. The true 
 theory of vowel sounds was first stated by Sir. C. Wheat- 
 stone, and quite recently they have been made the subject 
 of exhaustive inquiry by Helmholtz. You will find little 
 difficulty in comprehending their origin. 
 
 Mounted on the acoustic bellows, without any pipe 
 associated with it, when air is urged through its orifice, 
 a free reed speaks in this forcible manner. When upon 
 
RESONANCE OF THE MOUTH. 227 
 
 the frame of the reed a pyramidal pipe is fixed, you notice 
 a change in the sound ; and by pushing my flat hand over 
 the open end of the pipe, the similarity between the 
 sound produced and that of the human voice is unmis- 
 takable. Holding the palm of the hand over the end of 
 the pipe so as to close it altogether, and then raising the 
 hand twice in quick succession, the word " mamma " is 
 heard as plainly as if it were uttered by an infant. For 
 this pyramidal tube I now substitute a shorter one, 
 and with it make the same experiment. The " mamma " 
 now heard is exactly such as would be uttered by a child 
 with a stopped nose. Thus, by associating with a vi- 
 brating reed a suitable pipe, we can impart to the sound 
 the qualities of the human voice. 
 
 In the organ of voice, the reed is formed by the vocal 
 chords, and associated with this reed is the resonant cavity 
 of the mouth, which can so alter its shape as to resound, 
 at will, either to the fundamental tone of the vocal chords 
 or to any of their overtones. With the aid of the 
 mouth, therefore, w r e can mix together the fundamental 
 tone and the overtones of the voice in different propor- 
 tions. Different vowel sounds are due to different ad- 
 mixtures of this kind. Striking one of this series of 
 tuning-forks, and placing it before my mouth, I adjust 
 the size of that cavity until it resounds forcibly to the 
 fork. Then, without altering in the least the shape or 
 size of my mouth, I urge air through the glottis. The 
 vowel sound " u " (oo in hoop) is produced, and no other. I 
 strike another fork, and, placing it in front of the mouth, 
 adjust the cavity to resonance. Then removing the fork 
 and urging air through the glottis, the vowel sound " o," 
 and it only, is heard. I strike a third fork, adjust my 
 mouth to it, and then urge air through the larynx ; the 
 vowel sound ah ! and no other, is heard. In all these cases 
 the vocal chords have been in the same constant condition. 
 
228 SOUND - 
 
 They have generated throughout the same fundamental 
 tone and the same overtones, the changes of sound which 
 you have heard being due solely to the fact that different 
 tones in the different cases were reenforced by the reso- 
 nance of the mouth. Donders first proved that the mouth 
 resounded differently for the different vowels. 
 
 In the formation of the different vowel sounds the 
 resonant cavity of the mouth undergoes, according to 
 Helmholtz, the following changes : 
 
 For the production of the sound " u " (oo in hoop), 
 the lips must be pushed forward, so as to make the cavity 
 of the mouth as deep as possible, and the orifice of the 
 mouth, by the contraction of the lips, as small as possible. 
 This arrangement corresponds to the deepest resonance of 
 which the mouth is capable. The fundamental tone itself 
 of the vocal chords is here reenforced, while the higher 
 tones retreat. 
 
 The vowel " o " requires a somewhat wider opening of 
 the mouth. The overtones which lie in the neighborhood 
 of the middle b of the soprano come out strongly in the 
 case of this vowel. 
 
 When " Ah " is sounded, the mouth assumes the shape 
 of a funnel, widening outward. It is thus tuned to a 
 note an octave higher than in the case of the vowel " o." 
 Hence, in sounding " Ah," those overtones are most 
 strengthened which lie near the higher b of the soprano. 
 As the mouth is in this case wide open, all the other over- 
 tones are also heard, though feebly. 
 
 In sounding "A" and "E," the hinder part of the 
 mouth is deepened, while the front of the tongue rises 
 against the gums and forms a tube ; this yields a higher 
 resonance-tone, rising gradually from " A " to " E," while 
 the hinder hollow space yields a lower resonance-tone, which 
 is deepest when " E " is sounded. 
 
 These examples sufficiently illustrate the subject of 
 
VOWEL SOUNDS. 229 
 
 vowel sounds. We may blend in various ways the elemen- 
 tary tints of the solar spectrum, producing innumerable 
 composite colors by their admixture. Out of violet and 
 red we produce purple, and out of yellow and blue we 
 produce white. Thus also may elementary sounds be 
 blended so as to produce all possible varieties of clang- 
 tint. After having resolved the human voice into its 
 constituent tones, Helmholtz was able to imitate these 
 tones by tuning-forks, and, by combining them appro- 
 priately together, to produce the sounds of all the vowels. 
 
 18. ITundtfs Experiments : New Modes of determining 
 Velocity of Sound. 
 
 Unwilling to interrupt the continuity of our reasonings 
 and experiments on the sound of organ-pipes, and their 
 relations to the vibrations of solid rods, I have reserved 
 for the conclusion of this discourse some reflections and 
 experiments which, in strictness, belong to an earlier 
 portion of the chapter. You have already heard the 
 tones, and made yourselves acquainted with the various 
 modes of division of a glass tube, free at both ends, 
 when thrown into longitudinal vibration. When it 
 sounds its fundamental tone, you know that the two 
 halves of such a tube lengthen and shorten in quick 
 alternation. If the tube were stopped at its ends, 
 the closed extremities would throw the air within the 
 tube into a state of vibration ; and if the velocity of 
 sound in air were equal to its velocity in glass, the air of 
 the tube would vibrate in synchronism with the tube 
 itself. But the velocity of sound in air is far less than 
 its velocity in glass, and hence, if the column of air is to 
 synchronize with the vibrations of the tube, it can only do 
 so by dividing itself into vibrating segments of a suitable 
 length. In an investigation of great interest, recently 
 published in Poggendorfs Annalen, M. Kundt, of Berlin, 
 
230 SOUND 
 
 has taught us how these segments may be rendered visible. 
 Into this six-foot tube is introduced the light powder of 
 lycopodium, being shaken all over the interior surface. A 
 small quantity of the powder clings to that surface. Stop- 
 ping the ends of the tube, holding its centre by a fixed 
 clamp, and sweeping a wet cloth briskly over one of its 
 halves, instantly the powder, w r hich a moment ago clung 
 to its interior surface, falls to the bottom of the tube in 
 the forms shown in Fig. 109, the arrangement of the lyco- 
 
 FIG. 109. 
 
 podium marking the manner in which the column of air 
 has been divided. Every node here is encircled by a ring 
 of dust, while from node to node the dust arranges itself 
 in transverse streaks along the ventral segments. 
 
 You will have little difficulty in seeing that we perform 
 here, with air, substantially the same experiment as that 
 of M. Melde with a vibrating string. "When the string was 
 too long to vibrate as a whole, it met the requirements of 
 the tuning-fork to which it was attached by dividing 
 into ventral segments. Now, in all cases, the length 
 from a node to its next neighbor is half that of the 
 sonorous wave : how many such half -waves then have we 
 in our tube in the present instance ? Sixteen (the figure 
 shows only four of them). But the length of our glass 
 tube vibrating thus longitudinally is also half that of the 
 sonorous wave in glass. Hence, in the case before us, 
 with the same rate of vibration, the length of the semi- 
 wave in glass is sixteen times the length of the semi-wave 
 in air. In other words, the velocity of sound in glass is 
 sixteen times its velocity in air. Thus, by a single sweep of 
 the wet rubber, we solve a most important problem. But, as 
 
KUNDT'S EXPERIMENTS. 231 
 
 M. Kundt lias shown, we need not confine ourselves to air. 
 Introducing any other gas into the tube, a single stroke of 
 our wet cloth enables us to determine the relative velocity 
 of sound in that gas and in glass. When hydrogen is 
 introduced, the number of ventral segments is less than 
 in air ; when carbonic acid is introduced, the number is 
 greater. 
 
 From the known velocity of sound in air, coupled with 
 the length of one of these dust segments, we can imme- 
 diately deduce the number of vibrations executed in a 
 second by the tube itself. Clasping a glass tube at its cen- 
 tre and drawing my wetted cloth over one of its halves, I 
 elicit this shrill note. The length of every dust segment, 
 now within the tube, is 3 inches. Hence the length of 
 the aerial sonorous wave corresponding to this note is 6 
 inches. But the velocity of sound in air of our present 
 temperature is 1,120 feet per second ; a distance which 
 would embrace 2,2iO of our sonorous waves. This num- 
 ber, therefore, expresses the number of vibrations per 
 second executed by the glass tube now before us. 
 
 Instead of damping the centre of the tube, and making 
 it a nodal point, we may employ any other of its subdi- 
 visions. Laying hold of it, for example, at a point mid- 
 way between its centre and one of its ends, and rubbing 
 it properly, it divides into three vibrating parts, separated 
 by two nodes. We know that in this division the note 
 elicited is the octave of that heard when a single node is 
 formed at the middle of the tube ; for the vibrations are 
 twice as rapid. If, therefore, we divide the tube, having 
 air within it, by two nodes instead of one, the number of 
 ventral segments revealed by the lycopodium dust will be 
 thirty-two instead of sixteen. The same remark applies, 
 of course, to all other gases. 
 
 Filling a series of four tubes with air, carbonic acid, 
 coal-gas, and hydrogen, and then rubbing each so as to 
 
232 SOUND. 
 
 produce two nodes, M. Kundt found the number of dust 
 segments formed within the tube in the respective cases 
 to be as follows : 
 
 Air . . . .32 dust segments. 
 Carbonic acid . 40 " 
 
 Coal-gas ... 20 " 
 
 Hydrogen ... 9 " 
 
 Calling the velocity in air unity, the following frac- 
 tions express the ratio of this velocity to those in the other 
 gases : 
 
 32 
 Carbonic acid . . 0'8 
 
 40 
 
 32 
 Coal-gas . . =1-6 
 
 20 
 
 32 
 
 Hydrogen . = 3'56 
 
 9 
 
 Referring to a table introduced in our first chapter, we 
 learn that Dulong by a totally different mode of experi- 
 ment found the velocity in carbonic acid to be 0*86, and 
 in hydrogen 3*8 times the velocity in air. The results of 
 Dulong were deduced from the sounds of organ-pipes filled 
 with the various gases ; but here, by a process of the ut- 
 most simplicity, we arrive at a close approximation to his 
 results. Dusting the interior surfaces of our tubes, filling 
 them with the proper gases, and sealing their ends, they 
 may be preserved for an indefinite time. By properly 
 shaking one of them at any moment, its inner surface 
 becomes thinly coated with the dust ; and afterward a 
 single stroke of the wet cloth produces the division from 
 which the velocity of sound in the gas may be immediately 
 inferred. 
 
 Savart found that a spiral nodal line is formed round 
 a tube or rod when it vibrates longitudinally, and Seebeck 
 showed that this line was produced, not by longitudinal, but 
 
SOUND FIGURES WITHIN TUBES. 233 
 
 by secondary transverse vibrations. Now this spiral nodal 
 line tends to complicate the division of the dust FIG. no. 
 in our present experiments. It is, therefore, de- 
 sirable to operate in a manner which shall alto- 
 gether avoid the formation of this line ; M. Kundt 
 has accomplished this, by exciting the longitudinal 
 vibrations in one tube, and producing the division 
 into ventral segments in another, into which the 
 first fits like a piston. Before you is a tube of 
 glass, Fig. 110, seven feet long, and two inches 
 internal diameter. One end of this tube is filled 
 by the movable stopper . The other end, K K, 
 is also stopped by a cork, through the centre of 
 which passes the narrower tube, A a, which is 
 firmly clasped at its middle by the cork, K K. 
 The end of the interior tube, A a, is also closed 
 with a projecting stopper, a, almost sufficient to 
 fill the larger tube, but still fitting into it so loose- 
 ly that the friction of a against the interior sur- 
 face is too slight to interfere practically with its 
 vibrations. The interior surface between a and 
 5 being lightly coated with the lycopodium dust, 
 a wet cloth is passed briskly over A K ; instantly 
 the dust between a and 5 divides into a number 
 of ventral segments. "When the length of the 
 column of air, a 5, is equal to that of the glass 
 tube, A #, the number of ventral segments is six- 
 teen. "When, as in the figure, a 1) is only one-half 
 the length of A &, the number of ventral segments 
 is eight. 
 
 But here you must perceive that the method 
 of experiment is capable of great extension. In- 
 stead of the glass tube, A a, we may employ a 
 rod of any other solid substance of wood or 
 metal, for example, and thus determine the rel- 
 
234: SOUND. 
 
 ative velocity of sound in the solid and in air. In the 
 place of the glass tube, for example, a rod of brass of 
 equal length may be employed. Rubbing its external 
 half by a resined cloth, it divides the column a ~b into the 
 number of ventral segments proper to the metal's rate of 
 vibrations. In this way M. Kundt operated with brass, 
 steel, glass, and copper, and his results prove the method 
 to be capable of great accuracy. Calling, as before, the 
 velocity of sound in air unity, the following numbers ex- 
 pressive of the ratio of the velocity of sound in brass to 
 its velocity in air were obtained in three different series of 
 experiments : 
 
 1st experiment 10*87 
 
 2nd experiment 10-87 
 
 3rd experiment 10'86 
 
 The coincidence is here extraordinary. To illustrate 
 the possible accuracy of the method, the length of the 
 individual dust segments was measured. In a series of 
 twenty-seven experiments, this length was found to vary 
 between 43 and 4A millimetres (each millimetre -^th of 
 an inch), never rising so high as the latter, and never fall- 
 ing so low as the former. The length of the metal rod, 
 compared with that of one of the segments capable of 
 this accurate measurement, gives us at once the velo- 
 city of sound in the metal, as compared with its velocity 
 in air. 
 
 Three distinct experiments, performed in the same man- 
 ner on steel, gave the following velocities, the velocity 
 through air, as before, being regarded as unity : 
 
 1st experiment 15-34 
 
 2nd experiment 15'33 
 
 3rd experiment 15 '34 
 
 Here the coincidence is quite as perfect as in the case 
 of brass. 
 
TELOCITY DEDUCED FROM SOUND FIGURES. 235 
 
 In glass, by this new mode of experiment, the velocity 
 was found to be 
 
 15-25. 1 
 
 Finally, in copper the velocity was found to be 
 
 11-96. 
 
 These results agree extremely well with those obtained 
 by other methods. "W'ertheim, for example, found the 
 velocity of sound in steel wire to be 15*108 ; M. Kundt 
 finds it to be 15*34: : "Wertheim also found the velocity in 
 copper to be 11-17 ; M. Kundt finds it to be 11*96. The 
 differences are not greater than might be produced by 
 differences in the materials employed by the two experi- 
 menters. 
 
 The length of the aerial column may or may not be an 
 exact multiple of the wave-length, corresponding to the 
 rod's rate of vibration. If not, the dust segments usually 
 take the form shown in Fig. 111. But if, by means of the 
 
 FIG. 111. 
 
 | i 
 
 stopper, 5, the column of air be made an exact multiple 
 of the wave-length, then the dust quits the vibrating seg- 
 
 Fio. 112. 
 
 ments altogether, and forms, as in Fig. 112, little isolated 
 heaps at the nodes. 
 
 1 The velocity in glass varies with the quality ; the result of each experi- 
 ment has therefore reference only to the particular kind of glass employed in 
 the experiment. 
 
236 SOUND. 
 
 19. Explanation of a Difficulty. 
 
 And here a difficulty presents itself. The stopped end 
 5 of the tube Fig. 110 is, of course, a place of no vibration, 
 where in all cases a nodal dust-heap is formed ; but, when- 
 ever the column of air was an exact multiple of the wave- 
 length, M. Kundt always found a dust-heap close to the 
 end a of the vibrating rod also. Thus the point from 
 which all the vibration emanated seemed itself to be a 
 place of no vibration. 
 
 This difficulty was pointed out by M. Kundt, but he 
 did not attempt its solution. We are now in a condition 
 to explain it. In Lecture III. it was remarked that in 
 strictness a node is not a place of no vibration ; that it is 
 a place of minimum vibration ; and that by the addition 
 of the minute pulses which the node permits, vibrations 
 of vast amplitude may be produced. The ends of M. 
 Kundt's tube are such points of minimum motion, the 
 lengths of the vibrating segments being such that, by the 
 coalescence of direct and reflected pulses, the air at a dis- 
 tance of half a ventral segment from the end of the tube 
 vibrates much more vigorously than that at the end of the 
 tube itself. This addition of impulses is more perfect when 
 the aerial column is an exact multiple of the wave-length, 
 and hence it is that, in this case, the vibrations become 
 sufficiently intense to sweep the dust altogether away from 
 the vibrating segments. The same point is illustrated by 
 M. Melde's tuning-forks, which, though they are the 
 sources of all the motion, are themselves nodes. 
 
 An experiment of Helmholtz's is here capable of in- 
 structive application. Upon the string of the sonometer 
 described in our third lecture I place the iron stem of this 
 tuning-fork, which executes 512 complete vibrations in a 
 second. At present you hear no augmentation of the 
 sound of the fork ; the string remains quiescent. But on 
 
SOLUTION OF A DIFFICULTY. 237 
 
 moving the fork along the string, at the number 33, a 
 loud, swelling note issues from the string. At this par- 
 ticular tension the length 33 exactly synchronizes with 
 the vibrations of the fork. By the intermediation of the 
 string, therefore, the fork is enabled to transfer its motion 
 to the sonometer, and through it to the air. The sound 
 continues as long as the fork vibrates, but the least move- 
 ment to the right or to the left from this point causes a 
 sudden fall of the sound. Tightening the string, the note 
 disappears ; for it requires a greater length of this more 
 highly tensioned string to respond to the fork. But, on 
 moving the fork further away, at the number 36 the note 
 again bursts forth. Tightening still more, 40 is found to 
 be the point of maximum power. When the string is 
 slackened, it must, of course, be shortened in order to make 
 it respond to the fork. Moving the fork now toward the 
 end of the string, at the number 25 the note is found as 
 before. Again, shifting the fork to 35, nothing is heard ; 
 but, by the cautious turning of the key, the point of syn- 
 chronism, if I may use the term, is moved further from the 
 end of the string. It finally reaches the fork, and at that 
 moment a clear, full note issues from the sonometer. In 
 all cases, before the exact point is attained, and imme- 
 diately in its vicinity, we hear " beats," which, as we shall 
 afterward understand, are due to the coalescence of the 
 sound of the fork with that of the string, when they are 
 nearly, but not quite, in unison with each other. 
 
 In these experiments, though the fork was the source 
 of all the motion, the point on which it rested was a nodal 
 point. It constituted the comparatively fixed extremity 
 of the wire, whose vibrations synchronized with those of 
 the fork. The case is exactly analogous to that of the 
 hand holding the India-rubber tube, and to the tuning- 
 fork in the experiments of M. Melde. It is also an effect 
 precisely the same in kind as that observed by M. Kundt, 
 
238 SOUND. 
 
 where the part of the column of air in contact with the 
 end of his vibrating rod proved to be a node instead of the 
 middle of a ventral segment. 
 
 ADDENDUM REGARDING RESONANCE. 
 
 The resonance of caves and of rocky inelosures is well 
 known. Bunsen notices the thunder-like sound produced 
 when one of the steam jets of Iceland breaks out near the 
 mouth of a cavern. Most travelers in Switzerland have 
 noticed the deafening sound produced by the fall of the 
 Keuss at the Devil's Bridge. The sound heard when a 
 hollow shell is placed close to the ear is a case of resonance. 
 Children think they hear in it the sound of the sea. The 
 noise is really due to the reinforcement of the feeble 
 sounds with which even the stillest air is pervaded, and 
 also in part to the noise produced by the pressure of the 
 shell against the ear itself. By using tubes of different 
 lengths, the variation of the resonance with the length of 
 the tube may be studied. The channel of the ear itself is 
 also a resonant cavity. When a poker is held by two 
 strings, and when the fingers of the hands holding the 
 poker are thrust into the ears, on striking the poker 
 against a piece of wood, a sound is heard as deep and 
 sonorous as that of a cathedral bell. When open, the 
 channel of the ear resounds to notes whose periods of 
 vibration are about 3,000 per second. This has been 
 shown by Helmholtz, and Madame Seiler has found that 
 dogs which howl to music are particularly sensitive to the 
 same notes. We may expect from Mr. Francis Galton 
 interesting results in connection with this subject. 
 
SUMMARY. 239 
 
 SUMMARY OF CHAPTEE Y. 
 
 WHEN a stretched wire is suitably rubbed, in the di- 
 rection of its length, it is thrown into longitudinal vibra- 
 tions: the wire can either vibrate as a whole or divide 
 itself into vibrating segments separated from each other 
 by nodes. 
 
 The tones of such a wire follow the order of the num- 
 bers 1, 2, 3, 4, etc. 
 
 The transverse vibrations of a rod fixed at both ends 
 do not follow the same order as the transverse vibrations 
 of a stretched wire ; for here the forces brought into play, 
 as explained in Lecture IY., are different. But the longi- 
 tudinal vibrations of a stretched wire do follow the same 
 order as the longitudinal vibrations of a rod fixed at both 
 ends, for here the forces brought into play are the same, 
 being in both cases the elasticity of the material. 
 
 A rod fixed at one end vibrates longitudinally as a 
 whole, or it divides into two, three, four, etc., vibrating 
 parts, separated from each other by nodes. The order of 
 the tones of such a rod is that of the odd numbers 1, 3, 5, 
 7, etc. 
 
 A rod free at both ends can also vibrate longitudinally. 
 Its lowest note corresponds to a division of the rod into 
 two vibrating parts by a node at its centre. The over- 
 tones of such a rod correspond to its division into three, 
 four, five, etc., vibrating parts, separated from each other 
 by two, three, four, etc., nodes. The order of the tones 
 of such a rod is that of the numbers 1, 2, 3, 4, 5, etc. 
 
 We may also express the order by saying that while 
 11 
 
240 SOUND. 
 
 the tones of a rod fixed at both ends follow the order of 
 the odd numbers 1, 3, 5, Y, etc., the tones of a rod free at 
 both ends follow the order of the even numbers 2, 4, 6, 8, 
 etc. 
 
 At the points of maximum vibration the rod suffers no 
 change of density; at the nodes, on the contrary, the 
 changes of density reach a maximum. This may be 
 proved by the action of the rod upon polarized light. 
 
 Columns of air of definite length resound to tuning- 
 forks of definite rates of vibration. 
 
 The length of a tube filled with air, and closed at one 
 end, which resounds to a fork is one-fourth of the length 
 of the sonorous wave produced by the fork. 
 
 This resonance is due to the synchronism which exists 
 between the vibrating period of the fork and that of the 
 column of air. 
 
 By blowing across the mouth of a tube closed at one 
 end, we produce a flutter of the air, and some pulse of this 
 flutter may be raised by the resonance of the tube to a 
 musical sound. 
 
 The sound is the same as that obtained when a tuning- 
 fork, whose rate of vibration is that of the tube, is placed 
 over the mouth of the tube. 
 
 "When a tube closed at one end a stopped organ-pipe, 
 for example sounds its lowest note, the column of air 
 within it is undivided by a node. The overtones of such 
 a column correspond to its division into parts, like those 
 of a. rod fixed at one end and vibrating longitudinally. 
 The order of its tones is that of the odd numbers, 1, 3, 5, 
 Y, etc. That this must be the order follows from the 
 manner in which the column is divided. 
 
 In organ-pipes the air is agitated by causing it to issue 
 from a narrow slit, and to strike upon a cutting edge. 
 Some pulse of the flutter thus produced is raised by the 
 resonance of the pipe to a musical sound. 
 
SUMMARY. 241 
 
 When, instead of the aerial flutter, a tuning-fork of 
 the proper rate of vibration is placed at the embouchure 
 of an organ-pipe, the pipe speaks in response to the fork. 
 In practice, the organ-pipe virtually creates its own tun- 
 ing-fork, by compelling the sheet of air at its embouchure 
 to vibrate in periods synchronous with its own. 
 
 An open organ-pipe yields a note an octave higher 
 than that of a closed pipe of the same length. This rela- 
 tion is a necessary consequence of the respective modes of 
 vibration. 
 
 When, for example, a stopped organ-pipe sounds its 
 deepest note, the column of air, as already explained, is 
 undivided. When an open pipe sounds its deepest note, 
 the column is divided by a node at its centre. The open 
 pipe in this case virtually consists of two stopped pipes 
 with a common base. Hence it is plain that the funda- 
 mental note of an open pipe must be the same as that of 
 a stopped pipe of half its length. 
 
 The length of a stopped pipe is one-fourth that of the 
 sonorous wave which it produces, while the length of an 
 open pipe is one-half that of its sonorous wave. 
 
 The order of the tones of an open pipe is that of the 
 even numbers 2, 4, 6, 8, etc., or of the natural numbers 
 1, 2, 3, 4, etc. 
 
 In both stopped and open pipes the number of vibra- 
 tions executed in a given time is inversely proportional to 
 the length of the pipe. 
 
 The places of maximum vibration in organ-pipes are 
 places of minimum changes of density ; while at the 
 places of minimum vibration the changes of density reach 
 a maximum. 
 
 The velocities of sound in gases, liquids, and solids, 
 may be inferred from the tones which equal lengths of 
 them produce ; or they may be inferred from the lengths 
 of these substances which yield equal tones. 
 
242 SOUND. 
 
 Reeds, or vibrating tongues, are often associated with 
 vibrating columns of air. They consist of flexible laminae, 
 which vibrate to and fro in a rectangular orifice, thus 
 rendering intermittent the air-current passing through the 
 orifice. 
 
 The action of the reed is the same as that of the 
 siren. 
 
 The flexible wooden reeds sometimes associated with 
 organ-pipes are compelled to vibrate in unison with the 
 column of air in the pipe ; other reeds are too stiff to be 
 thus controlled by the vibrating air. In this latter case 
 the column of air is taken of such a length that its vibra 
 tions synchronize with those of the reed. 
 
 By associating suitable pipes with reeds we impart to 
 their tones the qualities of the human voice. 
 
 The vocal organ in man is a reed instrument, the 
 vibrating reed in this case being elastic bands placed at 
 the top of the trachea, and capable of various degrees of 
 tension. 
 
 The rate of vibration, of these vocal chords is practi- 
 cally uninfluenced by the resonance of the mouth ; but 
 the mouth, by changing its shape, can be caused to resound 
 to the fundamental tone, or to any of the overtones of the 
 vocal chords. 
 
 By the strengthening of particular tones through the 
 resonance of the mouth, the clang-tint of the voice is 
 altered. 
 
 The different vowel-sounds are produced by different 
 admixtures of the fundamental tone and the overtones of 
 the vocal chords. 
 
 "When the solid substance of a tube stopped at one, or 
 at both ends, is caused to vibrate longitudinally, the air 
 within it is also thrown into vibration. 
 
 By covering the interior surface of the tube with a 
 light powder, the manner in which the aerial column di- 
 
SUMMARY. 243 
 
 vides itself may be rendered apparent. From the divis- 
 ion of the column the velocity of sound in the substance 
 of the tube, compared with its velocity in air, may be in- 
 ferred. 
 
 Other gases may be employed instead of air, and the 
 velocity of sound in these gases, compared with its velocity 
 in the substance of the tube, may be determined. 
 
 The end of a rod vibrating longitudinally may be 
 caused to agitate a column of air contained in a tube, com- 
 pelling the air to divide itself into ventral segments. 
 These segments may be rendered visible by light powders, 
 and from them the velocity of sound in the substance of 
 the vibrating rod, compared with its velocity in air, may 
 be inferred. 
 
 In this way the relative velocities of sound in all solid 
 substances capable of being formed into rods, and of vi- 
 brating longitudinally, may be determined. 
 
CHAPTEE YT. 
 
 Singing Flames. Influence of the Tube surrounding the Flame. In- 
 fluence of Size of Flame. Harmonic Notes of Flames. Effect of 
 Unisonant Notes od Singing Flames. Action of Sound on Naked 
 Flames. Experiments with Fish-Tail and Bat's-Wing Burners. Ex- 
 periments on Tall Flames. Extraordinary Delicacy of Flames as 
 Acoustic Keagents. The Vowel-Flame. Action of Conversational 
 Tones upon Flames. Action of Musical Sounds on Smoke-Jets. 
 Constitution of Water-Jets. Plateau's Theory of the Resolution of 
 a Liquid Vein into Drops. Action of Musical Sounds on Water- 
 Jets. A Liquid Vein may compete in Point of Delicacy with the 
 Ear. 
 
 1. Rhythm of Friction : Musical Flow of a Liquid 
 through a Small Aperture. 
 
 FRICTION is always rhythmic. When a resined bow 
 js passed across a string, the tension of the string se- 
 cures the perfect rhythm of the* friction. When the 
 wetted finger is moved round the edge of a glass, the 
 breaking up of the friction into rhythmic pulses expresses 
 itself in music. Savart's beautiful experiments on the 
 flow of liquids through small orifices bear immediately 
 upon this question. We have here the means of verifying 
 his results. The tube A B, Fig. 113, is filled with water, 
 its extremity, B, being closed by a plate of brass, which is 
 pierced by a circular orifice of a diameter equal to the 
 thickness of the plate. Removing a little peg which stops 
 the orifice, the water issues from it, and as it sinks in the 
 l tube a musical note of great sweetness issues from the 
 liquid column. This note is due to the intermittent flow 
 of the liquid through the orifice, by which the whole column 
 
MUSICAL FLOW OF WATER. 
 
 245 
 
 
 above it is thrown into vibration. The tendency to this 
 effect shows itself when tea is poured from a teapot, in the 
 circular ripples that cover the falling liquid. The same 
 intermittence is observed in the black, dense smoke which 
 rolls in rhythmic rings from the funnel of a steamer. The 
 unpleasant noise of unoiled machinery is also a declaration 
 of the fact that the friction is not uniform, but is due to 
 the alternate " bite " and release of 
 the rubbing surfaces. 
 
 "Where gases are concerned fric- 
 tion is of the same intermittent 
 character. A rifle-bullet sings in its 
 passage through the air ; while to the 
 rubbing of the wind against the boles 
 and branches of the trees are to be 
 ascribed the " waterfall tones " of an 
 agitated pine-wood. Pass a steadily- 
 burning candle rapidly through the 
 air ; an indented band of light, de- 
 claring intermittence, is often the 
 consequence, while the almost musi- 
 cal sound which accompanies the ap- 
 pearance of this band is the audible 
 expression of the rhythm. On the 
 other hand, if you blow gently 
 against a candle-flame, the fluttering 
 noise announces a rhythmic action. 
 We have already learned what can be done when a pipe is 
 associated with such a flutter ; we have learned that the 
 pipe selects a special pulse from the flutter, and raises it 
 by resonance to a musical sound. In a similar manner 
 the noise of a flame may be turned to account. The blow- 
 pipe flame of our laboratory, for example, when inclosed 
 within an appropriate tube, has its flutter raised to a roar. 
 The special pulse first selected soon reacts upon the flame 
 
246 SOUND. 
 
 so as to abolish in a great degree the other pulses, com- 
 pelling the flame to vibrate in periods answering to the 
 selected one. And this reaction can become so powerful 
 the timed shock of the reflected pulses may accumulate to 
 such an extent as to beat the flame, even when very large, 
 into extinction. 
 
 2. Musical Flames. 
 
 Nor is it necessary to produce this flutter by any extra- 
 neous means. When a gas-flame is simply inclosed within 
 a tube, the passage of the air over it is usually sufficient 
 to produce the necessary rhythmic action, so as to cause the 
 flame to burst spontaneously into song. This flame-music 
 may be rendered exceedingly intense. Over a flame issu- 
 ing from a ring burner with twenty-eight orifices, I place 
 a tin tube, 5 feet long, and 2J- inches in diameter. The 
 flame flutters at first, but it soon chastens its impulses 
 into perfect periodicity, and a deep and clear musical tone 
 is the result. By lowering the gas the note now sounded 
 is caused to cease, but, after a momentary interval of 
 silence, another note, which is the octave of the last, is 
 yielded by the flame. The first note was the fundamental 
 note of the surrounding tube ; this second note is its first 
 harmonic. Here, as in the case of open organ-pipes, we 
 have the aerial column dividing itself into vibrating seg- 
 ments, separated from each other by nodes. 
 
 A still more striking effect is obtained with this larger 
 tube, a &, Fig. 114, 15 feet long, and 4 inches wide, which 
 was made for a totally different purpose. It is supported 
 by a steady stand, s s', and into it is lifted the tall burner, 
 shown enlarged at B. You hear the incipient flutter: 
 you now hear the more powerful sound. As the flame is 
 lifted higher the action becomes more violent, until finally 
 a storm of music issues from the tube. And now all has 
 suddenly ceased; the reaction of its own pulses upon 
 
MUSICAL FLAMES. 
 
 247 
 
 FIG. 114. 
 
 the flame has beaten it into extinction. I 
 relight the flame and make it very small. 
 When raised within the tube, the flame 
 again sings, but it is one of the harmonics 
 of the tube that you now hear. On turn- 
 ing the gas fully on, the note ceases all 
 is silent for a moment ; but the storm is 
 brewing, and soon it bursts forth, as at 
 first, in a kind of hurricane of sound. 
 By lowering the flame the fundamental 
 note is abolished, and now you hear the 
 first harmonic of the tube. Making the 
 flame still smaller, the first harmonic dis- 
 appears, and the second is heard. Your 
 ears being disciplined to the apprehension 
 of these sounds, I turn the gas once more 
 fully on. Mingling with the deepest note 
 you notice the harmonics, as if struggling 
 to be heard amid the general uproar of 
 the flame. With a large Bunsen's rose 
 burner, the sound of this 
 tube becomes powerful 
 enough to shake the floor 
 and seats, and the large 
 audience that occupies 
 the seats of this room, 
 while the extinction of 
 the flame, by the re- 
 action of the sonorous 
 pulses, announces itself 
 by an explosion almost as 
 loud as a pistol-shot. It 
 must occur to you that a 
 chimney is a tube of this 
 -kind upon a large scale, 
 
248 
 
 SOUND. 
 
 FIG. 115. 
 
 and that the roar of a flame in a chimney is simply a 
 rough attempt at music. 
 
 Let us now pass on to shorter tubes and smaller 
 flames. Placing tubes of different lengths over eight 
 small flames, each of them starts into song, and you 
 notice that as the tubes lengthen the tones deepen. 
 The lengths of these tubes are so chosen that they 
 yield in succession the eight notes of the gamut. 
 Round some of them you observe a paper slider, s, Fig. 
 
 115, by which the tube 
 can be lengthened or 
 shortened. If while 
 the flame is sounding 
 the slider be raised, the 
 pitch instantly falls; 
 if lowered, the pitch 
 rises. These experi- 
 ments prove the flame 
 to be governed by the 
 tube. By the reaction 
 of the pulses, reflected 
 back upon the flame, 
 its flutter is rendered 
 perfectly periodic, the 
 length of that period 
 being determined, as 
 in the case of organ- 
 pipes, by the length of 
 the tube. 
 
 The fixed stars, es- 
 pecially those near the 
 horizon, shine with an 
 
 unsteady light, sometimes changing color as they twinkle. 
 I have often watched at night, upon the plateaux of the 
 Alps, the alternate flash of ruby and emerald in the lower 
 
ANALYSIS OF MUSICAL FLAMES. 249 
 
 and larger stars. If you place a piece of looking-glass so 
 that you can see in it the image of such a star, on tilting 
 the glass quickly to and fro, the line of light obtained will 
 not be continuous, but will form a string of colored beads 
 of extreme beauty. The same effect is obtained when an 
 opera-glass is pointed to the star and shaken. This ex- 
 periment shows that in the act of twinkling the light 
 of the star is quenched at intervals ; the dark spaces 
 between the bright beads corresponding 'to the periods of 
 extinction. Now, our singing flame is a twinkling flame. 
 When it begins to sing you observe a certain quivering 
 motion which may be analyzed with a looking-glass, or 
 an opera-glass, as in the case of the star. 1 I can now see 
 the image of this flame in a small looking-glass. On 
 tilting the glass, so as to cause the image to form a circle 
 of light, the luminous band is not seen to be continuous, 
 as it would be if the flame were perfectly steady ; it is 
 resolved into a beautiful chain of flames, Fig. 116. 
 
 3. Experimental Analysis of Musical Flame. 
 
 With a larger, brighter, and less rapidly-vibrating 
 flame, you may all see this 
 
 intermittent action. Over this ElQ ' 116> 
 
 gas-flame, /*, Fig. 117, is placed 
 a glass tube, A B, 6 feet long, 
 and 2 inches in diameter. The 
 back of the tube is blackened, 
 so as to prevent the light of the 
 flame from falling directly upon 
 the screen, which it is now de- 
 sirable to have as dark as possible. In front of the tube 
 is placed a concave mirror, M, which forms upon the screen 
 an enlarged image of the flame. I turn the mirror with 
 
 1 This experiment was first made with a hydrogen-flame by Sir C. 
 Wheatstone. 
 
250 
 
 SOUND. 
 
 my hand and cause the image to pass over the screen. 
 Were the flame silent and steady, we should obtain a con- 
 tinuous band of light ; but it quivers, and emits at the 
 same time a deep and powerful note. On twirling the 
 
 FIG. 117. 
 
 mirror, therefore, we obtain, instead of a continuous band, 
 a luminous chain of images. By fast turning, these 
 images are drawn more widely apart ; by slow turning, 
 they are caused to close up, the chain of flames passing 
 
RHYTHMIC IGNITION AND EXTINCTION. 251 
 
 through the most beautiful variations. Clasping the 
 lower end, B, of the tube with my hand, I so impede the 
 air as to stop the flame's vibration ; a continuous band is 
 the consequence. Observe the suddenness with which this 
 band breaks up into a rippling line of images the moment 
 my hand is removed, and the current of air is permitted 
 to pass over the flame. 
 
 4. Rate of Vibration of Flame : Toepler^s Experiment. 
 
 "When a small vibrating coal-gas flame is carefully 
 examined by the rotating mirror, the beaded line is a 
 series of yellow-tipped flames, each resting upon a base of 
 the richest blue. In some cases I have been unable to 
 observe any union of one flame with another ; the spaces 
 between the flames being absolutely dark to the eye. But 
 if dark, the flame must have been totally extinguished at 
 intervals, a residue of heat, however, remaining sufficient 
 to reignite the gas. This is at least possible, for gas may 
 be ignited by non-luminous air. 1 By means of the siren, 
 we can readily determine the number of times this flame 
 extinguishes and relights itself in a second. As the note 
 of the instrument approaches that of the flame, unison is 
 preceded by these well-known beats, which become gradu- 
 ally less rapid, and now the two notes melt into perfect 
 unison. Maintaining the siren at this pitch for a minute, 
 at the end of that time I find recorded upon our dials 
 1,700 revolutions. But the disk being perforated by 16 
 holes, it follows that every revolution corresponds to 16 
 pulses. Multiplying 1,700 by 16, we find the number of 
 pulses in a minute to be 27,200. This number of times 
 did our little flame extinguish and rekindle itself during 
 the continuance of the experiment ; that is to say, it was 
 put out and relighted 453 times in a second. 
 
 1 A gas-jet, for example, can be ignited five inches above the tip of a 
 visible gas-flame, where platinum-leaf shows no redness. 
 
252 SOUND. 
 
 A flash of light, though instantaneous, makes an im- 
 pression upon the retina which endures for the tenth of a 
 second or more. A flying rifle-bullet, illuminated by a 
 single flash of lightning, would seem to stand still in the 
 air for the tenth of a second. A black disk with radial 
 white strips, when rapidly rotated, causes the white and 
 black to blend to an impure gray ; while a spark of elec- 
 tricity, or a flash of lightning, reduces the disk to appar- 
 ent stillness, the white radial strips being for a time 
 plainly seen. Now, the singing flame is a flashing flame, 
 and M. Toepler has shown that by causing a striped disk 
 to rotate at the proper speed in the presence of such a 
 flame it is brought to apparent stillness, the white stripes 
 being rendered plainly visible. The experiment is both 
 easy and interesting. 
 
 5. Harmonic Sounds of Flame. 
 
 A singing flame yields so freely to the pulses falling upon 
 it that it is almost wholly governed by the surrounding 
 tube ; almost, but not altogether. The pitch of the note 
 depends in some measure upon the size of the flame. 
 This is readily proved, by causing two flames to emit the 
 same note, and then slightly altering the size of either 
 of them. . The unison is instantly disturbed by beats. By 
 altering the size of a flame we can also, as already illus- 
 trated, draw forth the harmonic overtones of the tube 
 which surrounds it. This experiment is best performed 
 with hydrogen, its combustion being much more vigorous 
 than that of ordinary gas. When a glass tube Y feet long 
 is placed over a large hydrogen-flame, the fundamental 
 note of the tube is obtained, corresponding to a division 
 of the column of air within it by a single node at the 
 centre. Placing a second tube, 3 feet 6 inches long, over 
 the same flame, no musical sound whatever is obtained ; 
 the large flame, in fact, is not able to accommodate 
 
HISTORY OF SINGING FLAMES. 253 
 
 itself to the vibrating period of the shorter tube. But, 
 on lessening the flame, it soon bursts into vigorous song, 
 its note being the octave of that yielded by the longer 
 tube. I now remove the shorter tube, and once more 
 cover the flame with the longer one. It no longer sounds 
 its fundamental notes, but the precise note of the shorter 
 tube. To accommodate itself to the vibrating period of 
 the diminished flame, the longer column of air divides 
 itself like an open organ-pipe when it yields its first har- 
 monic. By varying the size of the flame, it is possible, 
 with the tube now before you, to obtain a series of notes 
 whose rates of vibration are in the ratio of the numbers 
 1:2:3:4:5; that is to say, the fundamental tone and 
 its first four harmonics. 
 
 These sounding flames, though probably never before 
 raised to the intensity in which they have been exhibited 
 here to-day, are of old standing. In 1777, the sounds of 
 a hydrogen-flame were heard by Dr. Higgins. In 1802, 
 they were investigated to some extent by Chladni, who also 
 refers to an incorrect account of them given by De Luc. 
 Chladni showed that the tones are those of the open tube 
 which surrounds the flame, and he succeeded in obtaining 
 the first two harmonics. In 1802, G. De la Rive experi- 
 mented on this subject. Placing a little water in the bulb 
 of a thermometer, and heating it, he showed that musical 
 tones of force and sweetness could be produced by the 
 periodic condensation of the vapor in the stem of the 
 thermometer. He accordingly referred the sounds of 
 flames to the alternate expansion and condensation of the 
 aqueous vapor produced by the combustion. We can 
 readily imitate his experiments. Holding, with its stem 
 oblique, a thermometer-bulb containing water in the flame 
 of a spirit-lamp, the sounds are heard soon after the water 
 begins to boil. In 1818, however, Faraday showed that 
 the tones are produced when the tube surrounding the 
 
254: SOUND. 
 
 flame is placed in air of a temperature higher than 100 
 0., condensation being then impossible. He also showed 
 that the tones could be obtained from flames of carbonic 
 oxide, where aqueous vapor is entirely out of the question. 
 
 6. Action of Extraneous Sounds on Flame : Experi- 
 ments of Schaffgotsch and Tyndall. 
 
 After these experiments, the first novel acoustic ob- 
 servation on flames was made in Berlin by the late Count 
 Schaffgotsch, who showed that when an ordinary gas-flame 
 was surmounted by a short tube, a strong falsetto voice 
 pitched to the note of the tube, or to its higher octave, 
 caused the flame to quiver. In some cases when the note 
 of the tube was high, the flame could even be extinguished 
 by the voice. 
 
 In the spring of 1857, this experiment came to my 
 notice. No directions were given in the short account 
 of the observation published in Poggendorff^s Annalen ; 
 but, in endeavoring to ascertain the conditions of success, a 
 number of singular effects forced themselves upon my at- 
 tention. Meanwhile, Count Schaffgotsch also followed up 
 the subject. To a great extent we traveled over the same 
 ground, neither of us knowing how the other was en- 
 gaged ; but, so far as the experiments then executed are 
 common to us both, to Count Schaffgotsch belongs the 
 priority. 
 
 Let me here repeat his first observation. Within this 
 tube, 11 inches long, burns a small gas-flame, bright and 
 silent. The note of the tube has been ascertained, and 
 now, standing at some distance from the flame, I sound 
 that note ; the flame quivers. To obtain the extinction 
 of the flame it is necessary to employ a burner with a very 
 narrow aperture, from which the gas issues under consider- 
 able pressure. On gently sounding the note of the tube 
 
EXPERIMENTS OF SCHAFFGOTSCH AND TYNDALL. 255 
 
 surrounding such a flame, it quivers; but on throwing 
 more power into the voice the flame is extinguished. 
 
 The cause of the quivering of the flame will be best 
 revealed by an experiment with the siren. As the note 
 of the siren approaches that of the flame you hear beats, 
 and at the same time you observe a dancing of the flame 
 synchronous with the beats. The jumps succeed each 
 other more slowly as unison is approached. They cease 
 when the unison is perfect, and they begin again as soon 
 as the siren is urged beyond unison, becoming more rapid 
 as the discordance is increased. The cause of the quiver 
 observed by M. Schaffgotsch was revealed to me. The 
 flame jumped because the note of the tube surrounding it 
 was nearly, but not quite, in unison with the voice of the 
 experimenter. 
 
 That the jumping of the flame proceeds in exact accord- 
 ance with the beats is well shown by a tuning-fork, which 
 yields the same note as the flame. Loading such a fork 
 with a bit of wax, so as to throw it slightly out of unison, 
 and bringing it, when agitated, near the tube in which 
 the flame is singing, the beats and the leaps of the flamo 
 occur at the same intervals. "When the fork is placed over 
 a resonant jar, all of you can hear the beats, and see at 
 the same time the dancing of the flame. By changing 
 the load upon the tuning-fork, or by slightly altering 
 the size of the flame, the rate at which the beats succeed 
 each other may be altered; but in all cases the jumps 
 address the eye at the moments when the beats address 
 the ear. 
 
 While executing these experiments, I noticed that, on 
 raising my voice to the proper pitch, a flame which had 
 been burning silently in its tube began to sing. The same 
 observation had, without my knowledge, been made a 
 short time previously by Count Schaffgotsch. A tube, 12 
 inches long, is placed over this flame, which occupies a 
 
256 SOUND. 
 
 position about an inch and a half from the lower end of 
 the tube. "When the proper note is sounded the flame 
 trembles, but it does not sing. When the tube is lowered 
 until the flame is three inches from its end, the song is 
 spontaneous. Between these two positions there is a 
 third, at which, if the flame be placed, it will burn si- 
 lently ; but if it be excited by the voice it will sing, and 
 continue to sing. 
 
 Even when the back is turned toward the flame the 
 sonorous pulses run round the body, reach the tube, and 
 call forth the song. A pitch-pipe, or any other instrument 
 which yields a note of the proper height, produces the 
 same effect. Mounting a series of tubes, capable of emit- 
 ting all the notes of the gamut, over suitable flames, with 
 an instrument sufficiently powerful, and from a distance 
 of 20 or 30 yards, a musician, by running over the scale, 
 might call forth all the notes in succession, the whole series 
 of flames finally joining in the song. 
 
 When a silent flame, capable of being excited in the 
 manner here described, is looked at in a moving mirror, it 
 produces there a continuous band of light. Nothing can 
 be more beautiful than the sudden breaking up of this 
 band into a string of richly-luminous pearls at the instant 
 the voice is pitched to the proper note. 
 
 One singing flame may be caused to effect the musical 
 ignition of another. Before you are two small flames,/'' 
 and /*, Fig. 118, the tube over f being 10f inches, and 
 that over f 12 inches long. The shorter tube is clasped 
 by a paper slider, s. The flame f is now singing, but the 
 flame f, in the longer tube, is silent. I raise the paper 
 slider which surrounds f, so as to lengthen the tube, 
 and on approaching the pitch of the tube surrounding /', 
 that flame sings. The experiment may be varied by 
 making f the singing flame and f the silent one at start- 
 ing. Raising the telescopic slider, a point is soon attained 
 
SENSITIVE FLAMES. 257 
 
 where the flame f commences its song. In this way one 
 flame may excite another through considerable distances. 
 
 FIG. 118. 
 
 It is also possible to silence the singing flame by the 
 nrrmp.r manao-pTriPTit, of thft voine. 
 
 i 
 
 proper management of the voice. 
 
 SENSITIVE NAKED FLAMES. 
 
 7. D^scovery of Sensitive Flames by Le Conte. 
 
 WQ have hitherto dealt with flames surrounded by 
 resonant tubes ; and none of these flames, if naked, would 
 respond in any way to such noise or music as could be 
 here applied. Still it is possible to make naked flames 
 thus sympathetic. This action of musical sounds upon 
 
258 SOUND. 
 
 naked flames was first observed by Prof. Le Conte at a 
 musical party in the United States. His observation is 
 thus described : " Soon after the music commenced, I 
 observed that the flame exhibited pulsations which were 
 exactly synchronous with the audible beats. This phe- 
 nomenon was very striking to every one in the room, and 
 especially so when the strong notes of the violoncello 
 came in. It was exceedingly interesting to observe how 
 perfectly even the trills of this instrument were reflected 
 on the sheet of flame. A deaf man might have seen the 
 harmony. As the evening advanced, and the diminished 
 consumption of gas in the city increased the pressure^ the 
 phenomenon became more conspicuous. The jumping of 
 the flame gradually increased, became somewhat irregular, 
 and, finally, it began to flare continuously, emitting the 
 characteristic sound, indicating the escape of a greater 
 amount of gas than could be properly consumed. I then 
 ascertained, by experiment, that the phenomenon did not 
 take place unless the discharge of gas was so regulated 
 that the flame approximated to the condition of flaring. I 
 likewise determined, by experiment, that the effects were 
 not produced by jarring or shaking the floor and walls of 
 the room by means of repeated concussions. Hence it is 
 obvious that the pulsations of the flame were not owing to 
 indirect vibrations propagated through the medium of the 
 walls of the room to the burning-apparatus, but must have 
 been produced by the direct influence of aerial sonorous 
 pulses on the burning jet." 1 
 
 The significant remark, that the jumping of the flame 
 
 1 Philosophical Magazine, March, 1858, p. 235. In the Appendix Prof. 
 Le Conte's interesting paper is given in extenso. Some years subsequently 
 Mr. (now Professor) Barrett, while preparing some experiments for my 
 lectures, observed the action of a musical sound upon a flame, and by 
 the selection of suitable burners he afterward succeeded in rendering the 
 flame extremely sensitive. Le Conte, of whose discovery I informed Mr, 
 Barrett, was my own starting-point. 
 
SENSITIVENESS OF A CANDLE-FLAME. 
 
 259 
 
 was not observed until it was near flaring, suggests the 
 means of repeating the experiments of Dr. Le Conte ; while 
 a more intimate knowledge of the conditions of success 
 enables us to vary and exalt them in a striking degree. 
 Before you burns a bright candle-flame, but no sound that 
 can be produced here has any effect upon it. Though 
 sonorous waves of great power be sent through the air, the 
 candle-flame remains insensible. 
 
 But by proper precautions even a candle-flame may be 
 rendered sensitive. Urging from a small blow-pipe a 
 narrow stream of air through such a flame, an incipient 
 flutter is produced. The flame then jumps visibly to the 
 sound of a whistle, or to a chirrup. The experiment may 
 be so arranged that, when the whistle sounds, the flame 
 shall be either restored almost to its pristine brightness, or 
 that the small amount of light it still possesses shall disap- 
 pear. 
 
 The blow-pipe flame of our laboratory is totally un- 
 affected by the sound of the whistle as long as no air is 
 urged through it. By properly tempering the force of the 
 blast, a flame is obtained of the shape shown in Fig. 119. 
 
 FIG. 119. 
 
 FIG. 120. 
 
 On sounding the whistle the erect portion of the flame 
 drops down, and while the sound continues the flame 
 maintains the form shown in Fig. 120. 
 
260 SOUND. 
 
 8. Experiments on Fish-tail and JSafs-wing Flames. 
 
 We now pass on to a thin sheet of flame, issuing from 
 a common fish-tail burner, Fig. 121. You might sing to 
 this flame, varying the pitch of your voice, no shiver of 
 the flame would be visible. You might employ pitch- 
 
 FIG. 122. 
 
 FHJ. 121. 
 
 pipes, tuning-forks, bells, and trumpets, with a like ab- 
 sence of all effect. A barely perceptible motion of the 
 interior of the flame may be noticed when a shrill whistle 
 is blown close to it. But by turning the cock more fully 
 on, the flame is brought to the verge of flaring. And now, 
 when the whistle is blown, the flame thrusts suddenly out 
 seven quivering tongues, Fig. 122. The moment the 
 sound ceases, the tongues disappear, and the flame be- 
 comes quiescent. 
 
 Passing from a fish-tail to a bat's-wing burner, we 
 obtain a broad, steady flame, Fig. 123. It is quite insen- 
 sible to the loudest sound which would be tolerable here. 
 The flame is fed from a small gas-holder. 1 Increasing 
 
 1 A gas-bag properly weighted also answers for these experiments. 
 
BATS-WING FLAMES. 
 
 261 
 
 gradually the pressure, a slight flutter of the edge of the 
 flame at length answers to the sound of the whistle. Turn- 
 ing on the gas until the flame is on the point of roaring, 
 and blowing the whistle, it roars, and suddenly assumes 
 the form shown in Fig. 124. 
 
 When a distant anvil is struck with a hammer, the 
 flame instantly responds by thrusting forth its tongues. 
 
 An essential condition to entire success in these experi- 
 
 FIG. 124. 
 
 ments disclosed itself in the following manner : I was 
 operating on two fish-tail flames, one of which jumped to 
 a whistle while the other did not. The gas of the non- 
 sensitive flame was turned off, additional pressure being 
 thereby thrown upon the other -flame. It flared, and its 
 cock was turned so as to lower the flame ; but it now 
 proved non-sensitive, however close it might be brought to 
 the point of flaring. The narrow orifice of the half -turned 
 cock interfered with the action of the sound. When the 
 gas was turned fully on, the flame being lowered by open 
 ing the cock of the other burner, it became again sensi- 
 tive. Up to this time a great number of burners had 
 been tried, but with many of them the action was nil. 
 Acting, however, upon the hint conveyed by this observa- 
 
262 
 
 SOUND. 
 
 tion, the cocks which, fed the flames were more widely 
 opened, and our most refractory burners thus rendered 
 sensitive. 
 
 In this way the observation of Dr. Le Conte is easily 
 and strikingly illustrated ; in our subsequent, and far more 
 delicate experiments, the precaution just referred to is still 
 more essential. 
 
 9. Experiments on Flames from Circular Apertures. 
 
 A long flame may be shortened and a short one length- 
 ened, according to circumstances, by sonorous vibrations. 
 The flame shown in Fig. 125 is long, straight, and smoky ; 
 that in Fig. 126 is short, forked, and brilliant. On sound- 
 
 FIG. 128. 
 
 FIG. 126. 
 
 Fro. 129. 
 
 ing the whistle, the long flame becomes short, forked, and 
 brilliant, as in Fig. 127 ; while the forked flame becomes 
 
TALL FLAMES. 263 
 
 long and smoky, as in Fig. 128. As regards, therefore, 
 their response to the sound of the whistle, one of these 
 flames is the complement of the other. 
 
 In Fig. 129 is represented another smoky flame which, 
 when the whistle sounds, breaks up into the form shown 
 in Fig. 130. 
 
 When a brilliant sensitive flame illuminates an other- 
 wise dark room, in which a suitable bell is caused to strike, / 
 a series of periodic quenchings of the light by the soimcr 
 occurs. Every stroke of the bell is accompanied by a mo- 
 mentary darkening of the room. 
 
 The foregoing experiments illustrate the lengthening 
 and shortening of flames by sonorous vibrations. They 
 may also produce rotation. From some of our home-made 
 burners issue flat flames, about ten inches high, and three 
 inches across at their widest part. When the whistle 
 sounds, the plane of each flame turns ninety degrees round, 
 and continues in its new position as long as the sound 
 continues. 
 
 A flame of admirable steadiness and brilliancy now 
 burns before you. It issues from a single circular orifice 
 in a common iron nipple. This burner, which requires 
 great pressure to make its flame flare, has been specially 
 chosen for the purpose of enabling you to observe, with 
 distinctness, the gradual change from apathy to sensitive- 
 ness. The flame, now 4 inches high, is quite indifferent 
 to sound. On increasing the pressure its height becomes 
 6 inches ; but it is still indifferent. "When its length is 12 
 inches, a barely perceptible quiver responds to the whistle. 
 When 16 or 17 inches high, it jumps briskly the moment 
 an anvil is tapped or the whistle sounded. When the 
 flame is 20 inches long you observe a quivering at inter- 
 vals, which announces that it is near roaring. A slight 
 increase of pressure causes it to roar, and shorten at the 
 same time to 8 inches. 
 12 
 
264: SOUND. 
 
 Diminishing the pressure a little, the flame is again 
 20 inches long, but it is on the point of roaring and short- 
 ening. Like the singing flames which were started by 
 the voice, it stands on the brink of a precipice. The 
 proper note pushes it over. It shortens when the whistle 
 sounds, exactly as it did when the pressure is in excess. 
 The action reminds one of the story of the Swiss mule- 
 teers, who are said to tie up their bells at certain places 
 lest the tinkle should bring an avalanche down. The 
 snow must be very delicately poised before this could oc- 
 cur. It probably never did occur, but our flame illus- 
 trates the principle. We bring it to the verge of falling, 
 and the sonorous pulses precipitate what was already im- 
 minent. This is the simple philosophy of all these sensi- 
 tive flames. 
 
 When the flame flares, the gas in the orifice of the 
 burner is in a state of vibration ; conversely, when the 
 gas in the orifice is thrown into vibration, the flame, if 
 sufiiciently near the flaring point, will flare. Thus the 
 sonorous vibrations, by acting on the gas in the passage of 
 the burner, become equivalent to an augmentation of press- 
 ure in the holder. In fact, we have here revealed to ua 
 the physical cause of flaring through excess of pressure, 
 which, common as it is, has never been hitherto explained. 
 The gas encounters friction in the orifice of the burner, 
 which, when the force of transfer is sufiiciently great, 
 throws the issuing stream into the state of vibration that 
 produces flaring. It is because the flaring is thus caused, 
 that an infinitesimal amount of energy in the form of 
 vibrations of the proper period can produce an effect equiv- 
 alent to a considerable increase of pressure. 
 
 10. Seat of Sensitiveness. 
 
 That the external vibrations act upon the gas in the 
 orifice of the burner, and not first upon the burner itself, 
 
SEAT OF SENSITIVENESS. 
 
 265 
 
 the tube leading to it, or the flame above it, is thus 
 proved. A glass funnel K, Fig. 131, is attached to a tube 
 3 feet long, and half an inch in diameter. A sensitive 
 flame 5 is placed at the open end T of the tube, while a 
 email high-pitched reed is placed in the funnel at E. 
 
 FIG. 131. 
 
 When the sound is converged upon the root of the flame, 
 as in Fig. 131, the action is violent ; when converged on a 
 point half an inch above the burner, as in Fig. 132, or at 
 
 Fro. 182. FIG. 133. 
 
 
 half an inch below the burner, as in Fig. 133, there is no 
 action. The glass tube may be dispensed with and the 
 
266 SOUND. 
 
 funnel alone employed, if care be taken to screen off all 
 sound save that which passes through the shank of the 
 funnel. 1 
 
 11. Influence of Pitch. 
 
 All sounds are not equally effective on the flame; 
 waves of special periods are required to produce the maxi- 
 mum effect. The effectual periods are those which syn- 
 chronize with the waves produced by the friction of the 
 gas itself against the sides of its orifice. "With some of 
 these flames a low deep whistle is more effective than a 
 shrill one. "With others the exciting tremors must be 
 very rapid, and the sound consequently shrill. !N"ot one 
 of these four tuning-forks, which vibrate 256 times, 320 
 times, 384 times, and 512 times respectively in a second, 
 has any effect upon the flame from our iron nipple. But, 
 besides their fundamental tones, these forks, as you know, 
 can be caused to yield a series of overtones of very high 
 pitch. The vibrations of this series are 1,600, 2,000, 2,400, 
 and 3,200 per second, respectively. The flame jumps in 
 response to each of these sounds ; the response to that of 
 the highest pitch being the most prompt and energetic of 
 all. 
 
 To the tap of a hammer upon a board the flame re- 
 sponds ; but to the tap of the same hammer upon an anvil 
 the response is much more brisk and animated. The 
 reason is, that the clang of the anvil is rich in the higher 
 tones to which the flame is most sensitive. The powerful 
 tone obtained when our inverted bell is reenf orced by its 
 resonant tube has no power over this flame. But when a 
 halfpenny is brought into contact with the vibrating sur- 
 face the flame instantly shortens, flutters, and roars. I 
 
 1 In the actions described in the case of the blow-pipe and candle flames, 
 it was the jet of air issuing from the blow-pipe, and not the flame itself, that 
 was directly acted on by the external vibrations. 
 
INFLUENCE OF PITCH. 
 
 267 
 
 Bond an assistant with a smaller bell, worked by clock-work, 
 to the most distant part of the gallery. He there detaches 
 the hammer ; the strokes follow each other in rhythmic 
 succession, and at every stroke the flame FIG. 134. FIG. 135. 
 falls from a height of 20 to a height of 8 
 inches, roaring as it falls. 
 
 The rapidity with which sound is prop- 
 agated through air is well illustrated by 
 these experiments. There is no sensible 
 interval between the stroke of the bell 
 and the ducking of the flame. 
 
 When the sound acting on the flame 
 is of very short duration a curious and 
 instructive effect is observed. The sides 
 of the flame half-way down, and lower, 
 are seen suddenly fringed by luminous 
 tongues, the central flame remaining ap- 
 parently undisturbed in both height and 
 thickness. The flame in its normal state 
 is shown in Fig. 134, and with its fringes 
 in Fig. 135. The effect is due to the re- 
 tention of the impression upon the retina. 
 The flame actually falls as low as the 
 fringes, but its recovery is so quick that 
 to the eye it does not appear to shorten at all. 1 
 
 12. The Vowel-flame. 
 
 A flame of astonishing sensitiveness now burns before 
 you. It issues from the single orifice of a steatite burner, 
 and reaches a height of 24 inches. The slightest tap on 
 
 1 Numerous modifications of these experiments are possible. Other 
 inflammable gases than coal-gas may be employed. Mixtures of gases 
 have also been found to yield beautiful and striking results. An infini- 
 tesimal amount of mechanical impurity has been found to exert a powerful 
 influence. 
 
268 SOUND. 
 
 a distant anvil reduces its height to 7 inches. When a 
 bunch of keys is shaken the flame is violently agitated, 
 and emits a lend roar. The dropping of a sixpence into a 
 hand already containing coin, at a distance of 20 yards, 
 knocks the flame down. It is not possible to walk across 
 the floor without agitating the flame. The creaking of 
 boots sets it in violent commotion. The crumpling, 
 or tearing of paper, or the rustle of a silk dress, does the 
 same. It is startled by the patter of a rain-drop. I hold 
 a watch near the flame : nobody hears its ticks ; but you 
 all see their effect upon the flame. At every tick it falls 
 and roars. The winding up of the watch also produces 
 tumult. The twitter of a distant sparrow shakes the 
 flame ; the note of a cricket would do the same. A chir- 
 rup from a distance of 30 yards causes it to fall and roar. 
 I repeat a passage from Spenser : 
 
 " Her ivory forehead full of bounty brave, 
 
 Like a broad table did itself dispread ; 
 For love his lofty triumphs to engrave, 
 
 And write the battles of his great godhead. 
 All truth and goodness might therein be read, 
 
 For there their dwelling was, and when she spake, 
 Sweet words, like dropping honey she did shed ; 
 
 And through the pearls and rubies softly brake 
 A silver sound, which heavenly music seemed to make." 
 
 The flame selects from the sounds those to which it can 
 respond. It notices some by the slightest nod, to others 
 it bows more distinctly, to some its obeisance is very 
 profound, while to many sounds it turns an entirely deaf 
 ear. 
 
 In Fig. 136, this wonderful flame is represented. On 
 chiiTuping to it, or on shaking a bunch of keys within a 
 few yards of it, it falls to the size shown in Fig. 137, the 
 whole length, a 5, of the flame being suddenly abolished. 
 The light at the same time is practically destroyed, a pale 
 and almost non-luminous residue of it alone remain- 
 
THE VOWEL-FLAME. 269 
 
 ing. These figures are taken from photographs of the 
 flame. 
 
 To distinguish it from the others I have called this 
 FIG. 136. the " vowel-flame," because the different vowel- 
 sounds affect it differently. A loud and sonorous 
 u does not move the flame ; on changing the 
 sound to O 5 the flame quivers ; when E is sounded, 
 the flame is strongly affected. I utter the words 
 booty boat, and beat, in succession. To the first 
 there is no response ; to the second, the flame 
 starts ; by the third is thrown into greater com- 
 motion ; the sound Ah ! is still more powerful. 
 Did we not know the constitution of vowel-sounds 
 this deportment would be an insoluble enigma. 
 As it is, however, the flame illustrates the theory 
 of vowel-sounds. It is most sensitive to sounds 
 of high pitch ; hence we should infer that the 
 sound Ah ! contains higher notes than the sound 
 E ; that E contains higher notes than o ; and o 
 higher notes than u. I need not say that F re . 137. 
 this agrees perfectly with the analysis of 
 Helmholtz. 
 
 This flame is peculiarly sensitive to 
 the utterance of the letter s. A hiss 
 contains the elements that most forcibly 
 affect the flame. The gas issues from its 
 burner with a hiss, and an external sound 
 of this character is therefore exceedingly 
 effective. From a metal box containing 
 compressed air I allow a puff to escape ; 
 the flame instantly ducks down not by 
 any transfer of air from the box to the 
 flame, for the distance between both utterly excludes this 
 idea it is the sound that affects the flame. From the 
 most distant part of the gallery my assistant permits the 
 
270 
 
 SOUND. 
 
 FIG. 138. 
 
 compressed air to issue in puffs from the box ; at every 
 puff the flame suddenly falls. The hiss of the issuing air 
 at the one orifice precipitates the tumult of the flame at 
 the other. 
 
 When a musical-box is placed on the table, and per- 
 mitted to play, the flame behaves like a sentient and 
 motor creature bowing slightly to some tones, and cour- 
 tesying deeply to others. 
 
 13. Mr. Philip Barry's Sensitive Flame. 
 
 Mr. Philip Barry has discovered a new and very effec- 
 tive form of sensitive flame, which he thus describes in a 
 letter to myself : " It is the most sensitive of all the 
 flames that I am acquainted with, though from its smaller 
 size it is not so striking as your vowel-flame. It possesses 
 the advantage that the ordinary 
 pressure in the gas-mains is quite 
 sufficient to produce it. The 
 method of producing it consists in 
 igniting the gas (ordinary coal- 
 gas) not at the burner but some 
 inches above it, by interposing be- 
 tween the burner and the flame a 
 piece of wire-gauze." 
 
 I give a sketch of the arrange- 
 ment adopted, Fig. 138. The space 
 between the burner and gauze was 
 2 inches. The gauze was about 7 
 inches square, resting on the ring 
 of a retort - stand. It had 32 
 meshes to the lineal inch. The 
 burner was Sugg's steatite pinhole burner, the same as 
 used for the vowel-flame. 
 
 The flame is a slender cone about four inches high, 
 the upper portion giving a bright-yellow light, the base 
 
BARRY'S FLAME. 271 
 
 being a non-luminous blue flame. At the least noise this 
 flame roars, sinking down to the surface of the gauze, be- 
 coming at the same time invisible. It is very active in 
 its responses, and, being rather a noisy flame, its sympathy 
 is apparent to the ear as well as the eye. 
 
 " To the vowel-sounds it does not appear to answer 
 so discriminately as the vowel-flame. It is extremely 
 sensitive to A, very slightly to E, more so to i, entirely 
 non-sensitive to o, but slightly sensitive to u. 
 
 "It dances in the most perfect manner to a small 
 musical snuff-box, and is highly sensitive to most of the 
 sonorous vibrations which affect the vowel-flames." 
 
 14. Sensitive Smoke-jets. 
 
 It is not to the flame, as such, that we owe the ex- 
 traordinary phenomena which have been just described. 
 Effects substantially the same are obtained when a jet of 
 unignited gas, of carbonic acid, hydrogen, or even air itself, 
 issues from an orifice under proper pressure. None of 
 these gases, however, can be seen in its passage through 
 air, and, therefore, we must associate with them some 
 substance which, while sharing their motions, will reveal 
 them to the eye. The method employed from time to 
 time in this place of rendering aerial vortices visible is 
 well known to many of you. By tapping a membrane 
 which closes the mouth of a large funnel filled with 
 smoke, we obtain beautiful smoke-rings, which reveal the 
 motion of the air. By associating smoke with our gas- 
 jets, in the present instance, we can also trace their course, 
 and, when tin's is done, the unignited gas proves as sensi- 
 tive as the flames. The smoke-jets jump, shorten, split 
 into forks, or lengthen into columns, when the proper 
 notes are sounded. 
 
 Underneath this gas-holder are placed two small basins, 
 
272 SOUND. 
 
 the one containing hydrochloric acid, and the other am- 
 monia. Fumes of sal-ammoniac are thus copiously formed, 
 and mingle with the gas contained in the holder. "We 
 may, as already stated, operate with coal-gas, carbonic acid, 
 air, or hydrogen ; each of them yields good effects. From 
 our excellent steatite burner now issues a thin column of 
 smoke. On sounding the whistle, which was so effective 
 with the flames, it is found ineffective. When, more- 
 over, the highest notes of a series of Pandean pipes are 
 sounded, they are also ineffective. Nor will the lowest 
 notes answer. But when a certain pipe, which stands 
 about the middle of the series, is sounded, the smoke- 
 column falls, forming a short stem with a thick, bushy 
 head. It is also pressed down, as if by a vertical wind, by 
 a knock upon the table. At every tap it drops. A stroke 
 on an anvil, on the contrary, produces little or no effect. 
 In fact, the notes here effective are of a much lower pitch 
 than those which .were most efficient in the case of the 
 flames. 
 
 The amount of shrinkage exhibited by , some of these 
 smoke-columns, in proportion to their length, is far greater 
 than that of the flames. A tap on the table causes a smoke- 
 jet eighteen inches high to shorten to a bushy bouquet, 
 with a stem not more than an inch in height. The smoke- 
 column, moreover, responds to the voice. A cough knocks 
 it down; and it dances to the tune of a musical-box. 
 Some notes cause the mere top of the smoke-column to 
 gather itself up into a bunch ; at other notes the bunch 
 is formed midway down; while notes of more suitable 
 pitch cause the column to contract itself to a cumulus not 
 much more than an inch above the end of the burner. 
 Yarious forms of the dancing smoke-jet are shown in Fig. 
 139. As the music continues, the action of the smoke- 
 column consists of a series of rapid leaps from one of these 
 forms to another. 
 
SENSITIVE SMOKE-JETS. 
 
 273 
 
 1 
 
 In a perfectly still atmosphere these slender smoke- 
 colums rise sometimes to a height of nearly two feet, 
 apparently vanishing into air at the summit. "When this 
 is the case, our most Fm. 139. 
 
 sensitive flames fall far 
 behind them in delicacy ; 
 and though less striking 
 than the flames, the 
 smoke-wreaths are often 
 more graceful. Not only 
 special words, but every 
 word, and even every 
 syllable, of the foregoing 
 stanza from Spenser, 
 tumbles a really sensitive 
 smoke-jet into confusion. 
 
 To produce such effects, 
 a perfectly tranquil at- 
 mosphere is necessary. 
 Flame-experiments, in fact, are possible in an atmosphere 
 where smoke-jets are utterly unmanageable. 1 
 
 15. Constitution of Liquid Veins : Sensitive 
 Water-jets. 
 
 "We have thus far confined our attention to jets of 
 ignited and unignited coal-gas of carbonic acid, hydro- 
 gen, and air. We will now turn to jets of water. And 
 here a series of experiments, remarkable for their 
 
 1 Referring to these effects, Hehnholtz says : " Die erstaunliche Em- 
 pfindlichkeit eines mit Rauch impragnirten cylindrischen Luftstrahls gegen 
 Schall ist von Herrn Tyndall beschrieben worden ; ich habe dieselbe besta' 
 tigt gefunden. Es ist dies offenbar eine Eigenschaft der Trennungsflachen 
 die fiir das Anblasen der Pfeifen von grosster Wichtigkeit ist." (" Discon- 
 tinuirliche Luftbewegung," Monatsbericht, April 1868.) 
 
274 
 
 SOUND. 
 
 Fie. 140. 
 a 
 
 FIG. 141. 
 
 FIG. 142. 
 a 
 
 beauty, has long existed, which 
 claim relationship to those just 
 described. These are the ex- 
 periments of Felix Savart on 
 liquid veins. If the bottom 
 of a vessel containing water 
 be pierced by a circular ori- 
 fice, the descending liquid vein 
 will exhibit two parts unmis- 
 takably distinct. The part of 
 the vein nearest the orifice is 
 steady and limpid, presenting 
 the appearance of a solid glass 
 rod. It decreases in diameter 
 as it descends, reaches a point 
 of maximum contraction, from 
 which point downward it ap- 
 pears turbid and unsteady. The 
 course of the vein, moreover, is 
 marked by periodic swellings 
 and contractions. Savart has 
 represented these appearances 
 as in Fig. 140. The part a n 
 nearest the orifice is limpid 
 and steady, while all the part 
 
 */ * -I 
 
 below n is in a state of quiver- 
 ing motion. This lower part 
 of the vein appears continuous 
 to the eye ; but the finger can 
 be sometimes passed through 
 it without being wetted. This, 
 of course, could not be the 
 case if the vein were really 
 continuous. The upper por- 
 tion of the vein, moreover, 
 
CONSTITUTION OF LIQUID VEINS. 275 
 
 intercepts vision ; the lower portion, even when the liquid 
 is mercury, does not. In fact, the vein resolves itself, at 
 n, into liquid spherules, its apparent continuity being due 
 to the retention of the impressions made by the falling 
 drops upon the retina. If, while looking at the disturbed 
 portion of the vein, the head be suddenly lowered, the 
 descending column will be resolved for a moment into 
 separate drops. Perhaps the simplest way of reducing 
 the vein to its constituent spherules is to illuminate the 
 vein, in a dark room, by a succession of electric flashes. 
 Every flash reveals the drops, as if they were perfectly 
 motionless in the air. 
 
 Could the appearance of the vein illuminated by a 
 single flash be rendered permanent, it would be that rep- 
 resented in Fig. 141. And here we find revealed the 
 cause of those swellings and contractions which the dis- 
 turbed portion of the vein exhibits. The drops, as they 
 descend, are continually changing their forms. When first 
 detached from the end of the limpid portion of the vein, 
 the drop is a spheroid with its longest axis vertical. But 
 a liquid cannot retain this shape, if abandoned to the 
 forces of its own molecules. The spheroid seeks to become 
 a sphere the longer diameter, therefore, shortens ; but, 
 like a pendulum which seeks to return to its position of 
 rest, the contraction of the vertical diameter goes too far, 
 and the drop becomes a flattened spheroid. Now, the con- 
 tractions of the jet are formed at those places where the 
 longest axis of the drop is vertical, while the swellings 
 appear where the longest axis is horizontal. It will be 
 noticed that between every two of the larger drops is a 
 third one of much smaller dimensions. According to 
 Savart, their appearance is invariable. 
 
 I wish to make the constitution of a liquid vein evi- 
 dent to you by a simple but beautiful experiment. The 
 condensing lens has been removed from our electric lamp, 
 
276 SOUND. 
 
 tlie light being permitted to pass through a vertical slit 
 directly from the carbon-points. The slice of light thus 
 obtained is so divergent that it illuminates, from top to 
 bottom, a liquid vein several feet long, and placed at some 
 distance from the lamp. Immediately in front of the 
 camera is a large disk of zinc with six radial slits, about 
 ten inches long and an inch wide. By the rotation of the 
 disk the light is caused to fall in flashes upon the jet ; and, 
 when the suitable speed of rotation has been attained, the 
 vein is resolved into its constituent spherules. Receiving 
 the shadow of the vein upon a white screen, its constitu- 
 tion is rendered clearly visible to all here present. 
 
 This breaking-up of a liquid vein into drops has been 
 a subject of frequent experiment and much discussion. 
 Savart traced the pulsations to the orifice, but he did not 
 think that they were produced by friction. They are 
 powerfully influenced by sonorous vibrations. In the 
 midst of a large city it is hardly possible to obtain the 
 requisite tranquillity for the full development of the con- 
 tinuous portion of the vein ; still, Savart was so far able 
 to withdraw his vein from the influence of such irregular 
 vibrations, that its limpid portion became elongated to 
 the extent shown in Fig. 142. It will be understood that 
 Fig. 139 represents a vein exposed to the irregular vibra- 
 tions of the city of Paris, while Fig. 141 represents one 
 produced under precisely the same conditions, but with- 
 drawn from those vibrations. 
 
 The drops into which the vein finally resolves itself 
 are incipient even in its limpid portion, announcing 
 themselves there as annular protuberances, which become 
 more and more pronounced, until finally they separate. 
 Their birthplace is near the orifice itself, and under even 
 moderate pressure they succeed each other with sufficient 
 rapidity to produce a feeble musical note. By permitting 
 
ANALYSIS OF LIQUID VEINS. . 277 
 
 the drops to fall upon a membrane, the pitch of this note 
 may be fixed ; and now we come to the point which con- 
 nects the phenomena of liquid veins with those of sensi 
 tive flames and smoke-jets. If a note in unison with that 
 of the vein be sounded near it, the limpid portion in- 
 stantly shortens ; the pitch may vary to some extent, and 
 still cause a shortening; but the unisonant note is the 
 most effectual. Savart's experiments on vertically-de- 
 scending veins have been recently repeated in our labora- 
 tory with striking effect. From a distance of thirty yards 
 the limpid portion of the vein has been shortened by the 
 sound of an organ-pipe of the proper pitch and of moder- 
 ate intensity. 
 
 I have also recently gone carefully, not merely by read- 
 ing, but by experiment, over Plateau's account of the 
 resolution of a liquid vein into drops. In his researches 
 on the figures of equilibrium of bodies withdrawn from 
 the action of gravity, he finds that a liquid cylinder is sta- 
 ble as long as its length does not exceed three times its 
 diameter ; or, more accurately, as long as the ratio be- 
 tween them does not exceed that of the diameter of a cir- 
 cle to its circumference, or 3,1416. If this be a little ex- 
 ceeded the cylinder begins to narrow at some point or 
 other of its length ; nips itself together, breaks, and forms 
 immediately two spheres. If the rates of the length of 
 the cylinder to its diameter greatly exceed 3,1416, then, 
 instead of breaking up into two spheres, it breaks up into 
 several. 
 
 A liquid cylinder may be obtained by introducing 
 olive-oil into a mixture of alcohol and water, of the same 
 density as the oil. The latter forms a sphere. Two disks 
 of smaller diameter than the sphere are brought into 
 contact with it, and then drawn apart ; the oil clings to 
 the disks, and the sphere is transformed into a cylinder. 
 
278 SOUND. 
 
 If the quantity of oil be insufficient to produce the maxi- 
 mum length of cylinder, more may be added by a pipette. 
 In making this experiment it will be noticed that, when 
 the proper length is exceeded, the nipped portion of the 
 cylinder elongates, and exists for a moment as a very thin 
 liquid cylinder uniting the two incipient spheres; and 
 that, when rupture occurs, the thin cylinder, which has also 
 exceeded its proper length, breaks so as to form a small 
 spherule between the two larger ones. This is a point of 
 considerable significance in relation to our present ques- 
 tion. 
 
 Now, Plateau contends that the play of the molecular 
 forces in a liquid cylinder is not suspended by its motion 
 of translation. The first portion of a vein of water quit- 
 ting an orifice is a cylinder, to which the laws which he has 
 established regarding motionless cylinders apply. The 
 moment the descending vein exceeds the proper length it 
 begins to pinch itself so as to form drops ; but urged for- 
 ward as it is by the pressure above it, and by its own 
 gravity, in the time required for the rounding of the drop 
 it reaches a certain distance from the orifice. At this 
 distance, the pressure remaining constant, and the vein 
 being withdrawn from external disturbance, rupture inva- 
 riably occurs. And the rupture is accompanied by the 
 phenomenon which has just been called significant. Be- 
 tween every two succeeding large drops a small spherule 
 is formed, as shown in Fig. 141. 
 
 Permitting a vein of oil to fall from an orifice, not 
 through the air, but through a mixture of alcohol and 
 water of the proper density, the continuous portion of the 
 vein, its resolution into drops, and the formation of the 
 small spherule between each liberated drop and the end 
 of the liquid cylinder which it has just quitted, may be 
 watched with the utmost deliberation. The effect of this 
 
ACTION OF SOUND ON VERTICAL JETS. 279 
 
 a iid other experiments upon the mind will be to produce 
 the conviction that the very beautiful explanation offered 
 by Plateau is also the true one. The various laws estab- 
 lished experimentally by Savart all follow immediately 
 from Plateau's theory. 
 
 In a small paper published more than twenty years 
 ago I drew attention to the fact that when a descending 
 vein intersects a liquid surface above the point of rup- 
 ture, if the pressure be not too great, it enters the liquid 
 silently ; but when the surface intersects the vein below 
 the point of rupture a rattle is immediately heard, and 
 bubbles are copiously produced. In the former case, not 
 only is there no violent dashing aside of the liquid, but 
 round the base of the vein, and in opposition to its motion, 
 the liquid collects in a heap, by its surface tension or capil- 
 lary attraction. This experiment can be combined with two 
 other observations of Savart' s, in a beautiful and instruc- 
 tive manner. In addition to the shortening of the contin- 
 uous portion by sound, Savart found that, when he per- 
 mitted his membrane to intersect the vein at one of its 
 protuberances, the sound was louder than when the inter- 
 section occurred at the contracted portion. 
 
 I permitted a vein to descend, under scarcely any 
 pressure, from a tube three-quarters of an inch in diam- 
 eter, and to enter silently a basin of water placed nearly 
 20 inches below the orifice. On sounding vigorously a 
 TJt 2 tuning-fork the pellucid jet was instantly broken, 
 and as many as three of its swellings were seen above the 
 surface. The rattle of air-bubbles was instantly heard, 
 and the basin was seen to be filled with them. The sound 
 was allowed slowly to die out ; the continuous portion of 
 the vein lengthened, and a series of alternations in the 
 production of the bubbles was observed. "When the swell- 
 ings of the vein cut the surface of the water, the bubbles 
 
280 SOUND. 
 
 were copious and loud; when the contracted portions 
 crossed the surface, the bubbles were scanty and scarcely 
 audible. 
 
 Removing the basin, placing an iron tray in its place, 
 and exciting the fork, the vein, which at first struck 
 silently upon the tray, commenced a rattle which rose and 
 sank with the dying out of the sound, according as the 
 swellings or contractions of the jet impinged upon the sur- 
 face. This is a simple and beautiful experiment. 
 
 Savart also caused his vein to issue horizontally and 
 at various inclinations to the horizon, and found that, in 
 certain cases, sonorous vibrations were competent to cause 
 a jet to divide into two or three branches. In these ex- 
 periments the liquid was permitted to issue through an 
 orifice in a thin plate. Instead of this, however, we will 
 resort to our favorite steatite burner ; for with water 
 also it asserts the same mastery over its fellows that it 
 exhibited with flames and smoke-jets. It will, moreover, 
 reveal to us some entirely novel results. By means of an 
 India-rubber tube the burner is connected with the water- 
 pipes of the Institution, and, by pointing it obliquely 
 upward, we obtain a fine parabolic jet (Fig. 143). At a 
 certain distance from the orifice, the vein resolves itself 
 into beautiful spherules, whose motions are not rapid 
 enough to make the vein appear continuous. At the 
 vertex of the parabola the spray of pearls is more than an 
 inch in width, and, farther on, the drops are still more 
 widely scattered. On sweeping a fiddle-bow across a 
 tuning-fork which executes 512 vibrations in a second, 
 the scattered drops, as if drawn together by their mutual 
 attractions, instantly close up, and form an apparently 
 continuous liquid arch several feet in height and span 
 (shown in Fig. 144). As long as the proper note is main- 
 tained the vein looks like a frozen band, so motionless 
 
ACTION OF SOUND ON OBLIQUE JETS. 
 
 281 
 
 does it appear. On stopping the fork the arch is shaken 
 asunder, and we have the same play of liquid pearls as 
 "before. Every sweep of the bow, however, causes the 
 drops to fall into a common line of march. 
 
 A pitch-pipe, or an organ-pipe yielding the note of 
 
 FIG. 143. 
 
 this tuning-fork, also powerfully controls the vein. The 
 voice does the same. On pitching it to a note of moder- 
 ate intensity, it causes the wandering drops to gather 
 themselves together. At a distance of twenty yards, the 
 voice is, to all appearance, as powerful in curbing the vein, 
 
282 SOUND. 
 
 and causing its drops to close up, as it is when close to 
 the issuing jet. 
 
 The effect of " beats " upon the vein is also beautiful 
 and instructive. They may be produced either by organ- 
 pipes or by tuning-forks. "When two forks vibrate, the 
 one 512 times and the other 508 times in a second, you 
 will learn in our next lecture that they produce four beats 
 in a second. "When the forks are sounded the beats are 
 heard, and the liquid vein is seen to gather up its pearls, 
 and scatter them in synchronism with the beats. The 
 sensitiveness of this vein is astounding ; it rivals that of 
 the ear itself. Placing the two tuning-forks on a distant 
 table, and permitting the beats to die gradually out, the 
 vein continues its rhythm almost as long as hearing is 
 possible. A more sensitive vein might actually prove 
 superior to the ear a very surprising result, considering 
 the marvelous delicacy of this organ. 1 
 
 By introducing a Leyden-jar into the circuit of a 
 powerful induction-coil, a series of dense and dazzling 
 flashes of light, each of momentary duration, is obtained. 
 Every such flash in a darkened room renders the drops 
 distinct, each drop being transformed into a little star of 
 intense brilliancy. If the vein be then acted on by a 
 sound of the proper pitch, it instantly gathers its drops 
 together into a necklace of inimitable beauty. 
 
 In these experiments the whole vein gathers itself into 
 a single arched band when the proper note is sounded ; 
 but, by varying the conditions, it may be caused to divide 
 into two or more such bands, as shown in Fig. 145. Draw- 
 ings, however, are ineffectual here ; for* the wonder of 
 these experiments depends mainly on the sudden transi- 
 tion of the vein from one state to the other. In the 
 
 1 When these two tuning - forks were placed in contact with a vessel 
 from which a liquid vein issued, the visible action on the vein continued 
 long after the forks had ceased to be heard. 
 
ACTION OF SOUND ON OBLIQUE JETS. 283 
 
 motion dwells the surprise, and this no drawing can 
 render. 1 
 
 1 The experiments on sounding flames have been recently considerably 
 extended by my assistant Mr. Cottrell. By causing flame to rub against 
 flame, various musical sounds can be obtained some resembling those of 
 a trumpet, others those of a lark. By the friction of unignited gas-jets, 
 similar though less intense effects are produced. When the two flames of 
 a fish-tail burner are permitted to impinge upon a plate of platinum, as in 
 Scholl's " perfectors," the sounds are trumpet-like, and very loud. Two 
 ignited gas-jets may be caused to flatten out like Savart's water-jets. Or 
 they may be caused to roll themselves into two hollow horns, forming a 
 most instructive example of the Wirbelflachen of Helmholtz. The carbon- 
 particles liberated in the flame rise through the horns in continuous red- 
 hot or white-hot spirals, which are extinguished at a height of some 
 inches from their place of generation. 
 
284: SOUND. 
 
 SUMMARY OF CHAPTER VI. 
 
 a gas-flame is placed in a tube, the air in pass- 
 ing over the flame is thrown into vibration, musical sounds 
 being the consequence. 
 
 Making allowance for the high temperature of the 
 column of air associated with the flame, the pitch of the 
 note is that of an open organ-pipe of the length of the tube 
 surrounding the flame. 
 
 The vibrations of the flame, while the sound continues, 
 consist of a series of periodic extinctions, total or partial, 
 between every two of which the flame partially recovers its 
 brightness. 
 
 The periodicity of the phenomenon may be demon- 
 strated by means of a concave mirror which forms an 
 image of the vibrating flame upon a screen. "When the 
 image is sharply defined, the rotation of the mirror reduces 
 the single image to a series of separate images of the flame. 
 The dark spaces between the images correspond to the ex- 
 tinctions of the flame, while the images themselves corre- 
 spond to its periods of recovery. 
 
 Besides the fundamental note of the associated tube, 
 the flame can also be caused to excite the higher overtones 
 of the tube. The successive divisions of the column of air 
 are those of an open organ-pipe when its harmonic tones 
 are sounded. 
 
 On sounding a note nearly in unison with a tube con- 
 taining a silent flame, the flame jumps ; and if the position 
 of the flame in the tube be rightly chosen, the extraneous 
 sound will cause the flame to sing. 
 
SUMMARY. 285 
 
 While the flame is singing, a note nearly in unison 
 with its own produces beats, and the flame is seen to jump 
 in synchronism with the beats. The jumping is also ob- 
 served when the position of the flame within its tube is 
 not such as to enable it to sing. 
 
 NAKED FLAMES. 
 
 When the pressure of the gas which feeds a naked 
 flame is augmented, the flame, up to a certain point, in- 
 creases in size. But if the pressure be too great, the flame 
 roars or flares. 
 
 The roaring or flaring of the flame is caused by the state 
 of vibration into which the gas is thrown in the orifice of 
 the burner, when the pressure which urges it through the 
 orifice is excessive. 
 
 If the vibrations in the orifice of the burner be super- 
 induced by an extraneous sound, the flame will flare under 
 a pressure less than that which, of itself, would produce 
 flaring. 
 
 The gas under excessive pressure has vibrations of a 
 definite period impressed upon it as it passes through the 
 burner. To operate with a maximum effect upon the 
 flame the external sound must contain vibrations synchro- 
 nous with those of the issuing gas. 
 
 When such a sound is chosen, and when the flame is 
 brought sufficiently near its flaring-point, it furnishes an 
 acoustic reagent of unexampled delicacy. 
 
 At a distance of 30 yards, far example, the chirrup of 
 a house-sparrow would be competent to thtow the flame 
 into commotion. 
 
 It is not to the flame, as such, that we are to ascribe 
 these effects. Effects substantially similar are produced 
 when we employ jets of unignited coal-gas, carbonic acid, 
 hydrogen, or air. These jets may be rendered visible by 
 
286 SOUND. 
 
 smoke, and the smoke-jets show a sensitiveness to sonorous 
 vibrations even greater than that of the flames. 
 
 When a brilliant sensitive flame illuminates an other- 
 wise dark room, in which a suitable bell is caused to strike, 
 a series of periodic quenchings of the light by the sound 
 occurs. Every stroke of the bell is accompanied by a mo- 
 mentary darkening of the room. 
 
 A jet of water descending from a circular orifice is 
 composed of two distinct portions, the one pellucid and 
 calm ; the other in commotion. When properly analyzed 
 the former portion is found continuous ; the latter being a 
 succession of drops. 
 
 If these drops be received upon a membrane, a musical 
 sound is produced. When an extraneous sound of this par- 
 ticular pitch is produced in the neighborhood of the vein, 
 the continuous portion is seen to shorten. 
 
 The continuous portion of the vein presents a series of 
 swellings and contractions, in the former of which the 
 drops are flattened, and in the latter elongated. The sound 
 produced by the flattened drops on striking the membrane 
 is louder than that produced by the elongated ones. 
 
 Above its point of rupture a vein of water may be 
 caused to enter water silently / but on sounding a suitable 
 note, the rattle of bubbles is immediately heard ; the dis- 
 continuous part of the vein rises above the surface, and as 
 the sound dies out the successive swellings and contrac- 
 tions produce alternations of the quantity and sound of the 
 bubbles. 
 
 In veins propelled obliquely, the scattered water-drops 
 may be called* together by a suitable sound, so as to form 
 an apparently continuous liquid arch. 
 
 Liquid veins may be analyzed by the electric spark, or 
 by a succession of flashes illuminating the veins. 
 
CHAPTER VII. 
 
 RESEARCHES ON THE ACOUSTIC TRANSPARENCY OF THE ATMOS- 
 PHERE IN RELATION TO THE QUESTION OF FOG-SIGNALING. 
 
 PART L 
 
 Introduction. Instruments and Observations. Contradictory Results from 
 the 19th of May to the 1st of July inclusive. Solution of Contradic- 
 tions. Aerial Reflection and its Causes. Aerial Echoes. Acoustic 
 Clouds. Experimental Demonstration of Stoppage of Sound by Aerial 
 Reflection. 
 
 1. Introduction. 
 
 WE are now fully equipped for the investigation of an 
 important practical problem. The cloud produced by the 
 puff of a locomotive can quench the rays of the noonday 
 sun ; it is not, therefore, surprising that in dense fogs our 
 most powerful coast-lights, including even the electric 
 light, should become useless to the mariner. 
 
 Disastrous shipwrecks are the consequence. During 
 the last ten years no less than two hundred and seventy- 
 three vessels have been reported as totally lost on our own 
 coasts in fog or thick weather. The loss, I believe, has 
 been far greater on the American seaboard, where trade is 
 more eager, and fogs more frequent, than they are here. 
 No wonder, then, that earnest efforts should be made to 
 find a substitute for light in sound-signals, powerful enough 
 to give warning and guidance to mariners while still at a 
 safe distance from the shore. 
 13 
 
288 SOUND 
 
 Such signals have been established to some extent upon 
 our own coasts, and to a still greater extent along the 
 coasts of Canada and the United States. But the evidence 
 as to their value and performance is of the most conflicting 
 character, and no investigation sufficiently thorough to 
 clear up the uncertainty has hitherto been made. In fact, 
 while the velocity of sound has formed the subject of re- 
 fined and repeated experiment by the ablest philosophers, 
 the publication of Dr. Derhani's celebrated paper in the 
 " Philosophical Transactions " for 1708 marks the latest 
 systematic inquiry into the causes which affect the inten- 
 sity of sound in the atmosphere. 
 
 Jointly with the Elder Brethren of the Trinity House, 
 and as their scientific adviser, I have recently had the 
 honor of conducting an inquiry designed to fill the blank 
 here indicated. 
 
 One or two brief references will suffice to show the 
 state of the question when this investigation began. " Der- 
 ham," says Sir John Herschel, " found that fogs and falling 
 rain, but more especially snow, tend powerfully to obstruct 
 the propagation of sound, and that the same effect was 
 produced by a coating of fresh-fallen snow on the ground, 
 though when glazed and hardened at the surface by freez- 
 ing it had no such influence." 1 
 
 In a very clear and able letter, addressed to the Presi- 
 dent of the Board of Trade in 1863, a Dr. Eobinson, of 
 Armagh, thus summarizes our knowledge of fog-signals: 
 " Nearly all that is known about fog-signals is to be found 
 in the ' Heport on Lights and Beacons ; ' and of it much is 
 little better than conjecture. Its substance is as follows : 
 
 " c Light is scarcely available for this purpose. Blue 
 lights are used in the Hooghly; but it is not stated at 
 what distance they are visible in fog ; their glare may be 
 
 1 " Essay on Sound," par. 21. 
 
 8 "Report of the British Association for 1863," p. 105. 
 
SUMMARY OF EXISTING KNOWLEDGE. 289 
 
 seen farther than their flame. 1 It might, however, be 
 desirable to ascertain how far the electric light, or its flash, 
 can be traced. 8 
 
 "'Sound is the only known means really effective; 
 but about it testimonies are conflicting, and there is 
 scarcely one fact relating to its use as a signal which can 
 be considered as established. Even the most important of 
 all, the distance at which it ceases to be heard, is unde- 
 cided. 
 
 " c Up to the present time all signal-sounds have been 
 made in air, though this medium has grave disadvantages : 
 its own currents interfere with the sound-waves, so that a 
 gun or bell which is heard several miles down the wind is 
 inaudible more than a few furlongs up it. A still greater 
 evil is that it is least effective when most needed ; for fog 
 is a powerful damper of sound.' " 
 
 Dr. Robinson here expresses the universally-prevalent 
 opinion,' and he then assigns the theoretic cause. " Fog," 
 he says, " is a mixture of air and globules of water, and at 
 each of the innumerable surfaces where these two touch, 
 a portion of the vibration is reflected and lost. 3 . . . 
 Snow produces a similar effect, and one still more inju- 
 rious." 
 
 Reflection being thus considered to take place at the 
 surfaces of the suspended particles, it followed that the 
 greater the number of particles, or, in other words, the 
 denser the fog, the more injurious would be its action 
 upon sound. Hence optic transparency came to be con- 
 sidered a measure of acoustic transparency. On this 
 point Dr. Robinson, in the letter referred to, expresses 
 himself thus : " At the outset, it is obvious that, to make 
 
 1 A very sagacious remark, as observation proves. 
 
 8 Powerful electric lights have since been established and found inef- 
 fectual- 
 
 8 This is also Sir John Herschers way of regarding the subject. "Essaj 
 on Sound," par. 88. 
 
290 SOUND. 
 
 experiments comparable^ we must have some measure of 
 the fog's power of stopping sound, without attending to 
 which the most anomalous results may be expected. It 
 seems probable that this will bear some simple relation to 
 its opacity to light, and that the distance at which a given 
 object, as a flag or pole, disappears may be taken as the 
 measure." " Still, clear air" was regarded in this letter as 
 the best vehicle of sound, the alleged action of fogs, rain, 
 and snow, being ascribed to their rendering the atmosphere 
 " a discontinuous medium." 
 
 Prior to the investigation now to be described the views 
 here enunciated were those universally entertained. That 
 sound is unable to penetrate fogs was taken to be " a matter 
 of common observation." The bells and horns of ships were 
 affirmed " not to be heard so far in fogs as in clear weather." 
 In the fogs of London the noise of the carriage-wheels was 
 reported to be so much diminished that " they seem to be 
 at a distance where really close by." My knowledge does 
 not inform me of the existence of any other source for 
 these opinions regarding the deadening power of fog than 
 the paper of Derham, published one hundred and sixty- 
 seven years ago. In consequence of their a priori prob- 
 ability, his conclusions seem to have been transmitted 
 unquestioned from generation to generation of scientific 
 men. 
 
 2. Instruments and Observations. 
 
 On the 19th of May, 1873, this inquiry began. The 
 South Foreland, near Dover, was chosen as the signal- 
 station, steam-power having been already established 
 there to work two powerful magneto-electric lights. The 
 observations for the most part were made afloat, one of 
 the yachts of the Trinity Corporation being usually em- 
 ployed for this purpose. Two stations had been established, 
 the one at the top, the other at the bottom, of the South 
 
FOG-SIGNAL STATION AT SOUTH FORELAND. 291 
 
 Foreland Cliff ; and at each of them trumpets, air- whistles, 
 and steam-whistles of great size, were mounted. The 
 whistles first employed were of English manufacture. To 
 these was afterward added a large United States whistle, 
 and also a Canadian whistle, of great reputed power. 
 
 On the 8th of October another instrument, which has 
 played a specially important part in these observations, 
 was introduced. This was a steam -siren, constructed 
 and patented by Mr. Brown, of New York, and introduced 
 by Prof. Henry into the lighthouse system of the United 
 States. As an example of international courtesy worthy 
 of imitation, I refer with pleasure to the fact that when 
 informed by Major Elliott, of the United States Army, 
 that our experiments had begun, the Lighthouse Board 
 at "Washington, of their own spontaneous kindness, for- 
 warded to us for trial a very noble instrument of this de- 
 scription, which was immediately mounted at the South 
 Foreland. 
 
 In the steam-siren, as in the ordinary one, described 
 in Chapter II., a fixed disk and a rotating disk are em- 
 ployed, but radial slits are used instead of circular aper- 
 tures. One disk is fixed vertically across the throat of a 
 conical trumpet 16 feet long, 5 inches in diameter where 
 the disk crosses it, and gradually opening out till at the 
 other extremity it reaches a diameter of 2 feet 3 inches. 
 Behind the fixed disk is the rotating one, which is driven 
 by separate mechanism. The trumpet is connected with a 
 boiler. In our experiments steam of TO Ibs. pressure was 
 for the most part employed. Just as in the ordinary 
 siren, when the radial slits of the two disks coincide, and 
 then only, a strong puff of steam escapes. Sound-waves 
 of great intensity are thus sent through the air, the 
 pitch of the note depending on the velocity of rotation. 
 (A drawing of the steam-siren constitutes our frontis* 
 piece.) 
 
292 SOUND. 
 
 To the siren, trumpets, and whistles were added three 
 g lins an 18-pounder, a 5^-inch howitzer, and a 13-inch 
 mortar. In our summer experiments all three were fired ; 
 but the howitzer having shown itself superior to the other 
 guns it was chosen in our autumn experiments as not only 
 a fair but a favorable representative of this form of sig- 
 nal. The charges fired were for the most part those now 
 employed at Holyhead, Lundy Island, and the Kish light- 
 vessel namely, 3 Ibs. of powder. Gongs and bells were 
 not included in this inquiry, because previous observations 
 had clearly proved their inferiority to the ' trumpets and 
 whistles. 
 
 On the 19th of May the instruments tested were : 
 
 On the top of the cliff 
 
 a. Two brass trumpets or horns, 11 feet 2 inches long, 
 2 inches in diameter at the mouth-piece, and opening out 
 at the other end to a diameter of 22J inches. They were 
 provided with vibrating steel reeds 9 inches long, 2 inches 
 wide, and J inch thick, and were sounded by air of 18 Ibs. 
 pressure. 
 
 ~b. A whistle, shaped like that of a locomotive, 6 inches 
 in diameter, also sounded by air of 18 Ibs. pressure. 
 
 c. A steam- whistle, 12 inches in diameter, attached to 
 a boiler, and sounded by steam of 64 Ibs. pressure. 
 
 At the bottom of the cliff : 
 
 d. Two trumpets or horns, of the same size and ar 
 rangement as those above, and sounded by air of the same 
 pressure. They were mounted vertically on the reservoir 
 of compressed air ; but within about two feet of their ex- 
 tremities they were bent at a right angle, so as to present 
 their mouths to the sea. 
 
 e. A 6-inch air-whistle, similar to the one above, and 
 sounded by the same means. 
 
 The upper instruments were 235 feet above high- 
 water mark, the lower ones 40 feet. A vertical distance 
 
INSTRUMENTS. 293 
 
 of 195 feet, therefore, separated the instruments. A shaft, 
 provided with a series of twelve ladders, led from the one 
 to the other. 
 
 Numerous comparative experiments made at the outset 
 gave a slight advantage to the upper instruments. They, 
 therefore, were for the most part employed throughout the 
 subsequent inquiry. 
 
 Our first observations were a preliminary discipline 
 rather than an organized effort at discovery. On May 19th 
 the maximum distance reached by the sound was about 
 three and a half miles. 1 The wind, however, was high and 
 the sea rough, so that local noises interfered to some ex- 
 tent with our appreciation of the sound. 
 
 Mariners express the strength of the wind by a series 
 of numbers extending from = calm to 12 = a hurri- 
 cane, a little practice in common producing a remarkable 
 unanimity between different observers as regards the force 
 of the wind. Its force on May 19th was 6, and it blew 
 at right angles to the direction of the sound. 
 
 The same instruments on May 20th covered a greater 
 range of sound ; but not much greater, though the dis- 
 turbance due to local noises was absent. At 4 miles, 
 distance in the axes of the horns they were barely heard, 
 the air at the time being calm, the sea smooth, and 
 all other circumstances exactly those which have been 
 hitherto regarded as most favorable to the transmission 
 of sound. We crept a little farther away, and by stretched 
 attention managed to hear at intervals, at a distance of 6 
 miles, the faintest hum of the horns. A little farther out 
 we again halted ; but though local noises were absent, and 
 though we listened intently, we heard nothing. 
 
 This position, clearly beyond the range of whistles and 
 trumpets, was expressly chosen with the view of making 
 what might be considered a decisive comparative experi- 
 
 1 In all cases nautical miles are meant. 
 
294 SOUND. 
 
 ment between horns and guns as instruments for fog- 
 signaling. The distinct report of the 12 o'clock gun 
 fired at Dover on the 19th suggested this comparison, and 
 through the prompt courtesy of General Sir A. Hereford 
 we were enabled to carry it out. At 12.30 precisely the 
 puff of an IS-pounder, with a 3-lb. charge, was seen at 
 Dover Castle, which was about a mile farther off than the 
 South Foreland. Thirty-six seconds afterward the loud 
 report of the gun was heard, its complete superiority over 
 the trumpets being thus, to all appearance, demonstrated. 
 
 We clinched this observation by steaming out to a 
 distance of 8J miles, where the report of a second gun 
 was well heard by all of us. At a distance of 10 miles the 
 report of a third gun was heard by some, and at 9*7 miles 
 the report of a fourth gun was heard by all. 
 
 The result seemed perfectly decisive. Applying the 
 law of inverse squares, the sound of the gun at a distance 
 of 6 miles from the Foreland must have had more than 
 two and a half times the intensity of the sound of the 
 trumpets. It would not have been rash under the circum- 
 stances to have reported without qualification the su- 
 periority of the gun as a fog-signal. !No single experi- 
 ment is, to my knowledge, on record to prove that a sound 
 once predominant would not be always predominant, or 
 that the atmosphere on different days would show pref- 
 erences to different sounds. On many subsequent occa- 
 sions, however, the sound of the horns proved distinctly 
 superior to that of the gun. This selective power of the 
 atmosphere revealed itself more strikingly in our autumn 
 experiments than in our summer ones ; and it was some- 
 times illustrated within a few hours of the same day : of 
 two sounds, for example, one might have the greatest 
 range at 10 A. M., and the other the greatest range at 2 p. M. 
 
 In the experiments 011 May 19th and 20th the superior- 
 ity of the trumpets over the whistles was decided ; and in- 
 
RANGE OF GUNS, TRUMPETS, AND WHISTLES. 295 
 
 deed, with few exceptions, this superiority was maintained 
 throughout the inquiry. But there were exceptions. On 
 June 2d, for example, the whistles rose in several instances 
 to full equality with, and on rare occasions subsequently 
 even surpassed the horns. The sounds were varied from 
 day to day, and various shiftings of the horns and reeds 
 were resorted to, with a view of bringing out their maxi- 
 mum power. On the date last mentioned a single horn 
 was sounded, two were sounded, and three were sounded 
 together ; but the utmost range of the loudest sound, even 
 with the paddles stopped, did not exceed 6 miles. With 
 the view of concentrating their power, the axes of the 
 horns had been pointed in the same direction, and, unless 
 stated to the contrary, this in all subsequent experiments 
 was the case. 
 
 On June 3d the three guns already referred to were 
 permanently mounted at the South Foreland. They were 
 ably served by gunners from Dover Castle. 
 
 On the same day dense clouds quite covered the firma- 
 ment, some of them particularly black and threatening, but 
 a marked advance was observed in the transmissive power 
 of the air. At a distance of 6 miles the horn-sounds were 
 not quite quenched by the paddle-noises; at 8 miles the 
 whistles were heard, and the horns better heard ; while at 
 9 miles, with the paddles stopped, the horn-sounds alone 
 were fairly audible. During the day's observations a 
 remarkable and instructive phenomenon was observed. 
 Over us rapidly passed a torrential shower of rain, which, 
 according to Derham, is a potent damper of sound. We 
 could, however, notice no subsidence of intensity as the 
 shower passed. It is even probable that, had our minds 
 been free from bias, we should have noticed an augmenta- 
 tion of the sound, such as occurred with the greatest dis- 
 tinctness on various subsequent occasions during violent 
 rain. 
 
296 SOUND. 
 
 The influence of "beats" was tried on June 3d, by 
 throwing the horns slightly out of unison ; but though the 
 beats rendered the sound characteristic, they did not seem 
 to augment the range. At a distance from the station 
 curious fluctuations of intensity were noticed. !N"ot only 
 did the different blasts vary in strength, but sudden swell- 
 ings and fallings off, even of the same blast, were observed. 
 This was not due to any variation on the part of the in- 
 struments, but purely to the changes of the medium trav- 
 ersed by the sound. What these changes were shall be 
 indicated subsequently. 
 
 The range of our best horns on June 10th was 8f miles. 
 The guns at this distance were very feeble. That the 
 loudness of the sound depends on the shape of the gun 
 was proved by the fact that thus far the howitzer, with a 
 3-lb. charge, proved more effective than the other guns. 
 
 On June 25th a gradual improvement in the transmis- 
 sive power of the air was observed from morning to even- 
 ing ; but at the last the maximum range was only moderate. 
 The fluctuations in the strength of the sound were remark- 
 able, sometimes sinking to inaudibility and then rising to 
 loudness. A similar effect, due to a similar cause, is often 
 noticed with church-bells. The acoustic transparency of 
 the air was still further augmented on the 26th : at a dis- 
 tance of 9J miles from the station the whistles and horns 
 were plainly heard against a wind with a force of 4 ; while 
 on the 25th, with a favoring wind, the maximum range 
 was only 6J miles. Plainly, therefore, something else 
 than the wind must be influential in determining the 
 range of the sound. 
 
 On Tuesday, July 1st, observations were made on the 
 decay of the sound at various angular distances from the 
 axis of the horn. As might be expected the sound in the 
 axis was loudest, the decay being gradual on both sides. 
 
VARIATIONS OF RANGE. 297 
 
 In the case of the gun, however, the direction of pointing 
 has very little influence. 
 
 The day was acoustically clear ; at a distance of 10 
 miles the horn yielded a plain sound, while the American 
 whistle seemed to surpass the horn. Dense haze at this 
 time quite hid the Foreland. At 10J miles occasional 
 blasts of the horn came to us, but after a time all sound 
 ceased to be audible ; it seemed as if the air, after having 
 been exceedingly transparent, had become gradually more 
 opaque to the sound. 
 
 At 4.45 P. M. we took the master of the Yarne light- 
 ship on board the Irene. He and his company had heard 
 the sound at intervals during the day, although he was 
 dead to windward and distant 12f miles from the source qf 
 sound. 
 
 Here a word of reflection on our observations may be 
 fitly introduced. It is, as already shown, an opinion en- 
 tertained in high quarters that the waves of sound are re- 
 flected at the limiting surfaces of the minute particles 
 which constitute haze and fog, the alleged waste of sound 
 in fog being thus explained. If, however, this be an effi- 
 cient practical cause of the stoppage of sound, and if clear 
 calm air be, as alleged, the best vehicle, it would be impos- 
 sible to understand how to-day, in a thick haze, the sound 
 reached a distance of 12f miles, while on May 20th, in a 
 calm and hazeless atmosphere, the maximum range was 
 only from 5 to 6 miles. Such facts foreshadow a revolu- 
 tion in our notions regarding the action of haze and fogs 
 upon sound. 
 
 An interval of 12 hours sufficed to change in a surpris- 
 ing degree the acoustic transparency of the air. On the 
 1st of July the sound had a range of nearly 13 miles; on 
 the 2d the range did not exceed 4 miles. 
 
298 SOUND. 
 
 3. Contradictory Results. 
 
 Thus far the investigation proceeded with hardly a 
 gleam of a principle to connect the inconstant results. 
 The distance reached by the sound on the 19th of May 
 was 3 J miles ; on the 20th it was 5-J miles ; on the 2d of 
 June 6 miles ; on the 3d more than 9 miles ; on the 10th 
 it was also 9 miles ; on the 25th it fell to 6-J- miles ; on the 
 26th it rose again to more than 9J miles ; on the 1st of 
 July, as we have just seen, it reached 12 J, whereas on the 
 2d the range shrunk to 4 miles. None of the meteoro- 
 logical agents observed could be singled out as the cause 
 of these fluctuations. The wind exerts an acknowledged 
 power over sound, but it could not account for these phe- 
 nomena. On the 25th of June, for example, when the 
 range was only 6 miles, the wind was favorable ; on the 
 26th, when the range exceeded 9J miles, it was opposed 
 to the sound. Nor could the varying optical clearness of 
 the atmosphere be invoked as an explanation ; for on July 
 1st, when the range was 12f miles, a thick haze hid the 
 white cliffs of the Foreland, while on many other days, 
 when the acoustic range was not half so great, the atmos- 
 phere was optically clear. Up to July 3d all remained 
 enigmatical ; but on this date observations were made 
 which seemed to me to displace surmise and perplexity by 
 the clearer light of physical demonstration. 
 
 4. Solution of Contradictions. 
 
 On July 3d we first steamed to a point 2 '9 miles S. W. 
 by "W. of the sijjg&l-station. No sounds, not even the 
 guns, were heard "at this distance. At 2 miles they were 
 equally inaudible. But this being a position at which the 
 sounds, though strong in the axis of the horn, invariably 
 subsided, we steamed to the exact bearing from which our 
 observations had been made on July 1st. At 2.15 p. M., and 
 
EXTRAORDINARY CASE OF ACOUSTIC OPACITY. 299 
 
 at a distance of 3| miles from the station, with calm, clear 
 air and a smooth sea, the horns and whistle (American) 
 were sounded, but they were inaudible. Surprised at this 
 result, I signaled for the guns. They were all fired, but, 
 though the smoke seemed at hand, no sound whatever 
 reached us. On July 1st, in this bearing, the observed 
 range of both horns and guns was 10 J miles, while on the 
 bearing of the Yarne light-vessel it was nearly 13 miles. 
 We steamed in to 3 miles, paused, and listened with all 
 attention ; but neither horn nor whistle was heard. The 
 guns were again signaled for ; five of them were fired in 
 succession, but not one of them was heard. We steamed 
 on in the same bearing to 2 miles, and had the guns fired 
 point-blank at us. The howitzer and the mortar, with 
 3-lb. charges, yielded a feeble thud, while the 18-pounder 
 was wholly unheard. Applying the law of inverse squares, 
 it follows that, with the air and sea, according to accepted 
 notions, in a far worse condition, the sound at 2 miles' dis- 
 tance on July 1st must have had more than forty times the 
 intensity which it possessed at the same distance at 3 p. M. 
 on the 3d. 
 
 "On smooth water," says Sir John Herschel, "sound 
 is propagated with remarkable clearness and strength." 
 Here was the condition; still, with the Foreland so close to 
 us, the sea so smooth, and the air so transparent, it was 
 difficult to realize that the guns had been fired or the 
 trumpets blown at all. What could be the reason ? Had 
 the sound been converted by internal friction into heat ? 
 or had it been wasted in partial reflections at the limiting 
 surfaces of non-homogeneous masses of air ? I ventured, 
 two or three years ago, to say something regarding the 
 function of the Imagination in Science, and, notwithstand- 
 ing the care then taken, to define and illustrate its real 
 province, some persons, among whom were one or two 
 able men, deemed me loose and illogical. They mis- 
 
300 SOUND. 
 
 understood nie. The faculty to which I referred was 
 that power of visualizing processes in space, and the rela- 
 tions of space itself, which must be possessed by all great 
 physicists and geometers. Looking, for example, at two 
 pieces of polished steel, we have not a sense, or the rudi- 
 ment of a sense, to distinguish the inner condition of the 
 one from 1 that of the other. And yet they may differ 
 materially, for one may be a magnet, the other not. What 
 enabled Ampere to surround the atoms of such a magnet 
 with channels in which electric currents ceaselessly run, 
 and to deduce from these pictured currents all the phe- 
 nomena of ordinary magnetism ? What enabled Faraday 
 to visualize his lines of force, and make his mental pict- 
 ure a guide to discoveries which have rendered his name 
 immortal ? Assuredly it was the disciplined imagination. 
 Figure the observers on the deck of the Irene, with 
 the invisible air stretching between them and the South 
 Foreland, knowing that it contained something which 
 stifled the sound, but not knowing what that something 
 is. Their senses are not of the least use to them ; nor 
 could all the philosophical instruments in the world ren- 
 der them any assistance. They could not, in fact, take a 
 single step toward the solution without the formation of a 
 mental image in other words, without the exercise of the 
 imagination. 
 
 Sulphur, in homogeneous crystals, is exceedingly trans- 
 parent to radiant heat, whereas the ordinary brimstone of 
 commerce is highly impervious to it the reason being 
 that the brimstone does not possess the molecular con- 
 tinuity of the crystal, but is a mere aggregate of minute 
 grains not in perfect optical contact with each other. 
 Where this is the case, a portion of the heat is always 
 reflected on entering and on quitting a grain ; hence, when 
 the grains are minute and numerous, this reflection is so 
 often repeated that the heat is entirely wasted before it 
 
ANALOGIES OF SOUND, LIGHT, AND HEAT. 301 
 
 can plunge to any depth into tlie substance. The same 
 remark applies to snow, f oanij clouds, and common salt, 
 indeed, to all transparent substances in powder ; they are 
 all impervious to light, not through the immediate absorp 
 tion or extinction of the light, but through repeated inter- 
 nal reflection. 
 
 Humboldt, in his observations at the Falls of the 
 Orinoco, is known to have applied these principles to 
 sound. He found the noise of the falls far louder by 
 night than by day, though in that region the night is far 
 noisier than the day. The plain between him and the 
 falls consisted of spaces of grass and rock intermingled. 
 In the heat of the day he found the temperature of the 
 rock to be considerably higher than that of the grass. 
 Over every heated rock, he concluded, rose a column of 
 air rarefied by the heat ; its place being supplied by the 
 descent of heavier air. He ascribed the deadening of 
 the sound to the reflections which it endured at the limit- 
 ing surfaces of the rarer and denser air. This philo- 
 sophical explanation made it generally known that a non- 
 homogeneous atmosphere is unfavorable to the transmission 
 of sound. 
 
 But what on July 3d, not with the variously-heated 
 plain of Antures, but with a calm sea as a basis for the 
 atmosphere, could so destroy its homogeneity as to enable 
 it to quench in so short a distance so vast a body of sound ? 
 My course of thought at the time was thus determined : 
 As I stood upon the deck of the Irene pondering the 
 question, I became conscious of the exceeding power of 
 the sun beating against my back and heating the objects 
 near me. Beams of equal power were falling on the sea, 
 and must have produced copious evaporation. That the 
 vapor generated should so rise and mingle with the air 
 as to form an absolutely homogeneous medium, was in the 
 highest degree improbable. It would be sure, I thought, 
 
302 SOUND. 
 
 to rise in invisible streams, breaking through the super- 
 incumbent air now at one point, now at another, thus ren- 
 dering the air flocculent with wreaths and striae, charged 
 in different degrees with the buoyant vapor. At the 
 limiting surfaces of these spaces, though invisible, we 
 should have the conditions necessary to the production of 
 partial echoes and the consequent waste of sound. Ascend- 
 ing and descending air-currents, of different tempera- 
 tures, as far as they existed, would also contribute to the 
 effect. 
 
 Curiously enough, the conditions necessary for the test- 
 ing of this explanation immediately set in. At 3.15 p. M. 
 a solitary cloud threw itself athwart the sun, and shaded 
 the entire space between us and the South Foreland. 
 The heating of the water and the production of vapor- 
 and air-currents were checked by the interposition of this 
 screen ; hence the probability of suddenly- improved trans- 
 mission. To test this inference, the steamer was imme- 
 diately turned and urged back to our last position of in- 
 audibility. The sounds, as I expected, were distinctly 
 though faintly heard. This was at 3 miles' distance. At 
 3f miles, the guns were fired, both point-blank and ele- 
 vated. The faintest pop was all that we heard ; but we 
 did hear a pop, whereas we had previously heard nothing, 
 either here or three-quarters of a mile nearer. "We steamed 
 out to 4J miles, where the sounds were for a moment faint 
 ly heard ; but they fell away as we waited ; and though 
 the greatest quietness reigned on board, and though the 
 sea was without a ripple, we could hear nothing. "We 
 could plainly see the steam-puffs which announced the be- 
 ginning and the end of a series of trumpet-blasts, but the 
 blasts themselves were quite inaudible. 
 
 It was now 4- P. M., and my intention at first was to 
 halt at this distance, which was beyond the sound-range, 
 but not far beyond it, and see whether the lowering of the 
 
GREAT CHANGE OF ACOUSTIC TRANSPARENCY. 303 
 
 sun would not restore the power of the atmosphere to 
 transmit the sound. But after waiting a little the anchor- 
 ing of a boat was suggested, so as to liberate the steamer 
 for other work ; and though loath to lose the anticipated 
 revival of the sounds myself , I agreed to this arrangement. 
 Two men were placed in the boat and requested to give all 
 attention, so as to hear the sound if possible. With per- 
 feet stillness around them they heard nothing. They 
 were then instructed to hoist a signal if they should hear 
 the sounds, and to keep it hoisted as long as the sounds 
 continued. 
 
 At 4.45 we quitted them and steamed toward the South 
 Sand Head light-ship. Precisely 15 minutes after we had 
 separated from them the flag was hoisted ; the sound had 
 at length succeeded in piercing the body of air between 
 the boat and the shore. 
 
 We continued our journey to the light-ship, went on 
 board, heard the report of the lightsmen, and returned to 
 our anchored boat. We then learned that when the flag 
 was hoisted the horn-sounds were heard, that they were suc- 
 ceeded after a little time by the whistle-sounds, and that 
 both increased in intensity as the evening advanced. On 
 our arrival, of course we heard the sounds ourselves. 
 
 We pushed the test further by steaming farther out. 
 At 5f miles we halted and heard the sounds : at 6 miles 
 we heard them distinctly, but so feebly that we thought we 
 had reached the limit of the sound-range ; but while we 
 waited the sounds rose in power. We steamed to the 
 Yarne buoy, \vhich is 7f miles from the signal-station, and 
 heard the sounds there better than at 6 miles' distance. 
 We continued our course outward to 10 miles, halted there 
 i'or a brief interval, but heard nothing. 
 
 Steaming, however, on to the Yarne light-ship, which 
 is situated at the other end of the Yarne shoal, we hailed 
 the master, and were informed by him that up to 5 P. M 
 
304 SOUND. 
 
 nothing had been heard, but that at that hour the sounds 
 began to be audible. He described one of them as " very 
 gross, resembling the bellowing of a bull," which verv ac- 
 curately characterizes the sound of the large American 
 steam-whistle. At the Yarne light-ship, therefore, the 
 sounds had been heard toward the close of the day, though 
 it is 12J miles from the signal-station. I think it probable 
 that, at a point 2 miles from the Foreland, the sound at 5 
 p. M. possessed fifty times the intensity which it possessed 
 at 2 P. M. To such undreamed-of fluctuations is the atmos- 
 phere liable. On our return to Dover Bay, at 10 p. M., we 
 heard the sounds, not only distinct but loud, where noth- 
 ing could be heard in the morning. 
 
 5. Oilier Remarkable Instances of Acoustic Opacity. 
 
 In his excellent lecture entitled " Wirkungen aus der 
 Feme," Dove has collected some striking cases of the in- 
 terception of sound. The Duke of Argyll has also favored 
 me with some highly-interesting illustrations. But noth- 
 ing of this description that I have read equals in point of 
 interest the following account of the battle of Gaines's 
 Farm, for which I am indebted to the Rector of the Uni- 
 versity of Virginia : 
 
 "LYNCHBURG, VIRGINIA, March 19, 1874. 
 
 " SIR : I have just read with great interest your lecture 
 of January 16th, on the acoustic transparency and opacity 
 of the atmosphere. The remarkable observations you men- 
 tion induce me to state to you a fact which I have occa- 
 sionally mentioned, but always, where I am not well known, 
 with the apprehension that my veracity would be ques- 
 tioned. It made a strong impression on me at the time, 
 but was an insoluble mystery until your discourse gave me 
 a possible solution. 
 
 " On the afternoon of June 28, 1862, I rode, in com- 
 
NOISE OF BATTLE UNHEARD. 305 
 
 pany with General G. W. Kandolph, then Secretary of 
 War of the Confederate States, to Price's house, about nine 
 miles from Richmond ; the evening before General Lee 
 had begun his attack on McClellan's army, by crossing the 
 Chickahominy about four miles above Price's, and driving 
 in McClellan's right wing. The battle of Gaines's Farm 
 was fought the afternoon to which I refer. The valley of 
 the Chickahominy is about one and a half miles wide from 
 hill-top to hill-top. Price's is on one hill-top, that nearest 
 to Richmond ; Gaines's farm, just opposite, is on the 
 other, reaching back in a plateau to Cold Harbor. 
 
 " Looking across the valley I saw a good deal of the 
 battle, Lee's right resting in the valley, the 'Federal left 
 wing the same. My line of vision was nearly in the line 
 of the lines of battle. I saw the advance of the Confeder- 
 ates, their repulse two or three times, and in the gray of 
 the evening the final retreat of the Federal forces. 
 
 " I distinctly saw the musket-fire of both lines, the 
 smoke, individual discharges, the flash of the guns. I saw 
 batteries of artillery on both sides come into action and fire 
 rapidly. Several field-batteries on each side were plainly 
 in sight. Many more were hid by 1:he timber which bound- 
 ed the range of vision. 
 
 " Yet looking for nearly two hours, from about 5 to 7 
 p. M. on a midsummer afternoon, at a battle in which at 
 least 50,000 men were actually engaged, and doubtless at 
 least 100 pieces of field-artillery, through an atmosphere 
 optically as limpid as possible, not a single sound of the 
 battle was audible to General Randolph and myself. I re- 
 marked it to him at the time as astonishing. 
 
 " Between me and the battle was the deep broad valley 
 of the Chickahominy, partly a swamp shaded from the de- 
 clining sun by the hills and forest in the west (my side). 
 Part of the valley on each side of the swamp was cleared ; 
 some in cultivation, some not. Here were conditions capa- 
 
306 SOUND. 
 
 ble of providing several belts of air, varying in the amount 
 of watery vapor (and probably in temperature), arranged 
 like laminae at right angles to the acoustic waves as they 
 came from the battle-field to me. 
 
 " Respectfully, 
 
 " Your obedient servant, 
 
 " K. G. H. KEAN. 
 
 " PROF. JOHN TYNDALL." 
 
 I learn from a subsequent letter that during the battle 
 the air was still. J. T. 
 
 6. Echoes from Invisible Acoustic Clouds. 
 
 But both the argument and the phenomena have a 
 complementary side, which we have now to consider. A 
 stratum of air less than 3 miles thick on a calm day has 
 been proved competent to stifle both the cannonade and 
 the horn-sounds employed at the South Foreland ; while, 
 according to the foregoing explanation, this result was due 
 to the reflection of the sound from invisible acoustic clouds 
 which filled the atmosphere on a day of perfect optical 
 transparency. But, granting this, it is incredible that so 
 great a body of sound could utterly disappear in so short 
 a distance without rendering some account of itself. Sup- 
 posing, then, instead of placing ourselves behind the acous- 
 tic cloud, we were to place ourselves in front of it, might 
 we not, in accordance with the law of conservation, expect 
 to receive by reflection the sound which had failed to reach 
 us by transmission ? The case would then be strictly analo- 
 gous to the reflection of light from an ordinary cloud to an 
 observer between it and the sun. 
 
 My first care in the early part of the day in question 
 was to assure myself that our inability to hear the sound 
 did not arise from any derangement of the instruments on 
 shore. Accompanied by the private secretary of the 
 
ACOUSTIC CLOUDS. 307 
 
 Deputy Master of the Trinity House, at 1 P. M. I was 
 rowed to the shore, and landed at the base of the South 
 Foreland Cliff. The body of air which had already shown 
 such extraordinary power to intercept the sound, and 
 which manifested this power still more impressively later 
 in the day, was now in front of us. On it the sonorous 
 waves impinged, and from it they were sent back with 
 astonishing intensity. The instruments, hidden from view, 
 were on the summit of a cliff 235 feet above us, the sea 
 was smooth and clear of ships, the atmosphere was with- 
 out a cloud, and there was no object in sight which could 
 possibly produce the observed effect. From the perfectly 
 transparent air the echoes came, at first with a strength 
 apparently little less than that of the direct sound, and 
 then dying away. A remark made by my talented com- 
 panion in his note-book at the time shows how the phe- 
 nomenon affected him : " Beyond saying that the echoes 
 seemed to come from the expanse of ocean, it did not 
 appear possible to indicate any more definite point oi 
 reflection." Indeed no such point was to be seen ; the 
 echoes reached us, as if by magic, from the invisible 
 acoustic clouds with which the optically transparent at- 
 mosphere was filled. The existence of such clouds in all 
 weathers, whether optically cloudy or serene, is one of the 
 most important points established by this inquiry. 
 
 Here, in my opinion, we have the key to many of the 
 mysteries and discrepancies of evidence which beset this 
 question. The foregoing observations show that there is 
 no need to doubt either the veracity or the ability of the 
 conflicting witnesses, for the variations of the atmosphere 
 are more than sufficient to account for theirs. The mis- 
 take, indeed, hitherto has been, not in reporting incorrect- 
 ly, but in neglecting the monotonous operation of repeat- 
 ing the observations during a sufficient time. I shall have 
 occasion to remark subsequently on the mischief likely to 
 
308 SOUND. 
 
 arise from giving instructions to mariners founded on 
 observations of this incomplete character. 
 
 It required, however, long pondering and repeated 
 observation before this conclusion took firm root in my 
 mind; for it was opposed to the results of great observers, 
 and to the statements of celebrated writers. In science 
 as elsewhere, a mind of any depth which accepts a doc- 
 trine undoubtingly, discards it unwillingly. The question 
 of aerial echoes has an historic interest. While cloud- 
 echoes have been accepted as demonstrated by observa- 
 tion, it has been hitherto held as established that audible 
 ^echoes never occur in optically clear air. We owe this 
 opinion to the admirable report of Arago on the experi- 
 ments made to determine the velocity of sound at Mont- 
 lhery and Yillejuif in 1822. 1 Arago's account of the phe- 
 nomenon observed by him and his colleagues is as fol 
 lows : " Before ending this note we will only add that the 
 shots fired at Montlhery were accompanied by a rumbling 
 like that of thunder, which lasted from 20 to 25 sec- 
 onds. Nothing of this kind occurred at Yillejuif. Once 
 we heard two distinct reports, a second apart, of the 
 Montlhery cannon. In two other cases the report of the 
 same gun was followed by a prolonged rumbling. These 
 
 1 Sir John Herschel gives the following account of Arago's observa- 
 tion : " The rolling of thunder has been attributed to echoes among the 
 clouds ; and, if it is considered that a cloud is a collection of particles of 
 water, however minute, in a liquid state, and therefore each individually 
 capable of reflecting sound, there is no reason why very large sounds should 
 not be reverberated confusedly (like bright lights) from a cloud. And that 
 such is the case has been ascertained by direct observation on the sound of 
 cannon. Messrs. Arago, Matthieu, and Prony, in their experiments on the 
 velocity of sound, observed that under a perfectly clear sky the explosions 
 of their guns were always single and sharp ; whereas, when the sky waa 
 overcast, and even when a cloud came in sight over any considerable part of 
 the horizon, they were frequently accompanied by a long-continued roll like 
 thunder." (" Essay on Sound," par. 38.) The distant clouds would imply a 
 long interval between sound and echo, but nothing of the kind is reported. 
 
REPUTED CLOUD-ECHOES 309 
 
 phenomena never occurred without clouds. Under a clear 
 sky the sounds were single and instantaneous. May we 
 not, therefore, conclude that the multiple reports of the 
 Montlhery gun heard at Yillejuif were echoes from the 
 clouds, and may we not accept this fact as favorable to 
 the explanation given by certain physicists of the rolling 
 of thunder ? " 
 
 This explanation of the Montlhery echoes is an infer- 
 ence from observations made at Yillejuif . The inference 
 requires qualification. Some hundreds of cannon-shots 
 have been fired at the South Foreland, many of them 
 when the heavens were completely free from clouds, and 
 never in a single case has a roidement similar to that 
 noticed at Montlhery been absent. It follows, moreover, 
 so hot upon the direct sound as to present hardly a sensible 
 breach of continuity between the sound and the echo. 
 This could not be the case if the clouds were its origin. 
 A reflecting cloud, at the distance of a mile, would leave a 
 silent interval of nearly ten seconds between sound and 
 echo; and had such an interval been observed at Mont- 
 lhery, it could hardly have escaped record by the philoso 
 phers stationed there ; but they have not recorded it. 
 
 I think both the fact and the inference need recon 
 sideration. For our observations prove to demonstration 
 that air of perfect visual transparency is competent to 
 produce echoes of great intensity and long duration. The 
 subject is worthy of additional illustration. On the 8th 
 of October, as already stated, the siren was established at 
 the South Foreland. I visited the station on that day, 
 and listened to its echoes. They were far more power- 
 ful than those of the horn. Like the others they were 
 perfectly continuous, and faded, as if into distance, gradu- 
 ally away. The direct sound seemed rendered complex 
 and multitudinous by its echoes, which resembled a band 
 of trumpeters, first responding close at hand, and then re- 
 
310 SOUND. 
 
 treating rapidly toward the coast of France. The siren- 
 echoes on that day had 11 seconds', those of the horn 8 
 seconds' duration. 
 
 In the case of the siren, moreover, the reenf orcement 
 of the direct sound by its echo was distinct. About a 
 second after the commencement of the siren-blast the echo 
 struck in as a new sound. This first echo, therefore, must 
 have been flung back by a body of air not more than 600 
 or TOO feet in thickness. The few detached clouds visible 
 at the time were many miles away, and could clearly have 
 had nothing to do with the effect. 
 
 On the 10th of October I was again at the Foreland 
 listening to the echoes, with results similar to those just 
 described. On the 15th I had an opportunity of remark- 
 ing something new concerning them at Dungeness, where 
 a horn similar to, but not so powerful as, those at the 
 South Foreland, has been mounted. It rotates automati- 
 cally through an arc of 210, halting at four different 
 points on the arc and emitting a blast of 6 seconds' dura- 
 tion, these blasts being separated from each other by inter- 
 vals of silence of 20 seconds. 
 
 The new point observed was this : as the horn rotated 
 the echoes were always returned along the line in which 
 the axis of the horn pointed. Standing either behind or 
 in front of the lighthouse tower, or closing the eyes so as 
 to exclude all knowledge of the position of the horn, the 
 direction of its axis when sounded could always be inferred 
 from the direction in which the aerial echoes reached the 
 shore. Not only, therefore, is knowledge of direction 
 given by a sound, but it may also be given by the aerial 
 echoes of the sound. 
 
 On the 17th of October, at about 5 p. M., the air being 
 perfectly free from clouds, we rowed toward the Foreland, 
 landed, and passed over the sea-weed to the base of the cliff. 
 As I reached the base the position of the " Galatea " was 
 
AEHIAL ECHOES. 311 
 
 such that an echo of astonishing intensity was sent back 
 from her side ; it came as if from an independent source 
 of sound established on board the steamer. This echo 
 ceased suddenly, leaving the aerial echoes to die gradually 
 into silence. 
 
 At the base of the cliff a series of concurrent observa- 
 tions made the duration of the aerial siren-echoes from 13 
 to 14 seconds. 
 
 Lying on the shingle under a projecting roof of chalk, 
 the somewhat enfeebled diffracted sound reached me, and 
 I was able to hear with great distinctness, about a second 
 after the starting of the siren-blast, the echoes striking in 
 and reenforcing the direct sound. The first rush of echoed 
 sound was very powerful, and it came, as usual, from a 
 stratum of air 600 or YOO feet in thickness. On again 
 testing the duration of the echoes, it was found to be from 
 14 to 15 seconds. The perfect clearness of the afternoon 
 caused me to choose it for the examination of the echoes. 
 It is worth remarking that this was our day of longest^ 
 echoes, and it was also our day of greatest acoustic trans- 
 parency, this association suggesting that the duration of 
 the echo is a measure of the atmospheric depths from which 
 it comes. On no day, it is to be remembered, was the at- 
 mosphere free from invisible acoustic clouds ; and on this 
 day, and when their presence did not prevent the direct 
 sound from reaching to a distance of 15 or 16 nautical 
 miles, they were able to send us echoes of 15 seconds' 
 duration. 
 
 On various occasions, when fully three miles from the 
 shore, the Foreland bearing north, we have had the dis- 
 tinct echoes of the siren sent back to us from the cloud- 
 less southern air. 
 
 To sum up this question of aerial echoes. The siren 
 sounded three blasts a minute, each of 5 seconds' duration. 
 From the number of days and the number of hours per 
 14 
 
312 SOUND. 
 
 day during which the instrument was in action we can 
 infer the number of blasts. They reached nearly twenty 
 thousand. The blasts of the horns exceeded this number, 
 while hundreds of shots were fired from the guns. What- 
 ever might be the state of the weather, cloudy or serene, 
 stormy or calm, the aerial echoes, though varying in 
 strength and duration from day to day, were never absent ; 
 and on many days, " under a perfectly clear sky," they 
 reached, in the case of the siren, an astonishing intensity. 
 It is doubtless to these air-echoes, and not to cloud-echoes, 
 that the rolling of thunder is to be ascribed. 
 
 7. Experimental Demonstration of Reflection from 
 
 Gases. 
 
 Thus far we have dealt in inference merely, for the 
 interception of sound through aerial reflection has never 
 been experimentally demonstrated ; and, indeed, according 
 to Arago's observation, which has hitherto held undisputed 
 possession of the scientific field, it does not sensibly exist. 
 But the strength of science consists in verification, and I 
 was anxious to submit the question of aerial reflection to 
 an experimental test. The knowledge gained in the last 
 lecture enables us to apply such a test ; but, as in most 
 similar cases, it was not the simplest combinations that 
 were first adopted. Two gases of different densities were 
 to be chosen, and I chose carbonic acid and coal gas. With 
 the aid of my skillful assistant, Mr. John Cottrell, a tunnel 
 was formed, across which five-and-twenty layers of carbonic 
 acid were permitted to fall, and five-and-twenty alternate 
 layers of coal-gas to rise. Sound was sent through this 
 tunnel, making fifty passages from medium to medium in 
 its course. These, I thought, would waste in aerial echoes 
 a sensible portion of sound. 
 
 To indicate this waste an objective test was found in 
 one of the sensitive flames described in the last chapter 
 
AERIAL REFLECTION PROVED EXPERIMENTALLY. 313 
 
 Acquainted with it, we are prepared to understand a 
 drawing and description of the apparatus first employed 
 in the demonstration of aerial reflection. The following 
 clear account of the apparatus was given by a writer in 
 Nature, February 5, 1874 : 
 
 " A tunnel 1 1' (Fig. 146), 2 in. square, 4 ft. 8 in. long, 
 open at both ends, and having a glass front, runs through 
 the box a ~b c d. The spaces above and below are divided 
 into cells opening into the tunnel by transverse orifices 
 exactly corresponding vertically. Each alternate cell of 
 the upper series the 1st, 3d, 5th, etc. communicates by 
 a bent tube (e e e) with a common upper reservoir (<?), its 
 counterpart cell in the lower series having a free outlet 
 into the air. In like manner the 2d, 4th, 6th, etc., of the 
 lower series of cells are connected by bent tubes (n n n) 
 with the lower reservoir (i) 9 each having its direct passage 
 into the air through the cell immediately above it. The 
 gas-distributors (g and *) are filled from both ends at the 
 same time, the upper with carbonic-acid gas, the lower 
 with coal-gas, by branches from their respective supply- 
 pipes (f and h). A well-padded box (p) open to the end of 
 the tunnel forms a little cavern, whence the sound-waves 
 are sent forth by an electric bell (dotted in the figure). A 
 few feet from the other end of the tunnel, and in a direct 
 line with it, is a sensitive flame (&), provided with a fun- 
 nel as sound-collector, and guarded from chance currents 
 by a shade. 
 
 " The bell was set ringing. The flame, with quick re- 
 sponse to each blow of the hammer, emitted a sort of 
 musica. roar, shortening and lengthening as the succes- 
 sive sound-pulses reached it. The gases were then ad- 
 mitted. Twenty-five flat jets of coal-gas ascended from 
 the tubes below, and twenty-five cascades of carbonic 
 acid fell from the tubes above. That which was an ho- 
 mogeneous medium had now fifty limiting surfaces, from 
 
314 
 
 SOUND. 
 
REFLECTION FROM CARBONIC ACID AND COAL GAS. 315 
 
 each of which a portion of the sound was thrown back. 
 In a few moments these successive reflections became so 
 effective that no sound having sufficient power to affect 
 the flame could pierce the clear, optically -transparent, 
 but acoustically-opaque, atmosphere in the tunnel. So 
 long as the gases continued to flow the flame remained 
 perfectly tranquil. When the supply was cut off, the 
 gases rapidly diffused into the air. The atmosphere of 
 the tunnel became again homogeneous, and therefore 
 acoustically transparent, and the flame responded to each 
 sound-pulse as before." 
 
 Not only do gases of different densities act thus upon 
 sound, but atmospheric air in layers of different tempera- 
 tures does the same. Across a tunnel resembling 1 1 ', Fig. 
 146, sixty-six platinum wires were stretched, all of them 
 being in metallic connection. The bell, in its padded box, 
 was placed at one end of the tunnel, and the sensitive 
 flame &, near its flaring-point, at the other. When the 
 bell rang the flame flared. A current from a strong vol- 
 taic battery being sent through the platinum wires, they 
 became heated : layers of warm air rose from them through 
 the tunnel, and immediately the agitation of the flame 
 was stilled. On stopping the current, the agitation recom- 
 menced. In this experiment the platinum wires had not 
 reached a red heat. Employing half the number and the 
 same battery, they were raised to a red heat, the action in 
 this case upon the sound-waves being also energetic. Em- 
 ploying one-third of the number of wires, and the same 
 strength of battery, the wires were raised to a white heat. 
 Here also the flame was immediately rendered tranquil by 
 the stoppage of the sound. 
 
 8. Reflection from Vapors. 
 
 But not only do gases of different densities, and air of 
 different temperatures, act thus upon sound, but air satu- 
 
316 SOUND. 
 
 rated in different degrees, with the vapors of volatile 
 liquids, can be shown by experiment to produce the same 
 effect. Into the path pursued by the carbonic acid in our 
 first experiment a flask, which I have frequently employed 
 to charge air with vapor, was introduced. Through a 
 volatile liquid, partially filling the flask, air was forced into 
 the tunnel tt', which was thus divided into spaces of air 
 saturated with the vapor, and other spaces in their ordi- 
 nary condition. The action of such a medium upon the 
 sound-waves issuing from the bell is very energetic, in- 
 stantly reducing the violently-agitated flame to stillness 
 and steadiness. The removal of the heterogeneous medium 
 instantly restores the noisy flaring of the flame. 
 
 A few illustrations of the action of non-homogeneous 
 atmospheres, produced by the saturation of layers of air 
 with the vapors of volatile liquids, may follow here : 
 
 Bisulphide of Carbon. Flame very sensitive, and 
 noisily responsive to the sound. The action of the non- 
 homogeneous atmosphere was prompt and strong, stilling 
 the agitated flame. 
 
 Chloroform. Flame still very sensitive; action simi- 
 lar to the last. 
 
 Iodide of Methyl. Action prompt and energetic. 
 
 Amylene. Yery fine action; a short and violently- 
 agitated flame was immediately rendered tall and quies- 
 cent. 
 
 Sulphuric Ether. Action prompt and energetic. 
 
 The vapor of water at ordinary temperatures is so small 
 in quantity and so attenuated, that it requires special 
 precautions to bring out its action. But with such pre- 
 cautions it was found competent to reduce to quiescence 
 the sensitive flame. 
 
 As the skill and knowledge of the experimenter aug- 
 ment he is often able to simplify his experimental combi- 
 nations. Thus, in the present instance, by the suitable 
 
REFLECTION FROM HEATED AIR AND VAPORS. 317 
 
 arrangement of the source of sound and the sensitive 
 flame, it was found that not only twenty-five layers, but 
 three or four layers of coal-gas and carbonic acid, sufficed 
 to still the agitated flame. Nay, with improved manip- 
 ulation, the action of a single layer of either gas was 
 rendered perfectly sensible. So also as regards heated 
 layers of air, not only were sixty-six or twenty-two 
 heated platinum wires found sufficient, but the heated air 
 from two or three candle-flames, or even from a single 
 flame, or a heated poker, was found perfectly competent 
 to stop the flame's agitation. The same remark applies 
 
 FIG. 147, 
 
 to vapors. Three or four heated layers of air, saturated 
 with the vapor of a volatile liquid, stilled the flame ; and, 
 by improved manipulation, the action of a single saturated 
 layer could be rendered sensible. In all these cases, 
 moreover, a small, high-pitched reed might be substituted 
 for the bell. 
 
 My assistant has devised the simple apparatus sketched 
 in Fig. 147, for showing reflection by gases, vapors, and 
 heated air. At the end A of the square pipe AB is a small 
 
318 SOUND. 
 
 vibrating reed of high pitch, the sound of which violently 
 agitates the sensitive flame/*. To the horizontal tube g g' 
 are attached four email burners, and above them four chim- 
 neys, through which the heated gases from the flames can 
 ascend into A B. When the coverings of the chimneys 
 are removed and the gas is ignited, the air within A B is 
 rendered rapidly non-homogeneous, and immediately stills 
 the agitated flame. 
 
 The pipe AB may be turned upside down, an orifice 
 seen between A and B fitting on to the stand which sup- 
 ports the tube. The conduit t leads into a shallow rectan- 
 gular box, which communicates by a series of transverse 
 apertures with A B. When air, saturated with the vapor 
 of a volatile liquid, is forced through these apertures, the 
 atmosphere in A B is immediately rendered heterogeneous, 
 the agitated flame being as rapidly stilled. 
 
 In the experiments at the South Foreland, not only 
 was it proved that the acoustic clouds stopped the sound ; 
 but, in the proper position, the sounds which had been re- 
 fused transmission were received by reflection. I wished 
 very much to render this echoed sound evident experi- 
 mentally ; and stated to my assistant that we ought to be 
 able to accomplish this. Mr. Cottrell met my desire by 
 the following beautiful experiment, which has been thus 
 described before the Royal Society : 
 
 " A vibrating reed B (Fig. 148) was placed so as to send 
 sound-waves through a tin tube, 38 inches long, and If 
 inch diameter, in the direction B A, the action of the 
 sound being rendered manifest by its causing a sensitive 
 flame placed at F ' to become violently agitated. 
 
 " The invisible heated layer immediately above the lu- 
 minous portion of an ignited coal-gas flame issuing from 
 an ordinary bat's-wing burner was allowed to stream up- 
 ward across the end A of the tin tube. A portion of the 
 sound issuing from the tube was reflected at the limiting 
 
ECHO FROM FLAME. 
 
 319 
 
 surfaces of the heated layer ; the part transmitted being 
 now only competent to slightly agitate the sensitive flame 
 atF ; . 
 
 " The heated layer was then placed at such an angle 
 that the reflected portion of the sound was sent through a 
 second tin tube, A F (of the same dimensions as B A). 
 Its action was rendered visible by causing a second sensi- 
 tive flame placed at the end of the tube at F to become vio- 
 lently affected. This echo continued active as long as the 
 heated layer intervened ; but upon its withdrawal the sen- 
 sitive flame placed at F', receiving the whole of the direct 
 
 pulse, became again violently agitated, and at the same 
 moment the sensitive flame at F, ceasing to be affected by 
 the echo, resumed its former tranquillity. 
 
 " Exactly the same action takes place when the luminous 
 portion of a gas-flame is made the reflecting layer ; but in 
 the experiments above described the invisible layer above 
 the flame only was used. By proper adjustment of the 
 pressure of the gas the flame at F' can be rendered so 
 moderately sensitive to the direct sound-wave that the 
 portion transmitted through the reflecting layer shall be 
 
320 SOUND. 
 
 incompetent to affect the flame. Then by the introduction 
 and withdrawal of the bat's-wing flame the two sensitive 
 flames can be rendered alternately quiescent and strongly 
 agitated. 
 
 " An illustration is here afforded of the perfect analogy 
 between light and sound ; for if a beam of light be pro- 
 jected from B to F', and a plate of glass be introduced 
 at A in the exact position of the reflecting layer of gas, 
 the beam will be divided, one portion being reflected in 
 the direction A F, and the other portion transmitted 
 through the glass toward F', exactly as the sound-wave is 
 divided into a reflected and transmitted portion by the 
 layer of heated gas or flame." 
 
 Thus far, therefore, we have placed our subject in the 
 firm grasp of experiment ; nor shall we find this test fail- 
 ing us further on. 
 
 PART II. 
 
 INVESTIGATION OF THE CAUSES WHICH HAVE HITHERTO BEEN 
 SUPPOSED EFFECTIVE IN PREVENTING THE TRANSMISSION 
 OF SOUND THROUGH THE ATMOSPHERE. 
 
 Action of Hail and Rain. Action of Snow. Action of Fog; Observations 
 in London. Experiments on Artificial Fogs. Observations on Fogs at 
 the South Foreland. Action of Wind. Atmospheric Selection. Influ- 
 ence of Sound-Shadow. 
 
 1. Action of Hail and Pain. 
 
 In the first part of this chapter it was demonstrated 
 that the optic transparency and acoustic transparency of 
 our atmosphere were by no means necessarily coincident ; 
 that on days of marvelous optical clearness the atmosphere 
 may be filled with impervious acoustic clouds, while days 
 
ACTION OF HAIL AND RAIN. 321 
 
 optically turbid may be acoustically clear. We have now 
 to consider, in detail, the influence of various agents which 
 have hitherto been considered potent in reference to the 
 transmission of sound through the atmosphere. 
 
 Derham, and after him all other writers, considered 
 that falling rain tended powerfully to obstruct sound. An 
 observation on June 3d has been already referred to as tend- 
 ing to throw doubt on this conclusion. Two other crucial 
 instances will suffice to show its untenability. On the 
 morning of October 8th, at 7.45 A.M., a thunderstorm 
 accompanied by heavy rain broke over Dover. But the 
 clouds subsequently cleared away, and the sun shone 
 strongly on the sea. For a time the optical clearness of 
 the atmosphere was extraordinary, but it was acoustically 
 opaque. At 2.30 p. M. a densely-black scowl again over- 
 spread the heavens to the W. S. "W. The distance being 
 6 miles, and all hushed on board, the horn was heard very 
 feebly, the siren more distinctly, while the howitzer was 
 better than either, though not much superior to the siren. 
 
 A squall approached us from the west. In the Alps 
 or elsewhere I have rarely seen the heavens blacker. 
 Vast cumuli floated to the "N. E. and S. E. ; vast streamers 
 of rain descended in the W. "N. W. ; huge scrolls of cloud 
 hung in the !N". ; but spaces of blue were to be seen to the 
 K K E. 
 
 At 7 miles' distance the siren and horn were both feeble, 
 while the gun sent us a very faint report. A dense shower 
 now enveloped the Foreland. 
 
 The rain at length reached us, falling heavily all the 
 way between us and the Foreland ; but the sound, instead 
 of being deadened, rose perceptibly in power. Hail was 
 now added to the rain, and the shower reached a tropical 
 violence, the hailstones floating thickly on the flooded 
 deck. In the midst of this furious squall both the horns 
 and the siren were distinctly heard ; and as the shower 
 
322 SOUND. 
 
 lightened, thus lessening the local pattering, the sounds so 
 rose in power that we heard them at a distance of T-J miles 
 distinctly louder than they had been heard through the 
 rainless atmosphere at 5 miles. 
 
 At 4 P. M. the rain had ceased and the sun shone clearly 
 through the calm air. At 9 miles' distance the horn was 
 heard feebly, the siren clearly, while the howitzer sent us 
 a loud report. All the sounds were better heard at this 
 distance than they had previously been at 5J- miles ; from 
 which, by the law of inverse squares, it follows that the 
 intensity of the sound at 5 miles' distance must have been 
 augmented at least threefold by the descent of the rain. 
 
 On the 23d of October our steamer had forsaken us 
 for shelter, and I sought to turn the weather to account 
 by making other observations on both sides of the fog- 
 signal station. Mr. Douglass, the chief-engineer of the 
 Trinity House, was good enough to undertake the obser- 
 vations 1ST. E. of the Foreland ; while Mr. Ayers, the 
 assistant engineer, walked in the other direction. At 
 12.50 P. M. the wind blew a gale, and broke into a thunder- 
 storm with violent rain. Inside and outside the Cornhill 
 Coast-guard Station, a mile from the instruments in the 
 direction of Dover, Mr. Ayers heard the sound of the 
 siren through the storm ; and after the rain had ceased, 
 all sounds were heard distinctly louder than before. Mr. 
 Douglass had sent a fly before him to Kingsdown, and the 
 driver had been waiting for fifteen minutes before he ar- 
 rived. During this time no sound had been heard, though 
 40 blasts had been blown in the interval; nor had the 
 coast-guard man on duty, a practised observer, heard any 
 of them throughout the day. During the thunderstorm, 
 and while the rain was actually falling with a violence 
 which Mr. Douglass describes as perfectly torrential, the 
 sounds became audible and were heard by all. 
 
 To rain, in short, I have never been able to trace the 
 
ACTION OF SNOW. 323 
 
 slightest deadening influence upon sound. The reputed 
 barrier offered by " thick weather " to the passage of sound 
 was one of the causes which tended to produce hesitation 
 in establishing sound-signals on our coasts. It is to be 
 hoped that the removal of this error may redound to the 
 advantage of coming generations of seafaring men. 
 
 2. Action of Snow. 
 
 Falling snow, according to Derham, is the most serious 
 obstacle of all to the transmission of sound. "We did not 
 extend our observations at the South Foreland into snowy 
 weather ; but a previous observation of my own bears di- 
 rectly upon this point. On Christmas-night, 1859, I ar- 
 rived at Chamouni, through snow so deep as to obliterate 
 the road-fences, and to render the labor of reaching the 
 village arduous in the extreme. On the 26th and 27th it 
 fell heavily. On the 27th, during a lull in the storm, I 
 reached the Montavert, sometimes breast-deep in snow. 
 On the 28th, with great difficulty, two lines of stakes were 
 set out across the glacier, with the view of determining its 
 winter motion. On the 29th the entry in my journal, 
 written in the morning, is : " Snow, heavy snow ; it must 
 have descended through the entire night, the quantity 
 freshly fallen is so great." 
 
 Under these circumstances I planted my theodolite 
 beside the Mer de Glace, having waded to my position 
 through snow, which, being dry, reached nearly to my 
 breast. Assistants were sent across the glacier with in- 
 structions to measure the displacement of a transverse line 
 of stakes planted previously in the snow. A storm drifted 
 up the valley, darkening the air as it approached. It 
 reached us, the snow falling more heavily than I had ever 
 seen it elsewhere. It soon formed a heap on the theodo- 
 lite, and thickly covered my own clothes. Here, then, was 
 a combination of snow in the air, and of soft fresh snow 
 
324 SOUND. 
 
 on the ground, such as Derham could hardly have enjoyed ; 
 still through such an atmosphere I was able to make my 
 instructions audible quite across the glacier, the distance 
 being half a mile, while the experiment was rendered re- 
 ciprocal by one of my assistants making his voice audible 
 to me. 
 
 3. Passage of Sound through Texile Fairies, and 
 through Artificial Showers. 
 
 The flakes here were so thick that it was only at in- 
 tervals that I was able to pick up the retreating forms of 
 the men. Still the air through which the flakes fell was 
 continuous. . Did the flakes merely yield passively to the 
 sonorous waves, swinging like the particles of air them- 
 selves to and fro as the sound-waves passed them ? Or did 
 the waves bend by diffraction round the flakes, and emerge 
 from them without sensible loss ? Experiment will aid us 
 here by showing the astonishing facility with which sound 
 makes its way among obstacles, and passes through tissues, 
 so long as the continuity of the air in their interstices is 
 preserved. 
 
 A piece of millboard or of glass, a plank of wood, or the 
 hand, placed across the open end. t' of the tunnel a ~b c d> 
 Fig. 146 (page 314), intercepts the sound of the bell, 
 placed in the padded box P, and stills the sensitive 
 flame ~k. 
 
 An ordinary cambric pocket-handkerchief, on the other 
 hand, placed across the tunnel-end produced hardly an ap- 
 preciable effect upon the sound. Through two layers of 
 the handkerchief the flame was strongly agitated ; through 
 four layers it was still agitated ; while through six layers, 
 though nearly stilled, it was not entirely so. 
 
 Dipping the same handkerchief into water, and stretch- 
 ing a single wetted layer across the tunnel-end, it stilled 
 the flame as effectually as the millboard or the wood 
 
PASSAGE OF SOUND THROUGH TISSUES. 325 
 
 Hence the conclusion that the sound-waves in the first in- 
 stance passed through the interstices of the cambric. 
 
 Through a single layer of thin silk the sound passed 
 without sensible interruption ; through six layers the flame 
 was strongly agitated; while through twelve layers the 
 agitation was quite perceptible. 
 
 A single layer of this silk, when wetted, stilled the 
 flame. 
 
 A layer of soft lint produced but little effect upon the 
 sound ; a layer of thick flannel was almost equally ineffect- 
 ual. Through four layers of flannel the flame was per- 
 ceptibly agitated. Through a single layer of green baize 
 the sound passed almost as freely as through air ; through 
 four layers of the baize the action was still sensible. 
 Through a layer of close hard felt, half an inch thick, the 
 sound-waves passed with sufficient energy to sensibly agi- 
 tate the flame. Through 200 layers of cotton-net the sound 
 passed freely. I did not witness these effects without 
 astonishment. 
 
 A single layer of thin oiled silk stopped the sound and 
 stilled the flame. A leaf of common note-paper, or a five- 
 pound note, also stopped the sound. 
 
 The sensitive flame is not absolutely necessary to these 
 experiments. Let a ticking watch be hung six inches 
 from the ear, a cambric handkerchief dropped between it 
 and the ear scarcely sensibly affects the ticking ; a sheet of 
 oil-skin or an intensely heated gas-column cuts it almost 
 wholly off. 
 
 But though oiled silk, foreign post, or a bank-note, can 
 stop the sound, a film sufficiently thin to yield freely to 
 the aerial pulses transmits it. A thick soap-film produces 
 an obvious effect upon the sensitive flame ; a very thin one 
 does not. The augmentation of the transmitted sound 
 may be observed simultaneously with the generation and 
 brightening of the colors which indicate the increasing 
 
326 SOUND. 
 
 thinness of the film. A very thin collodion-film acts in 
 the same way. 
 
 Acquainted with the foregoing facts regarding the pas- 
 sage of sound through cambric, silk, lint, flannel, baize, 
 felt, and cotton-net, you are prepared for the statement 
 that the sound-waves pass without sensible impediment 
 through heavy artificial showers of rain, hail, and snow. 
 "Water-drops, seeds, sand, bran, and flocculi of various 
 kinds, have been employed to form such showers ; through 
 all of these, as through the actual rain and hail already de- 
 scribed, and through the snow on the Her de Glace, the 
 sound passes without sensible obstruction. 
 
 4. Action of Fog. Observations in London. 
 
 But the mariner's greatest enemy, fog, is still to be 
 dealt with; and here for a long time the proper conditions 
 of experiment were absent. Up to the end of November 
 we had had frequent days of haze, sufficiently thick to ob- 
 scure the white cliffs of the Foreland, but no real fog. 
 Still those cases furnished demonstrative evidence that the 
 notions entertained regarding the reflection of sound by 
 suspended particles were wrong ; for on many days of the 
 thickest haze the sound covered twice the range attained on 
 other days of perfect optical transparency. Such instances 
 dissolved the association hitherto assumed to exist between 
 acoustic transparency and optic transparency, but they left 
 the action of dense fogs undetermined. 
 
 On December 9th a memorable fog settled down on 
 London. I addressed a telegram to the Trinity House 
 suggesting some gun observations. "With characteristic 
 promptness came the reply that they would be made in 
 the afternoon at Blackwall. I went to Greenwich in the 
 hope of hearing the guns across the river ; but the delay 
 of the train by the fog rendered my arrival too late. Over 
 the river the fog was very dense, and through it came 
 
ACTION OF FOG. 327 
 
 various sounds with, great distinctness. The signal-bell of 
 an unseen barge rang clearly out at intervals, and I could 
 plainly hear the hammering at Cubitt's Town, half a mile 
 away, on the opposite side of the river. No deadening of 
 the sound by the fog was apparent. 
 
 Through this fog and various local noises, Captain At- 
 kins and Mr. Edwards heard the report of a 12-pounder 
 carronade with a 1-lb. charge distinctly better than the 
 18-pounder with a 3-lb. charge, an optically clear atmos- 
 phere, and all noise absent, on July 3d. 
 
 Anxious to turn to the best account a phenomenon for 
 which we had waited so long, I tried to grapple with the 
 problem by experiments on a small scale. On the 10th, I 
 stationed my assistant with a whistle and organ-pipe on 
 the walk below the southwest end of the bridge dividing 
 Hyde Park from Kensington Gardens. From the eastern 
 end of the Serpentine I heard distinctly both the whistle 
 and the pipe, which produced 380 waves a second. On 
 changing places with my assistant, I heard for a time 
 the distinct blast of the whistle only. The deeper note 
 of the organ-pipe at length reached me, rising sometimes 
 to great distinctness, and sometimes falling to inaudi- 
 bility. The whistle showed the same intermittence as to 
 period, but in an opposite sense ; for, when the whistle 
 was faint, the pipe was strong, and vice versa. To obtain 
 the fundamental note of the pipe, it had to be blown 
 gently, and on the whole the whistle proved the most 
 efficient in piercing the fog. 
 
 An extraordinary amount of sound filled the air during 
 these experiments. The resonant roar of the Bayswater 
 and Knightsbridge roads ; the clangor of the great bell 
 of "Westminster ; the rail way- whistles, which were fre- 
 quently blown, and the fog-signals exploded at the various 
 metropolitan stations, were all heard with extraordinary 
 intensity. This could by no means be reconciled with the 
 
328 SOUND. 
 
 statements so categorically made regarding the acoustic 
 impenetrability of a London fog. 
 
 On the llth of December, the fog being denser than 
 before, I heard every blast of the whistle, and occasional 
 blasts of the pipe, over the distance between the bridge 
 and the eastern end of the Serpentine. On joining my 
 assistant at the bridge, the loud concussion of a gun was 
 heard by both of us. A police-inspector affirmed that it 
 came from "Woolwich, and that he had heard several shots 
 about 2 P. M. and previously. The fact, if a fact, was of 
 the highest importance ; so I immediately telegraphed "to 
 Woolwich for information. Prof. Abel kindly furnished 
 me with the following particulars : 
 
 " The firing took place at 1*40 p. M. The guns proved 
 were of comparatively small size 64-pounders, with 10-lb. 
 charges of powder. 
 
 " The concussion experienced at my house and office, 
 about three-quarters of a mile from the butt, was decidedly 
 more severe than that experienced when the heaviest guns 
 are proved with charges of 110 to 120 Ibs. of powder. 
 There was a dense fog here at the time of firing." 
 
 These were the guns heard by the police-inspector ; on 
 subsequent inquiry it was ascertained that two guns were 
 fired about 3 p. M. These were the guns heard by myself. 
 
 Prof. Abel also communicated to me the following 
 fact : " Our workman's bell at the Arsenal Gate, which is 
 of moderate size and anything but clear in tone, is pretty 
 distinctly heard by Prof. Bloxam only when the wind 
 is northeast. During the whole of last week the bell 
 was heard with great distinctness, the wind being south- 
 westerly (opposed to the sound). The distance of the bell 
 from Bloxam's house is about three-quarters of a mile as 
 the crow flies/' 
 
 Assuredly no question of science ever stood so much 
 in need of revision as this of the transmission of sound 
 
OBSERVATIONS IN HYDE PARK. 329 
 
 through the atmosphere. Slowly, but surely, we mastered 
 the question; and the further we advanced, the more 
 plainly it appeared that our reputed knowledge regarding 
 it was erroneous from beginning to end. 
 
 On the morning of the 12th the fog attained its maxi- 
 mum density. It was not possible to read at my window, 
 which fronted the open western sky. At 10.30 I sent an 
 assistant to the bridge, and listened for his whistle and 
 pipe at the eastern end of the Serpentine. The whistle 
 rose to a shrillness far surpassing anything previously 
 heard, but it sank sometimes almost to inaudibility ; 
 proving that, though the air was on the whole highly 
 homogeneous, acoustic clouds still drifted through the fog. 
 A second pipe, which was quite inaudible yesterday, was 
 plainly heard this morning. We were able to discourse 
 across the Serpentine to-day with much greater ease than 
 yesterday. 
 
 During our summer observations I had once or twice 
 been able to fix the position of the Foreland in thick haze 
 by the direction of the sound. To-day my assistant, hid- 
 den by the fog, walked up to the Watermen's Boat-house 
 sounding his w r histle ; and I walked along the opposite side 
 of the Serpentine, clearly appreciating for a time that the 
 line joining us was oblique to the axis of the river. Com- 
 ing to a point which seemed to be exactly abreast of him, 
 I marked it ; and on the following day, when the fog had 
 cleared away, the marked position was found to be per- 
 fectly exact. When undisturbed by echoes, the ear, with 
 a little practice, becomes capable of fixing with great pre- 
 cision the direction of a sound. 
 
 On reaching the Serpentine this morning, a peal of 
 bells, which then began to ring, seemed so close at hand 
 that it required some reflection to convince me that they 
 were ringing to the north of Hyde Park. The sounds 
 fluctuated wonderfully in power. Prior to the striking of 
 
330 SOUND. 
 
 eleven by the great bell of Westminster, a nearer bell 
 struck with loud clangor. The first five strokes of the 
 Westminster bell were afterward heard, one of them being 
 extremely loud ; but the last six strokes were inaudible. 
 An assistant was stationed to attend to the 12 o'clock bells. 
 The clock which had struck so loudly at 11 was unheard 
 at 12, while of the Westminster bell eight strokes out of 
 twelve were inaudible. To such astonishing changes is the 
 atmosphere liable. 
 
 At 7 P. M. the Westminter bell, striking seven, was not 
 at all heard from the Serpentine, while the nearer bell 
 already alluded to was heard distinctly. The fog had 
 cleared away, and the lamps on the bridge could be seen 
 from the eastern end of the Serpentine burning brightly ; 
 but, instead of the sound sharing the improvement of the 
 light, what might be properly called an acoustic fog took 
 the place of its optical predecessor. Several series of 
 the whistle and organ-pipe were sounded in succession ; 
 one series only of the whistle-sounds was heard, all the 
 others being quite inaudible. Three series of the organ- 
 pipe were heard, but exceedingly faintly. On reversing 
 the positions and sounding as before, nothing whatever 
 was heard. 
 
 At 8 o'clock the chimes and hour-bell of the Westmin- 
 ster clock were both very loud. The " acoustic fog " had 
 shifted its position, or temporarily melted away. 
 
 Extraordinary fluctuations were also observed in the 
 case of the church-bells heard in the morning : in a few 
 seconds they would sink from a loudly-ringing peal into 
 utter silence, from w r hich they would rapidly return to 
 loud-tongued audibility. The intermittent drifting of fog 
 over the sun's disk (by which his light is at times obscured^ 
 at times revealed) is the optical analogue of these effects. 
 As regards such changes, the acoustic deportment of the 
 atmosphere is a true transcript of its optical deportment. 
 
FLUCTUATIONS OF BELLS. 331 
 
 At 9 P. M. three strokes only of the Westminster clock 
 were heard; the others were inaudible. The air had re- 
 lapsed in part into its condition at 7 P. M., when all the 
 strokes were unheard. The quiet of the park this even- 
 ing, as contrasted with the resonant roar which filled the 
 air on the two preceding days, was very remarkable. The 
 sound, in fact, was stifled in the optically clear but acous- 
 tically flocculeiit atmosphere. 
 
 On the 13th, the fog being displaced by thin haze, I 
 went again to the Serpentine. The carriage-sounds were 
 damped to an extraordinary degree. The roar of the 
 Knightsbridge and Bayswater roads had subsided, the 
 tread of troops which passed us a little way off was un- 
 heard, while at 11 A. M. both the chimes and the hour-bell 
 of the Westminster clock were stifled. Subjectively con- 
 sidered, all was favorable to auditory impressions ; but the 
 very cause that damped the local noises extinguished our 
 experimental sounds. The voice across the Serpentine to- 
 day, with my assistant plainly visible in front of me, was 
 distinctly feebler than it had been when each of us was 
 hidden from the other in the densest fog. 
 
 Placing the source of sound at the eastern end of the 
 Serpentine I walked along its edge from the bridge toward 
 the end. The distance between these two points is about 
 1,000 paces. After 500 of them had been stepped, the 
 sound was not so distinct as it had been at the bridge on 
 the day of densest" fog ; hence, by the law of inverse 
 squares, the optical cleansing of the air through the melt- 
 ing away of the fog had so darkened it acoustically, that a 
 sound generated at the eastern end of the Serpentine was 
 lowered to one-fourth of its intensity at a point midway 
 between the end and the bridge. 
 
 To these demonstrative observations one or two sub- 
 sequent ones may be added. On several of the moist and 
 warm days, at the beginning of 1874, I stood at noon 
 
332 SOUND. 
 
 beside the railing of St. James's Park, near Buckingham 
 Palace, three-quarters of a mile from the clock-tower, 
 which was clearly visible. Not a single stroke of " Big 
 Ben " was heard. On January 19th fog and drizzling rain 
 obscured the tower; still from the same position I not 
 only heard the strokes of the great bell, but also the 
 chimes of the quarter-bells. 
 
 During the exceedingly dense and " dripping " fog of 
 January 22d, from the same railings, I heard every stroke 
 of the bell. At the end of the Serpentine, when the fog 
 was densest, the Westminster bell was heard striking loud- 
 ly eleven. Toward evening this fog began to melt away, 
 and at 6 o'clock I went to the end of the Serpentine to 
 observe the effect of the optical clearing upon the sound. 
 Not one of the strokes reached me. At 9 o'clock and at 
 10 o'clock my assistant was in the same position, and on 
 both occasions he failed to hear a single stroke of the bell. 
 It was a case precisely similar to that of December 13th, 
 when the dissolution of the fog was accompanied by a 
 decided acoustic thickening of the air. 1 
 
 5. Observations at the South Foreland. 
 
 Satisfactory, and indeed conclusive, as these results 
 seemed, I desired exceedingly to confirm them by experi- 
 ments with the instruments actually employed at the 
 South Foreland. On the 10th of February I had the 
 gratification of receiving the following note and inclosure 
 from the Deputy Master of Trinity House : 
 
 " My DEAR TYNDALL : The inclosed will show how 
 accurately your views have been verified, and I send them 
 on at once without waiting for the details. I think you 
 
 1 A friend informs me that he has followed a pack of hounds on a clear 
 calm day without hearing a single yelp from the dogs ; while on calm foggy 
 days from the same distance the musical uproar of the pack was loudly 
 audible. 
 
FOG-SIGNALS IN FOGS. 333 
 
 will be glad to have them, and as soon as I get the report 
 it shall be sent to you. I made up my mind ten days ago 
 that there would be a chance in the light foggy-disposed 
 weather at home, and therefore sent the Argus off at an 
 hour's notice, and requested the Fog Committee to keep 
 one member on board. On Friday I was so satisfied that 
 the fog would occur that I sent Edwards down to record 
 the observations. 
 
 " Yery truly yours, 
 
 " FEED. AREOW." 
 
 The inclosure referred to was notes from Captain At- 
 kins and Mr. Edwards. Captain Atkins writes thus : 
 
 " As arranged, I came down here by the mail express, 
 meeting Mr. Edwards at Cannon Street. We put up at 
 the Dover Castle, and next morning at 7 I was awoke by 
 sounds of the siren. On jumping up I discovered that 
 the long-looked-for fog had arrived, and that the Argus 
 had left her moorings. 
 
 " However, had I been on board, the instructions I left 
 with Troughton (the master of the Argus) could not have 
 been better carried out. About noon the fog cleared up, 
 and the Argus returned to her moorings, when I learned 
 that they had taken both siren and horn sounds to a dis- 
 tance of 11 miles from the station, where they dropped a 
 buoy. This I knew to be correct, as I have this morning 
 recovered the buoy, and the distances both in and out 
 agree with Troughton's statement. I have also been to 
 the Yarne light-ship (12f miles from the Foreland), and 
 ascertained that during the fog of Saturday forenoon they 
 1 distinctly ' heard the sounds." 
 
 Mr. Edwards, who was constantly at my side during 
 our summer and autumn observations, and who is thor- 
 oughly competent to form a comparative estimate of the 
 strength of the sounds, states that those of the 7th were 
 
334 SOUND. 
 
 " extraordinarily loud," both Captain Atkins and himself 
 being awoke by them. He does not remember ever before 
 hearing the sounds so loud in Dover ; it seemed as though 
 the observers were close to the instruments. 
 
 Other days of fog preceded this one, and they were all 
 days of acoustic transparency, the day of densest fog being 
 acoustically the clearest of all. 
 
 The results here recorded are of the highest impor- 
 tance, for they bring us face to face with a dense fog and 
 an actual fog-signal, and confirm in the most conclusive 
 manner the previous observations. The fact of Captain 
 Atkins and Mr. Edwards being awakened by the siren 
 proves, beyond all our previous experience, its power dur- 
 ing this dense fog. 
 
 It is exceedingly interesting to compare the transmis- 
 sion of sound on February 7th with its transmission on 
 October 14th. The wind on both days had the same 
 strength and direction. My notes of the observations show 
 the latter to have been throughout a day of extreme opti- 
 cal clearness. The range was 10 miles. During the fog 
 of February 7th the Argus heard the sound at 11 miles ; 
 and it was also heard at the Yarne light-vessel, which is 
 12f miles from the Foreland. 
 
 It is also worthy of note that through the same fog the 
 sounds' were well heard at the South Sand Head light- 
 vessel, which is in the opposite direction from the South 
 Foreland, and was actually behind the siren. For this 
 important circumstance is to be borne in mind : on Febru- 
 ary 7th the siren happened to be pointed, not toward the 
 Argus, but toward Dover. Had the yacht been in the 
 axis of the instrument it is highly probable that the 
 sound would have been heard all the way across to the 
 coast of France. 
 
 It is hardly necessary for me to say a word to guard 
 myself against the misconception that I consider sound 
 
FOG AT THE SOUTH FORELAND. 335 
 
 to be assisted by the fog itself. The fog-particles have no 
 more influence upon the waves of sound than the suspended 
 particles stirred up over the banks of Newfoundland have 
 upon the waves of the Atlantic. An homogeneous air is 
 the usual associate of fog, and hence the acoustic clearness 
 of foggy weather. 
 
 6. Experiments on Artificial Fogs. 
 
 These observations are clinched and finished by being 
 brought within the range of laboratory experiment. Here 
 we shall learn incidentally a lesson as to the caution re- 
 quired from an experimenter. 
 
 The smoke from smouldering brown paper was allowed 
 to stream upward through its rectangular apertures, into 
 the tunnel a ~b c d (Fig. 146) ; the action upon the sound- 
 waves was strong, rendering the short and agitated sensi- 
 tive flame Tc tall and quiescent. 
 
 Air first passed through ammonia, then through hydro- 
 chloric acid, and, thus loaded with thick fumes, was sent 
 into the tunnel ; the agitated flame was rendered imme- 
 diately quiescent, indicating a very decided action on the 
 part of the artificial fog. 
 
 Air passed through perchloride of tin and sent into 
 the tunnel produced exceedingly dense fumes. The action 
 upon the sound-waves was very strong. 
 
 The dense smoke of resin, burnt before the open end 
 of the tunnel, and blown into it with a pair of bellows, had 
 also the effect of stopping the sound-waves, so as to still 
 the agitated flame. 
 
 The conclusion seems clear, and its perfect harmony 
 with the prevalent a priori notions as to the action of fog 
 upon sound makes it almost irresistible. But caution is 
 here necessary. The smoke of the brown paper was hot / 
 the flask containing the hydrochloric acid was hot / that 
 containing the perchloride of tin was hot; while the resin- 
 15 
 
336 SOUND. 
 
 fumes produced by a red-hot poker were also obviously 
 hot. "Were the results, then, due to the fumes or to the 
 differences of temperature ? The observations might well 
 have proved a trap to an incautious reasoner. 
 
 Instead of the smoke and heated air, the heated air alone 
 from four red-hot pokers was permitted to stream upward 
 into the tunnel ; the action on the sound-waves was very 
 decided, though the tunnel was optically empty. The 
 flame of a candle was placed at the upper end, and the 
 hot air just above its tip was blown into the tunnel ; the 
 action on the sensitive flame was decided. A similar 
 effect was produced when the air, ascending from a red- 
 hot iron, was blown into the tunnel. 
 
 In these latter cases the tunnel remained optically 
 clear, while the same effect as that produced by the resin, 
 smoke, and fumes, was observed. Clearly, then, we are 
 not entitled to ascribe, without further investigation, to 
 the artificial fog an effect which may have been due to the 
 air which accompanied it. 
 
 Having eliminated the fog and proved the non-homo- 
 geneous air effective, our reasoning will be completed by 
 eliminating the heat, and proving the fog ineffective. 
 
 Instead of the tunnel a 5 c d, Fig. 146, a cupboard with 
 glass sides, 3 feet long, 2 feet wide, and about 5 feet high, 
 was filled with fumes of various kinds. Here it was thought 
 the fumes might remain long enough for differences of 
 temperature to disappear. Two apertures were made in 
 two opposite panes of glass 3 feet asunder. In front of one 
 aperture was placed the bell in its padded box, and behind 
 the other aperture, and at some distance from it, the 
 sensitive flame. 
 
 Phosphorus placed in a cup floating on water was 
 ignited within the closed cupboard. The fumes were so 
 dense that considerably less than the three feet traversed 
 by the sound extinguished totally a bright candle-flame. 
 
ARTIFICIAL FOGS. 337 
 
 At first there was a slight action upon the sound ; but 
 this rapidly vanished, the flame being no more affected 
 than if the sound had passed through pure air. The first 
 action was manifestly due to differences of temperature, 
 and it disappeared when the temperature was equalized. 
 
 The cupboard was next filled with the dense fumes of 
 gunpowder. At first there was a slight action ; but this 
 disappeared even more rapidly than in the case of the 
 phosphorus, the sound passing as if no fumes were there. 
 It required less than half a minute to abolish the action 
 in the case of the phosphorus, but a few seconds sufficed 
 in the case of the gunpowder. These fumes were far more 
 than sufficient to quench the candle-flame. 
 
 The dense smoke of resin, when the temperature had 
 become equable, exerted no action on the sound. 
 
 The fumes of gum-mastic were equally ineffectual. 
 
 The fumes of the perchloride of tin, though of ex- 
 traordinary density, exerted no sensible effect upon the 
 sound. . 
 
 Exceedingly dense fumes of chloride of ammonium 
 next filled the cupboard. A fraction of the length of the 
 3-foot tube sufficed to quench the candle-flame. Soon 
 after the cupboard was filled, the sound passed without 
 the least sensible deterioration. An aperture at the top 
 of the cupboard was opened ; but though a dense smoke- 
 column ascended through it, many minutes elapsed before 
 the candle-flame could be seen through the attenuated 
 fog. 
 
 Steam from a copper boiler was so copiously admitted 
 into the cupboard as to fill it with a dense cloud. No real 
 cloud was ever so dense ; still the sound passed through it 
 without the least sensible diminution. This being the 
 case, cloud-echoes are not a likely phenomenon. 
 
 In all of these cases, when a couple of Bunsen's burn- 
 ers were ignited within the cupboard continuing the 
 
338 SOUND. 
 
 fumes, less than a minute's action rendered the air so 
 heterogeneous that the sensitive flame was completely 
 stilled. 
 
 These acoustically inactive fogs were subsequently 
 proved competent to cut off the electric light. 
 
 Experiment and observation go, therefore, hand in hand 
 in demonstrating that fogs have no sensible action upon 
 sound. The notion of their impenetrability, which so 
 powerfully retarded the introduction of phonic coast-sig- 
 nals, being thus abolished, we have solid ground for the 
 hope that disasters due to fogs and thick weather will in 
 the future be materially mitigated. 
 
 7. Action of Wind. 
 
 In stormy weather we were frequently forsaken by our 
 steamer, which had to seek shelter in the Downs or Mar- 
 gate Roads, and on such occasions the opportunity was 
 turned to account to determine the effect of the wind. 
 On October llth, accompanied by Mr. Douglass and Mr. 
 Edwards, I walked along the cliffs from Dover Castle tow- 
 ard the Foreland, the wind blowing strongly against the 
 sound. About a mile and a half from the Foreland, we 
 first heard the faint but distinct sound of the siren. The 
 horn-sound was inaudible. A gun fired during our halt 
 was also unheard. 
 
 As we approached the Foreland we saw the smoke of 
 a gun. Mr. Edwards heard a faint crack, but neither 
 Mr. Douglass nor I heard anything. The sound of the 
 siren was at the same time of piercing intensity. We 
 waited for ten minutes, when another gun was fired. The 
 smoke was at hand, and I thought I heard a faint thud, 
 but could not be certain. My companions heard nothing. 
 On pacing the distance afterward we were found to be 
 only 550 yards from the gun. "We were shaded at the 
 time by a slight eminence from both the siren and the 
 
ACTION OF WIND. 339 
 
 gun, but this could not account for the utter extinction 
 of the gun-sound at so short a distance, and at a time when 
 the siren sent to us a note of great power. 
 
 Mr. Ayres at my request walked to windward along the 
 cliff, while Mr. Douglass proceeded to St. Margaret's Bay. 
 During their absence I had three guns fired. Mr. Ayres 
 heard only one of them. Favored by the wind, Mr. 
 Douglass, at twice the distance, and far more deeply im- 
 mersed in the sound-shadow, heard all three reports with 
 the utmost distinctness. 
 
 Joining Mr. . Douglass, we continued our walk to a 
 distance of three-quarters of a mile beyond St. Margaret's 
 Bay. Here, being dead to leeward, though the wind blew 
 with unabated violence, the sound of the siren was borne 
 to us with extraordinary power. 1 In this position we also 
 heard the gun loudly, and two other loud reports at the 
 proper interval of ten minutes, as we returned to the 
 Foreland. 
 
 It is within the mark to say that the gun on October 
 llth was heard five times, and might have been heard 
 fifteen times, as far to leeward as to windward. 
 
 In windy weather the shortness of its sound is a serious 
 drawback to the use of the gun as a signal. In the case 
 of the horn and siren, time is given for the attention to 
 be fixed upon the sound ; and a single puff, while cutting 
 out a portion of the blast, does not obliterate it wholly. 
 Such a puff, however, may be fatal to the momentary 
 gun-sound. 
 
 On the leeward side of the Foreland, on the 23d oi 
 October, the sounds were heard at least four times as far 
 as on the windward side, while in both .directions the si: en 
 possessed the greatest penetrative power. 
 
 On the 24th the wind shifted to E. S.E., and the 
 
 1 The horn here was temporarily suspended, but doubtless would 
 been well heard. 
 
SOUND. 
 
 sounds, which, when the wind was "W. S.W., failed to reach 
 Dover, were now heard in the streets through thick rain. 
 On the 27th the wind was E. "N. E. In our writing-room 
 in the Lord "Warden Hotel, in the bedrooms, and on the 
 staircase, the sound of the siren reached us with surprising 
 power, piercing through the whistling and moaning of the 
 wind, which blew through Dover toward Folkestone. The 
 sounds were heard by Mr. Edwards and myself at 6 miles 
 from the Foreland on the Folkestone road ; and had the 
 instruments not then ceased sounding, they might have 
 been heard much farther. At the South Sand Head 
 light-vessel, 3f miles on the opposite side, no sound had 
 been heard throughout the day. On the 28th, the wind 
 being "N. by E., the sounds were heard in the middle of 
 Folkestone, 8 miles off, while in the opposite direction 
 they failed to reach 3 miles. On the 29th the limits of 
 range were Eastware Bay on the one side, and Kingsdown 
 on the other ; on the 30th the limits were Kingsdown on 
 the one hand, and Folkestone Pier on the other. "With a 
 wind having a force of 4 or 5 it was a very common obser- 
 vation to hear the sound in one direction three times as 
 far as in the other. 
 
 This well-known effect of the wind is exceedingly 
 difficult to explain. Indeed, the only explanation worthy 
 of the name is one offered by Prof. Stokes, and sug- 
 gested by some remarkable observations of De la Roche. 
 In vol. i. of "Annales de Chimie" for 1816, p. 176, 
 Arago introduces De la Roche's memoir in these words : 
 " L'auteur arrive a des conclusions, qui d'abord pourront 
 paraitre paradoxales, mais ceux qui savent combien il met- 
 tait de soins et d'exactitude dans toutes ses recherches se 
 garderont sans doute d'opposer une opinion populaire a 
 des experiences positives." The strangeness of De la 
 Roche's results consisted in his establishing, by quantita- 
 tive measurements, not only that sound has a greater 
 
STOKES'S EXPLANATION. 
 
 range in the direction of the wind than in the opposite 
 direction, but that the range at right angles to the wind is 
 the maximum. 
 
 In a short but exceedingly able communication, pre- 
 sented to the British Association in 1857, the eminent 
 physicist above mentioned points out a cause which, if 
 sufficient, would account for the results referred to. The 
 lower atmospheric strata are retarded by friction against 
 the earth, and the upper ones by those immediately below 
 them ; the velocity of transition, therefore, in the case of 
 wind, increases from the ground upward. It may be 
 proved that this difference of velocity tilts the sound-wave 
 upward in a direction opposed to, and downward in a 
 direction coincident with, the wind. In this latter case 
 the direct wave is reenforced by the wave reflected from 
 the earth. Now the reenf orcement is greatest in the direc- 
 tion in which the direct and reflected waves inclose the 
 smallest angle ; and this is at right angles to the direction 
 of the wind. Hence the greater range in this direction. 
 It is not, therefore, according to Prof. Stokes, a stifling of 
 the sound to windward, but a tilting of the sound-wave 
 over the heads of the observers, that defeats the propaga- 
 tion in that direction. 
 
 This explanation calls for verification, and I wished 
 much to test it by means of a captive balloon rising high 
 enough to catch the deflected wave; but on communi- 
 cating with Mr. Coxwell, who has earned for himself so 
 high a reputation as an aeronaut, and who has always 
 shown himself so willing to promote a scientific object, I 
 learned with regret that the experiment was too dangerous 
 to be carried out. 1 
 
 1 Experiments so important as those of De la Roche ought not to be 
 left without verification. I have made arrangements with a view to this 
 object. 
 
342 SOUND. 
 
 8. Atmospheric Selection. 
 
 It has been stated that the atmosphere on different 
 days shows preferences to different sounds. This point is 
 worthy of further illustration. 
 
 After the violent shower which passed over us on 
 October 18th, the sounds of all the instruments, as already 
 stated, rose in power ; but it was noticed that the horn- 
 sound, which was of lower pitch than that of the siren, 
 improved most, at times not only equaling, but surpassing, 
 the sound of its rival. From this it might be inferred 
 that the atmospheric change produced by the rain favored 
 more especially the transmission of the longer sonorous 
 waves. 
 
 But our programme enabled us to go further than 
 mere inference. It had been arranged on the day men- 
 tioned, that up to 3.30 p. M. the siren should perform 2,400 
 revolutions a minute, generating 480 waves a second. As 
 long as this rate continued, the horn, after the shower, had 
 the advantage. The rate of rotation was then changed to 
 2,000 a minute, or 400 waves a second, when the siren- 
 sound immediately surpassed that of the horn. A clear 
 connection was thus established between aerial reflection 
 and the length of the sonorous waves. 
 
 The 10-inch Canadian whistle being capable of ad- 
 justment so as to produce sounds of different pitch, on 
 the 10th of October I ran through a series of its sounds. 
 The shrillest appeared to possess great intensity and pene- 
 trative power. The belief is common that a note of this 
 character (which affects so powerfully, and even painfully, 
 an observer close at hand) has also the greatest range. 
 Mr. A. Gordon, in his examination before the Committee 
 on Lighthouses, in 1845, expressed himself thus : " When 
 you get a shrill sound, high in the scale, that sound is 
 carried much farther than a lower note in the scale." I 
 
ATMOSPHERIC SELECTION. 343 
 
 have heard the same opinion expressed by other scientific 
 men. 
 
 On the 14th of October the point was submitted to an 
 experimental test. It had been arranged that up to 11.30 
 A. M. the Canadian whistle, which had been heard with such 
 piercing intensity on the 10th, should sound its shrillest 
 note. At the hour just mentioned we were beside the 
 Yarne buoy, Yf miles from the Foreland. The siren, as 
 we approached the buoy, was heard through the paddle- 
 noises ; the horns were also heard, but more feebly than 
 the siren. "We paused at the buoy and listened for the 
 11.30 gun. Its boom was heard by all. Neither before 
 nor during the pause was the shrill-sounding Canadian 
 w^histle once heard. At the appointed time it was adjusted 
 to produce its ordinary low-pitched note, which was im- 
 mediately heard. Farther out the low boom of the cannon 
 continued audible after all the other sounds had ceased. 
 
 But it was only during the early part of the day that 
 this preference for the longer wave was manifested. At 
 3 P.M. the case was completely altered, for then the high- 
 pitched siren was heard when all the other sounds were in- 
 audible. On many other days we had illustrations of the 
 varying comparative power of the siren and the gun. 
 On the 9th of October sometimes the one, sometimes the 
 other, was predominant. On the morning of the 13th the 
 siren was clearly heard on Shakespeare's Cliff, while 
 two guns with their puffs perfectly visible were unheard. 
 On October 16, 2 miles from the signal-station, the gun at 
 11 o'clock was inferior to the siren, but both were heard. 
 At 12.30, the distance being 6 miles, the gun was quite 
 unheard, while the siren continued faintly audible. Later 
 on in the day the experiment was twice repeated. The 
 puff of the gun was in each case seen, but nothing wag 
 heard. In the last experiment, when the gun was quenched, 
 the siren sent forth a sound so strong as to maintain itself 
 
344 SOUND. 
 
 through the paddle-noises. The day was clearly hostile to 
 the passage of the longer sonorous waves. 
 
 October ITth began with a preference for the shorter 
 waves. At 11.30 A. M. the mastery of the siren over the 
 gun was pronounced ; at 12.30 the gun slightly surpassed 
 the siren; at 1, 2, and 2.30 p. M. the gun also asserted its 
 mastery. This preference for the longer waves was con- 
 tinued on October 18th. On October 20th the day began in 
 favor of the gun, then both became equal, and finally the 
 siren gained the mastery ; but the day had become stormy, 
 and a storm is always unfavorable to the momentary gun- 
 sound. The same remark applies to the experiments of 
 October 21st. At 11 A. M., distance 6J miles, when the 
 siren made itself heard through the noises of wind, sea, 
 and paddles, the gun was fired ; but, though listened for 
 with all attention, no sound was heard. Half an hour 
 later the result was the same. On October 24th five ob- 
 servers saw the flash of the gun at a distance of 5 miles, but 
 heard nothing; all of them at this distance heard the 
 siren distinctly; a second experiment on the same day 
 yielded the same result. On the 27th also the siren was 
 triumphant; and on three several occasions on the 29th 
 its mastery over the gun was very decided. 
 
 Such experiments yield new conceptions as to the scat- 
 tering of sound in the atmosphere. !Nb sound here em- 
 ployed is a simple sound ; in every case the fundamental 
 note is accompanied by others, and the action of the at- 
 mosphere on these different groups of waves has its optical 
 analogue in that scattering of the waves of the luminif- 
 erous ether which produces the various shades and colors 
 of the sky. 
 
 9. Concluding Eemarks. 
 
 A few additional remarks and suggestions will fitly 
 wind up this chapter. It has been proved that in some 
 
DISADVANTAGES OF GUN. 345 
 
 states of the weather the howitzer firing a 3-Ib. charge 
 commands a larger range than the whistles, trumpets, or 
 siren. This was the case, for example, on the particular 
 day, October lYth, when the ranges of all the sounds 
 reached their maximum. 
 
 On many other days, however, the inferiority of the 
 gun to the siren was demonstrated in the clearest manner. 
 The gun-puffs were seen with the utmost distinctness at 
 the Foreland, but no sound was heard, the note of the siren 
 at the same time reaching us with distinct and consider- 
 able power. 
 
 The disadvantages of the gun are these : 
 
 a. The duration of the sound is so short that, unless 
 the observer is prepared beforehand, the sound, through 
 lack of attention rather than through its own powerless- 
 ness, is liable to be unheard. 
 
 5. Its liability to be quenched by a local sound is so 
 great, that it is sometimes obliterated by a puff of wind 
 taking possession of the ears at the time of its arrival. 
 This point was alluded to by Arago, in his report on the 
 celebrated experiments of 1822. By such a puff a momen- 
 tary gap is produced in the case of a continuous sound, but 
 not entire extinction. 
 
 <?. Its .liability to be quenched or deflected by an oppos- 
 ing wind, so as to be practically useless at a very short 
 distance to windward, is very remarkable. A case has 
 been cited in which the gun failed to be heard against a 
 violent wind at a distance of 550 yards from the place of 
 firing, the sound of the siren at the same time reaching us 
 with great intensity. 
 
 Still, notwithstanding these drawbacks, I think the gun 
 is entitled to rank as a first-class signal. I have had occa- 
 sion myself to observe its extreme utility at Holyhead 
 and the Kish light-vessel near Kingstown. The command- 
 ers of the Holyhead boats, moreover, are unanimous in 
 
346 SOUND. 
 
 their commendation of the gun. An important addition 
 in its favor is the fact that in a fog the flash or glare often 
 comes to the aid of the sound. On this point, the evi- 
 dence is quite conclusive. 
 
 There may be cases in which the combination of the 
 gun with one of the other signals may be desirable. 
 Where it is wished to confer an unmistakable individual- 
 ity on a fog-signal station, such a combination might with 
 advantage be resorted to. 
 
 If the gun be retained as one form of fog-signal (and 
 I should be sorry at present to recommend its total abo- 
 lition), it ought to be of the most suitable description. 
 Our experiments prove the sound of the gun to be depend- 
 ent on its shape ; but we do not know that we have em- 
 ployed the best shape. This suggests the desirability of 
 constructing a gun with special reference to the production 
 of sound. 1 
 
 An absolutely uniform superiority on all days cannot 
 be conceded to any one of the instruments subjected to 
 examination ; still, our observations have been so numer- 
 ous and long-continued as to enable us to come to the sure 
 conclusion that, on the whole, the steam-siren is the most 
 powerful fog-signal which has hitherto been tried in Eng- 
 land. It is specially powerful when local noises, such as 
 those of wind, rigging, breaking waves, shore-surf, and 
 the rattle of pebbles, have to be overcome. Its den- 
 sity, quality, pitch, and penetration, render it dominant 
 over such noises after all other signal-sounds have suc- 
 cumbed. 
 
 I have not, therefore, hesitated to recommend the in- 
 troduction of the siren as a coast-signal. 
 
 It will be desirable in each case to confer upon the 
 instrument a power of rotation, so as to enable the person 
 
 1 The Elder Brethren have already had plans of a new signal-gun laid 
 before them by the constructors of the War Department. 
 
MINIMUM RANGE OF FOG-SIGNALS. 34.7 
 
 in charge of it to point its trumpet against the wind or in 
 any other required direction. This arrangement was made 
 at the South Foreland, and it presents no mechanical dif- 
 ficulty. It is also desirable to mount the siren, so as to 
 permit of the depression of its trumpet fifteen or twenty 
 degrees below the horizon. 
 
 In selecting the position at which a fog-signal is to be 
 mounted, the possible influence of a sound-shadow, and 
 the possible extinction of the sound by the interference of 
 the direct waves with waves reflected from the shore, 
 must form the subject of the gravest consideration. Pre- 
 liminary trials may, in most cases, be necessary before 
 fixing on the precise point at which the instrument is to 
 be placed. 
 
 The siren which has been long known to scientific men 
 is worked with air ; and it would be worth while to try 
 how the fog-siren would behave supposing compressed air 
 to be substituted for steam. Compressed air might also 
 be tried with the whistles. 
 
 ~No fog-signal hitherto tried is able to fulfill the condi- 
 tion laid down in a very able letter already referred to, 
 namely, " that all fog-signals should T)e distinctly audible 
 for at least 4: miles, under every circumstance" Circum- 
 stances may exist to prevent the most powerful sound from 
 being heard at half this distance. What may with cer- 
 tainty be affirmed is, that in almost all cases the siren may 
 certainly be relied on at a distance of 2 miles ; in the great 
 majority of cases it may be relied upon at a distance of 3 
 miles, and in the majority of cases to a distance greater 
 than 3 miles. 
 
 Happily the experiments thus far made are perfectly 
 concurrent in indicating that at the particular time when 
 fog-signals are needed, the air holding the fog in suspen- 
 sion is in a highly-homogeneous condition ; hence it is in 
 the highest degree probable that in the case of fog we may 
 
348 SOUND. 
 
 rely upon the signals being effective at far greater dis- 
 tances than those just mentioned. 
 
 I am cautious not to inspire the mariner with a confi- 
 dence which may prove delusive. "When he hears a fog- 
 signal he ought, as a general rule (at all events until ex- 
 tended experience justifies the contrary), to assume the 
 source of sound to be not more than 2 or 3 miles distant, 
 and to heave his lead or to take other necessary precau- 
 tions. If he errs at all in his estimate of distance, it ought 
 to be on the side of safety. 
 
 "With the instruments now at our disposal wisely estab- 
 lished along coasts, I venture to think that the saving of 
 property in ten years will be an exceedingly large mul- 
 tiple of the outlay necessary for the establishment of such 
 signals. The saving of life appeals to the higher motives 
 of humanity. 
 
 In a report written for the Trinity House on the sub- 
 ject of fog-signals, my excellent predecessor, Prof. Fara- 
 day, expresses the opinion that a false promise to the 
 mariner would be worse than no promise at all. Casting 
 our eyes back upon the observations here recorded, we 
 find the sound-range on clear, calm days varying from 2J 
 miles to 16f miles. It must be evident that an instruc- 
 tion founded on the latter observation would be fraught 
 with peril in weather corresponding to the former. 
 Not the maximum but the minimum sound-range should 
 be impressed upon the mariner. "Want of atten- 
 tion to this point may be followed by disastrous conse- 
 quences. 
 
 This remark is not made without cause. I have 
 before me a " Notice to Mariners " regarding a fog-whistle 
 recently mounted at Cape Hace, which is reputed to have 
 a range of 20 miles in calm weather, 30 miles with the 
 wind, and in stormy weather or against the wind Y to 10 
 miles. Now, considering the distance reached by sound 
 
CONCLUSION. 34-9 
 
 in our observations, I should be willing to concede the 
 possibility, in a more homogeneous atmosphere than ours, 
 of a sound-range on some calm days of 20 miles, and on 
 some light windy days of 30 miles, to a powerful whistle ; 
 but I entertain a strong belief that the stating of these 
 distances, or of the distance 7 to 10 miles against a storm, 
 without any qualification, is calculated to inspire the 
 mariner with false confidence. I would venture to affirm 
 that at Cape Race calm days might be found in which the 
 range of the sound will be less than one-fourth of what 
 this notice states it to be. Such publications ought to be 
 without a trace of exaggeration, and furnish only data on 
 which the mariner may with perfect confidence rely. My 
 object in extending these observations over so long a period 
 was to make evident to all how fallacious it would be, and 
 how mischievous it might be, to draw general conclusions 
 from observations made in weather of great acoustic trans- 
 parency. 
 
 Thus ends, for the present at all events, an inquiry 
 which I trust will prove of some importance, scientific as 
 well as practical. In conducting it I have had to congratu- 
 late myself on the unfailing aid and cooperation of the 
 Elder Brethren of the Trinity House. Captain Drew, 
 Captain Close, Captain Were, Captain Atkins, and the 
 Deputy Master, have all from time to time taken part in 
 the inquiry. To the eminent arctic navigator, Admiral 
 Collinson, who showed throughout unflagging and, I would 
 add, philosophic interest in the investigation, I am indebted 
 for most important practical aid. He was almost always at 
 my side, comparing opinions with me, placing the steamer 
 in the required positions, and making with consummate 
 skill and promptness the necessary sextant observations. 
 I am also deeply sensible of the important services rendered 
 by Mr. Douglass, the able and indefatigable engineer, by 
 Mr. Ayres, the assistant engineer, and by Mr. Price 
 
350 SOUND. 
 
 Edwards, the private secretary of the Deputy Master of 
 the Trinity House. 
 
 The officers and gunners at the South Foreland also 
 merit my best thanks, as also Mr. Holmes and Mr. Laid- 
 law, who had charge of the trumpets, whistles, and 
 siren. 
 
 In the subsequent experimental treatment of the sub- 
 ject I have been most ably aided by my excellent assistant, 
 Mr. John CottrelL 
 
 NOTE. 
 
 In the Appendix will be found a brief paper on " Acoustic Reversibility." 
 in which I offer a solution of a difficulty encountered by the French 
 philosophers in their experiments on the velocity of sound m 1822. The 
 solution is based on the experiments and observations recorded in the fore- 
 going chapter. J. T. 
 
SUMMARY. 351 
 
 SUMMARY OF CHAPTER VII. 
 
 THE paper of Dr. Derham, published in the " Philosophi- 
 cal Transactions " for 1708, has been hitherto the almost 
 exclusive source of our knowledge of the causes which 
 affect the transmission of sound through the atmosphere. 
 
 Derham found that fog obstructed sound, that rain 
 and hail obstructed sound, but that above all things falling 
 snow, or a coating of fresh snow upon the ground, tended 
 to check the propagation of sound through the atmosphere. 
 
 With a view to the protection of life and property at 
 sea in the years 1873 and 1874, this subject received an 
 exhaustive examination, observational and experimental. 
 The investigation was conducted at the expense of the 
 Government and under the auspices of the Elder Breth- 
 ren of the Trinity House. 
 
 The most conflicting results were at first obtained. 
 On the 19th of May, 1873, the sound range was 3J- miles ; 
 on the 20th it was 5 miles ; on the 2d of June, 6 miles ; 
 on the 3d, more than 9 miles; on the 10th, 9 miles ; on 
 the 25th, 6 miles ; on the 26th, 9J miles ; on the 1st of 
 July, 12f miles ; on the 2d, 4 miles ; while on the 3d, 
 with a clear calm atmosphere and smooth sea, it was less 
 than 3 miles. 
 
 These discrepancies were proved to be due to a state 
 of the air which bears the same relation to sound that 
 cloudiness does to light. By streams of air differently 
 heated, or saturated in different degrees with aqueous 
 vapors, the atmosphere is rendered flocculent to sound. 
 
 Acoustic clouds, in fact, are incessantly floating or 
 
352 SOUND. 
 
 flying through the air. They have nothing whatever to 
 do with ordinary clouds, fogs, or haze. The most trans- 
 parent atmosphere may be filled with them ; converting 
 days of extraordinary optical transparency into days of 
 equally extraordinary acoustic opacity. 
 
 The connection hitherto supposed to exist between a 
 clear atmosphere and the transmission of sound is there- 
 fore dissolved. 
 
 The intercepted sound is wasted by repeated reflections 
 in the acoustic cloud, as light is wasted by repeated re- 
 flections in an ordinary cloud. And as from the ordinary 
 cloud the light reflected reaches the eye, so from the per- 
 fectly invisible acoustic cloud the reflected sound reaches 
 the ear. - 
 
 Aerial echoes of extraordinary intensity and of long 
 duration are thus produced. They occur, contrary to the 
 opinion hitherto entertained, in the clearest air. 
 
 It is to the wafting of such acoustic clouds through 
 the atmosphere that the fluctuations in the sounds of our 
 public clocks and of church-bells are due. 
 
 The existence of these aerial echoes has been proved 
 both by observation and experiment. They may arise 
 either from air-currents differently heated, or from air- 
 currents differently saturated with vapor. 
 
 Rain has no sensible power to obstruct sound. 
 
 Hail has no sensible power to obstruct sound. 
 
 Snow has no sensible power to obstruct sound. 
 
 Fog has no sensible power to obstruct sound. 
 
 The air associated with fog is, as a general rule, highly 
 homogeneous and favorable to the transmission of sound. 
 The notions hitherto entertained regarding the action of 
 fog are untenable. 
 
 Experiments on artificial showers of rain, hail, and 
 snow, and on artificial fogs of extraordinary density, con- 
 firm the results of observation. 
 
SUMMARY. 353 
 
 As long as the air forms a continuous medium the 
 amount of sound scattered by small bodies suspended in it 
 is astonishingly small. 
 
 This is illustrated by the case with which sound trav- 
 erses layers of calico, cambric, silk, flannel, baize, and felt. 
 It freely passes through all these substances in thicknesses 
 sufficient to intercept the light of the sun. 
 
 Through six layers of thin silk, for example, it passes 
 with little obstruction ; it finds its way through a layer 
 of close felt half an inch thick, and it is not wholly inter- 
 cepted by 200 layers of cotton-net. 
 
 The atmosphere exercises a selective choice upon the 
 waves of sound which varies from day to day, and even 
 from hour to hour. It is sometimes favorable to the trans- 
 mission of the longer, and at other times favorable to the 
 transmission of the shorter, sonorous waves. 
 
 The recognized action of the wind has been confirmed 
 by this investigation. 
 
354 
 
 CHAPTER VIII. 
 
 Law of Vibratory Motions in Water and Air. Superposition of Vibra- 
 tions. Interference of Sonorous Waves. Destruction of Sound by 
 Sound. Combined Action of Two Sounds nearly in Unison with each 
 other. Theory of Beats. Optical Illustration of the Principle of In- 
 terference. Augmentation of Intensity by Partial Extinction of Vi- 
 brations. Resultant Tones. Conditions of their Production. Experi- 
 mental Illustrations. Difference-Tones and Summation-Tones. Theo- 
 ries of Young and Helmholtz. 
 
 1. Interference of Water -Waves. 
 
 FROM a boat in Cowes Harbor, in moderate weather, I 
 Lave often watched the masts and ropes of the ships, as 
 mirrored in the water. The images of the ropes revealed 
 the condition of the surface, indicating by long and wide 
 protuberances the passage of the larger rollers, and, by 
 smaller indentations, the ripples which crept like parasites 
 over the sides of the larger waves. The sea was able to 
 accommodate itself to the requirements of all its undula 
 tions, great and small. When the surface was touched 
 with an oar, or when drops were permitted to fall from 
 the oar into the water, there was also room for the tiny 
 wavelets thus generated. This carving of the surface by 
 waves and ripples had its limit only in my powers of ob- 
 servation ; every wave and every ripple asserted its right 
 of place, and retained its individual existence, amid the 
 crowd of other motions which agitated the water. 
 
 The law that rules this chasing of the sea, this crossing 
 and intermingling of innumerable small waves, is that the 
 resultant motion of every particle of water is the sum of 
 
SUPERPOSITION OF VIBRATIONS. 355 
 
 the individual motions imparted to it. If a particle be 
 acted on at the same moment by two impulses, both of 
 which tend to raise it, it will be lifted by a force equal to 
 the sum of both. If acted upon by two impulses, one of 
 which tends to raise it, and the other to depress it, it will 
 be acted upon by a force equal to the difference of both. 
 When, therefore, the sum of the motions is spoken of, the 
 algebraic sum is meant the motions which tend to raise 
 the particle being regarded as positive, and those which 
 tend to depress it as negative. 
 
 When two stones are cast into smooth water, 20 or 30 
 feet apart, round each stone is formed a series of expand- 
 ing circular waves, every one of which consists of a ridge 
 and a furrow. The waves touch, cross each other, and 
 carve the surface into little eminences and depressions. 
 Where ridge coincides with ridge, we have the water raised 
 to a double height ; where furrow coincides with furrow, 
 we have it depressed to a double depth ; where ridge coin- 
 cides with furrow, we have the water reduced to its 
 average level. The resultant motion of the water at every 
 point is, as above stated, the algebraic sum of the motions 
 impressed upon that point. And if, instead of two sources 
 of disturbance, we had ten, or a hundred, or a thousand, 
 the consequence would be the same; the actual result 
 might transcend our powers of observation, but the law 
 above enunciated would still hold good. 
 
 Instead of the intersection of waves from two distinct 
 centres of disturbance, we may cause direct and reflected 
 waves, from the same centre, to cross each other. Many 
 of you know the beauty of the effects produced when light 
 is reflected from ripples of water. When mercury is 
 employed the effect is more brilliant still. Here, by a 
 proper mode of agitation, direct and reflected waves may 
 be caused to cross and interlace, and by the most wonder- 
 ful self-analysis to untie their knotted scrolls. The adja- 
 
356 SOUND. 
 
 cent figure (Fig. 149), which is copied from the excellent 
 " Wellenlehre " of the brothers "Weber, will give some idea 
 of the beauty of these effects. It represents the chasing 
 
 FIG. 149. 
 
 produced by the intersection of direct and reflected water- 
 waves in a circular vessel, the point of disturbance (marked 
 by the smallest circle in the figure) being midway between 
 the centre and the circumference. 
 
 This power of water to accept and transmit multitu- 
 dinous impulses is shared by air, which concedes the right 
 of space. and motion to any number of sonorous waves. 
 The same air is competent to accept and transmit the 
 vibrations of a thousand instruments at the same time. 
 When we try to visualize the motion of that air to pre- 
 sent to the eye of the mind the battling of the pulses 
 direct and reverberated the imagination retires baffled 
 from the attempt. Still, amid all the complexity, the 
 
INTERFERENCE OF SOUND. 357 
 
 law above enunciated holds good, every particle of air 
 being animated by a resultant motion, which, is the alge- 
 braic sum of all the individual motions imparted to it. 
 And the most wonderful thing of all is, that the human 
 ear, though acted on only by a cylinder of that air, which 
 does not exceed the thickness of a quill, can detect the 
 components of the motion, and, by an act of attention, can 
 even, isolate from the aerial entanglement any particular 
 sound. 
 
 2. Interference of Sound. 
 
 When two unisonant tuning-forks are sounded togeth- 
 er, it is easy to see that the forks may so vibrate that the 
 condensations of the one shall coincide with the conden- 
 sations of the other, and the rarefactions of the one with 
 the rarefactions of the other. If this be the case, the two 
 forks will assist each other. The condensations will, in 
 fact, become more condensed, the rarefactions more rare- 
 fied ; and as it is upon the difference of density between 
 the condensations and rarefactions that loudness depends, 
 the two vibrating forks, thus supporting each other, will 
 produce a sound of greater intensity than that of either of 
 them vibrating alone. 
 
 It is, however, also to see that the two forks may be 
 so related to each other that one of them shall require a 
 condensation at the place where the other requires a rare- 
 faction ; that the one fork shall urge the air-particles for- 
 ward, while the other urges them backward. If the op- 
 posing forces be equal, particles so solicited will move 
 neither backward nor forward, the aerial rest which corre- 
 sponds to silence being the result. Thus, it is possible, by 
 adding the sound of one fork to that of another, to abolish 
 the sounds of both. "We have here a phenomenon which, 
 above all others, characterizes wave-motion. It was this 
 phenomenon, as manifested in optics, that led to the undu- 
 
358 SOUND. 
 
 latory theory of light, the most cogent proof of that theory 
 being based upon the fact that, by adding light to light, 
 we may produce darkness, just as we can produce silence 
 by adding sound to sound. 
 
 During the vibration of a tuning-fork the distance 
 between the two prongs is alternately increased and dimin- 
 ished. Let us call the motion which increases the distance 
 the outward swing, and that which diminishes the dis- 
 tance the inward swing of the fork. And let us suppose 
 that our two forks, A and B, Fig. 150, reach the limits 
 of their outward swing and their inward swing at the same 
 moment. In this case the phases of their motion, to use 
 the technical term, are the same. For the sake of sim- 
 plicity we will confine our attention to the right-hand 
 prongs, A and B, of the two forks, neglecting the other two 
 
 FIG. 150. 
 
 prongs ; and now let us ask what must be the distance 
 between the prongs A and B, when the condensations and 
 rarefactions of both, indicated respectively by the dark 
 and light shading, coincide ? A little reflection will make 
 it clear that if the distance from B to A be equal to the 
 length of a whole sonorous wave, coincidence between 
 the two systems of waves must follow. The same would 
 evidently occur were the distance between A and B two 
 wave-lengths, three wave-lengths, four wave-lengths in 
 short, any number of whole wave-lengths. In all such 
 cases we shall have coincidence of the two systems of 
 waves, and consequently a reinforcement of the sound of 
 the one fork by that of the other. Both the condensa- 
 
REENFORCEMENT AND EXTINCTION OF SOUND BY SOUND. 359 
 
 tions and rarefactions between A and c are, in this case, 
 more pronounced than they would be if either of the forks 
 were suppressed. 
 
 But if the prong B be only half the length of a wave 
 behind A, what must occur? Manifestly the rarefactions 
 of one of the systems of waves will then coincide with the 
 condensations of the other system, the air to the right of A 
 being reduced to quiescence. This is shown in Fig. 151, 
 
 FIG. 151. 
 
 where the uniformity of shading indicates an absence both 
 of condensations and rarefactions. When B is two half 
 wave-lengths behind A, the waves, as already explained, 
 support each other ; when they are three half wave-lengths 
 apart, they destroy each other. Or, expressed generally, 
 we have augmentation or destruction according as the dis- 
 tance between the two prongs amounts to an even or an 
 odd number of semi-undulations. Precisely the same is 
 true of the waves of light. If through any cause one sys- 
 tem of ethereal waves be any even number of semi-undula- 
 tions behind another system, the two systems support each 
 other when they coalesce, and we have more light. If the 
 one system be any odd number of semi-undulations behind 
 the other, they oppose each other, and a destruction of light 
 is the result of their coalescence, 
 
 The action here referred to, both as regards sound and 
 light, is called Interference. 
 16 
 
360 SOUND. 
 
 3. Experimental lllustration-s. 
 
 Sir John Herschel was the first to propose to divide a 
 stream of sound into two branches, of different lengths, 
 causing the branches afterward to reunite, and interfere 
 with each other. This idea has been recently followed out 
 with success by M. Quincke ; and it has been still further 
 improved upon by M. Konig. The principle of these 
 experiments will be at once evident from Fig. 152. The 
 
 FIG. 152. 
 
 tube o f divides into two branches at f, the one branch 
 being carried round n, and the other round m. The two 
 branches are caused to reunite at g, and to end in a com- 
 mon canal, g p. The portion ~b n of the tube which slides 
 over a ~b can be drawn out as shown in the figure, and 
 thus the sound-waves can be caused to pass over different 
 distances in the two branches. Placing a vibrating 
 tuning-fork at 0, and the ear at p, when the two branches 
 are of the same length, the waves through both reach the 
 ear together, and the sound of the fork is heard. 
 Drawing n ~b out, a point is at length obtained where the 
 sound of the fork is extinguished. This occurs when the 
 distance a ~b is one-fourth of a wave-length ; or, in other 
 words, when the whole right-hand branch is half a wave- 
 length longer than the left-hand one. Drawing ~b n still 
 farther out, the sound is again heard ; and when twice 
 
BEATS. 361 
 
 the distance a ft amounts to a whole wave- length, it 
 reaches a maximum. Thus, according as the difference of 
 both branches amounts to half a wave length, or to a whole 
 wave-length, we have reinforcement or destruction of the 
 two series of sonorous waves. In practice, the tube o f 
 ought to be prolonged until the direct sound of the fork 
 is unheard, the attention of the ear being then wholly con- 
 centrated on the sounds that reach it through the tube. 
 
 It is quite plain that the wave-length of any simple 
 tone may be readily found by this instrument. It is only 
 necessary to ascertain the difference of path which pro- 
 duces complete interference. Twice this difference is the 
 wave-length ; and if the rate of vibration be at the same 
 time known, we can immediately calculate the velocity of 
 sound in air. 
 
 Each of the two forks now before you executes exactly 
 256 vibrations in a second. Sounded together, they are 
 in unison. Loading one of them with a bit of wax, it 
 vibrates a little more slowly than its neighbor. The wax, 
 say, reduces the number of vibrations to 255 in a second ; 
 how must their waves affect each other ? If they start at 
 the same moment, condensation coinciding with condensa- 
 tion, and rarefaction with rarefaction, it is quite manifest 
 that this state of things cannot continue. At the 128th 
 vibration their phases are in complete opposition, one of 
 them having gained half a vibration on the other. Here 
 the one fork generates a condensation where the other 
 generates a rarefaction : and the consequence is, that the 
 two forks, at this particular point, completely neutralize 
 each other. From this point onward, however, the forks 
 support each other more and more, until, at the end of a 
 second, when the one has completed its 255th, and the 
 other its 256th vibration, condensation again coincides with 
 condensation, and rarefaction with rarefaction, the full ef- 
 fect of both sounds being produced upon the ear. 
 
362 SOUND. 
 
 It is quite manifest that under these circumstances we 
 cannot have the continuous flow of perfect unison. We 
 have on the contrary, alternate reinforcements and dimi- 
 nutions of the sound. "We obtain, in fact, the effect 
 known to musicians by the name of beats, which, as here 
 explained, are a result of interference. 
 
 I now load this fork still more heavily, by attaching a 
 fourpenny-piece to the wax ; the coincidences and interfer- 
 ences follow each other more rapidly than before; we 
 have a quicker succession of beats. In our last experi- 
 ment, the one fork accomplished one vibration more than 
 the other in a second, and we had a single beat in the 
 same time. In the present case, one fork vibrates 250 
 times, while the other vibrates 256 times in a second, and 
 the number of beats per second is 6. A little reflection 
 will make it plain that in the interval required by the 
 one fork to execute one vibration more than the other, a 
 beat must occur ; and inasmuch as, in the case now before 
 us, there are six such intervals in a second, there must be 
 six beats in the same time. In short, the number of beats 
 per second is always equal to the difference between the two 
 rates of vibration. 
 
 4. Interference of Waves from Organ-pipes. 
 
 Beats may be produced by all sonorous bodies. These 
 two tall organ-pipes, for example, when sounded together, 
 give powerful beats, one of them being slightly longer 
 than the other. Here are two other pipes, which are now 
 in perfect unison, being exactly of the same length. But 
 it is only necessary to bring the finger near the embou- 
 chure of one of the pipes, Fig. 153, to lower its rate of 
 vibration, and produce loud and rapid beats. The placing 
 of the hand over the open top of one of the pipes also 
 lowers its rate of vibration, and produces beats, which fol- 
 
MODES OF PRODUCING BEATS. 
 
 363 
 
 FIG. 153. 
 
 low each other with augmented rapidity as the top of the 
 pipe is closed more and more. By a stronger blast the 
 first two harmonics of the pipes are brought out. These 
 higher notes also interfere, 
 and you have these quicker 
 beats. 
 
 ]STo more beautiful illus- 
 tration of this phenomenon 
 can be adduced than that 
 furnished by two sounding- 
 flames. Two such flames are 
 now before you, the tube sur- 
 rounding one of them being 
 provided with a telescopic 
 slider, Fig. 154 (next page). 
 There are, at present, no 
 beats, because the tubes are 
 not sufficiently near unison. 
 I gradually lengthen the 
 shorter tube by raising its 
 slider. Rapid beats are 
 now heard ; now they are 
 slower ; now slower still ; and now both flames sing to- 
 gether in perfect unison. Continuing the upward motion 
 of the slider, I make the tube too long ; the beats begin 
 again, and quicken, until finally their sequence is so 
 rapid as to appeal only as roughness to the ear. The 
 flames, you observe, dance within their tubes in time 
 to the beats. As already stated, these beats cause a 
 silent flame within a tube to quiver when the voice is 
 thrown to a proper pitch, and when the position of 
 the flame is rightly chosen, the beats set it singing. 
 With the flames of large rose-burners, and with tin tubes 
 from 3 to 9 feet long, we obtain beats of exceeding 
 power. 
 
364 
 
 SOUND. 
 
 You have just heard the beats produced by two tall 
 organ-pipes nearly in unison with each other. Two other 
 
 FIG. 154. 
 
 pipes are now mounted on our wind-chest. Fig. 155, each 
 of which, however, is provided at its centre with a mem- 
 brane intended to act upon a flame. 1 Two small tubes 
 lead from the spaces closed by the membranes, and unite 
 afterward, the membranes of both the organ-pipes being 
 thus connected with the same flame. By means of the 
 sliders, s, s f , near the summits of the pipes, they are either 
 brought into unison or thrown out of it at pleasure. They 
 are not at present in unison, and the beats they produce 
 follow each other with great rapidity. The flame con- 
 
 1 Described in Chapter V., p. 216. 
 
ACTION OF BEATS ON FLAME. 
 
 365 
 
 nected with the central membranes dances in time to the 
 beats. When brought nearer to unison, the beats are 
 
 FIG. 155. 
 
 slower, and the flame at succesive intervals withdraws its 
 light and appears to exhale it. A process which reminds 
 you of the inspiration and expiration of the breath is thus 
 carried on by the flame. If the mirror, M, be now turned, 
 the flame produces a luminous band continues' at certain 
 places, but for the most part broken into distinct images 
 of the flame. The continuous parts correspond to the 
 intervals of interference where the two sets of vibrations 
 abolish each other. 
 
 Instead of permitting both pipes to act upon the same 
 flame, we may associate a flame with each of them. The 
 deportment of the flames is then very instructive. Imag- 
 ine both flames to be in the same vertical line, the one 
 
366 SOUND. 
 
 of them being exactly under the other. Bringing the 
 pipes into unison, and turning the mirror, we resolve each 
 flame into a chain of images, but we notice that the im- 
 ages of the one occupy the spaces between the images of 
 the other. The periods of extinction of the one flame, 
 therefore, correspond to the periods of kindling of the 
 other. The experiment proves that, when two unisonant 
 pipes are placed thus close to each other, their vibrations 
 are in opposite phases. The consequence of this is, that 
 the two sets of vibrations permanently neutralize each 
 other, so that at a little distance from the pipes you fail to 
 hear the fundamental tone of either. For this reason we 
 cannot, with any advantage, place close to each other in an 
 organ several pipes of the same pitch. 
 
 5. Lissayous's Illustration of Beats of Two Tuning- 
 forks. 
 
 In the case of beats, the amplitude of the oscillating 
 air reaches a maximum and a minimum periodically. By 
 the beautiful method of M. Lissajous we can illustrate 
 optically this alternate augmentation and diminution of 
 amplitude. Placing a large tuning-fork, T', Fig. 156, in 
 front of the lamp L, a luminous beam is received upon 
 the mirror attached to the fork. This is reflected back to 
 the mirror of a second fork, T, and by it thrown on to the 
 screen, where it forms a luminous disk. When the bow is 
 drawn over the fork T 1 ', the beam, as in the experiments 
 described in the second chapter, is tilted up and down, the 
 disk upon the screen stretching to a luminous band three 
 feet long. If, in drawing the bow over this second fork, 
 the vibrations of both coincide in phase, the band will be 
 lengthened ; if the phases are in opposition, total or partial 
 neutralization of the one fork by the other will be the re- 
 sult. It so happens that in the present instance the second 
 
OPTICAL ILLUSTRATIONS OF BEATS. 
 
 367 
 
 fork adds something to the action of the first, the band of 
 light being now four feet long. These forks have been 
 tuned as perfectly as possible. Each of them executes ex- 
 actly 64 vibrations in a second ; the initial relation of their 
 phases remains, therefore, constant, and hence you notice 
 a gradual shortening of the luminous band, like that ob- 
 
 Fio. 156. 
 
 served during the subsidence of the vibrations of a single 
 fork. The band at length dwindles to the original disk, 
 which remains motionless upon the screen. 
 
 By attaching, with wax, a threepenny-piece to the 
 prong of one of these forks, its rate of vibration is lowered. 
 The phases of the two forks cannot now retain a constant 
 relation to each other. One fork incessantly gains upon 
 the other, and the consequence is that sometimes the phases 
 of both coincide, and at other times they are in opposition. 
 Observe the result. At the present moment the two forks 
 conspire, and we have a luminous band four feet long upon 
 the screen. This slowly contracts, drawing itself up to a 
 mere disk ; but the action halts here only during the moment 
 of opposition. That passed, the forks begin again to assist 
 
368 SOUND. 
 
 each other, and the disk once more slowly stretches into a 
 band. The action here is very slow ; but it may be quick- 
 ened by attaching a sixpence to the loaded fork. The 
 band of light now stretches, and contracts in perfect 
 rhythm. The action, rendered thus optically evident, is 
 impressed upon the air of this room ; its particles alternate- 
 ly vibrate and come to rest, and, as a consequence, beats 
 are heard in synchronism with the changes of the figure 
 upon the screen. 
 
 The time which elapses from maximum to maximum, 
 or from minimum to minimum, is that required for the 
 one fork to perform one vibration more than the other. 
 At present this time is about two seconds. In two seconds, 
 therefore, one beat occurs. When we augment the disso- 
 nance by increasing the load, the rhythmic lengthening 
 and shortening of the band is more rapid, while the in- 
 termittent hum of the forks is more audible. There are 
 now six elongations and shortenings in the interval taken 
 up a moment ago by one ; the beats at the same time be- 
 ing heard at the rate of three a second. By loading the 
 fork still more, the alternations may be caused to succeed 
 each other so rapidly that they can no longer be followed 
 by the eye, while the beats, at the same time, cease to be 
 individually distinct, and appeal as a kind of roughness to 
 the ear. 
 
 In the experiments with a single tuning-fork, already 
 described (Fig. 22, Chapter II.), the beam reflected from the 
 fork was received on a looking-glass, and, by turning the 
 glass, the band of light on the screen was caused to stretch 
 out into a long wavy line. It was explained at the time 
 that the loudness of the sound depended on the depth of 
 the indentations. Hence, if the band of light of varying 
 length now before us on the screen be drawn out in a sinu- 
 ous line, the indentations ought to be at some places deep, 
 while at others they ought to vanish altogether. This is 
 
EXPERIMENTS OF HOPKINS AND LISSAJOUS. 359 
 
 the case. By a little tact the mirror of the fork T (Fig. 
 156) is caused to turn through a small angle, a sinuous 
 line composed of swellings and contractions (Fig. 157) 
 being drawn upon the screen. The swellings correspond 
 
 FIG. 15T. 
 
 to the periods of sound, and the contractions to those of 
 silence. 1 
 
 Two vibrating bodies, then, each of which separately 
 produces a musical sound, can, when acting together, 
 neutralize each other. Hence, by quenching the vibra- 
 tions of one of them, we may give sonorous effect to the 
 other. It often happens, for instance, that when two 
 tuning-forks, on their resonant cases, are vibrating in 
 unison, the stoppage of one of them is accompanied by 
 an augmentation of the sound. This point may be further 
 illustrated by the vibrating bell, already described (Fig. 78, 
 Chapter IV.). Placing its resonant tube in front of one 
 of its nodes, a sound is heard, but nothing like what is 
 heard when the tube is opposed to a ventral segment. The 
 reason of this is that the vibrations of a bell on the oppo- 
 site sides of a nodal line are in opposite directions, and 
 they therefore interfere with each other. By introducing 
 a glass plate between the bell and the tube, the vibrations 
 on one side of the nodal line may be intercepted; an 
 instant augmentation of the sound is the consequence. 
 
 1 The figure is but a meagre representation of .the fact. The band of 
 light was two inches wide, the depth of the sinuosities varying from three 
 feet to zero. 
 
370 
 
 ROUND. 
 
 Fie. 168. 
 
 6. Interference of Waves from a Vibrating Disk. 
 Hopkins ' and Lissajoutfs Illustrations. 
 
 In a vibrating disk every two adjacent sectors move at 
 the same time in opposite directions. When the one 
 sector rises the other falls, the nodal line marking the 
 limit between them. Hence, at the moment when any 
 sector produces a condensation in the air above it, the 
 adjacent sector produces a rarefaction in the same air. A 
 partial destruction of the sound of one sector by the other 
 
 is the result. You will 
 now understand the in- 
 strument by which the 
 late "William Hopkins 
 illustrated the principle 
 of interference. The tube 
 A B, Fig. 158, divides at B 
 into two branches. The 
 end A of the tube is 
 closed by a membrane. 
 Scattering sand upon this 
 membrane, and holding 
 the ends of the branches 
 over adjacent sectors of 
 a vibrating disk, no mo- 
 tion (or, at least, an extremely feeble motion) of the sand 
 is perceived. Placing the ends of the two branches over 
 alternate sectors of the disk, the sand is tossed from the 
 membrane, proving that in this case we have coincidence 
 of vibration on the part of the two sectors. 
 
 We are now prepared for a very instructive experi- 
 ment, which we owe to M. Lissajous. Drawing a bow 
 over the edge of a brass disk, I divide it into six vibrat- 
 ing sectors. When the palm of the hand is brought 
 over any one of them, the sound, instead of being di- 
 
INTENSITY AUGMENTED BY PARTIAL EXTINCTION. 371 
 
 Fre. 159. 
 
 uiinished, is augmented. When two hands are placed 
 over two adjacent sectors, you notice no increase of 
 the sound; but when they are placed over alternate 
 sectors, as in Fig. 159, a striking augmentation of the 
 sound is the consequence. 
 By simply lowering and 
 raising the hands, marked 
 variations of intensity are 
 produced. By the approach 
 of the hands the vibrations 
 of the two sectors are in- 
 tercepted ; their interfer- 
 ence right and left being 
 thus abolished, the remain- 
 ing sectors sound more 
 loudly. Passing the single 
 hand to and fro along the 
 surface, you also hear a rise 
 and fall of the sound. It rises when the hand is over a 
 vibrating sector ; it falls when the hand is over a nodal 
 line. Thus, by sacrificing a portion of the vibrations, we 
 make the residue more effectual. Experiments similar to 
 these may be made with light and radiant heat. If of 
 two beams of the former, which destroy each other by 
 interference, one be removed, light takes the place of 
 darkness; and if of two interfering beams of the latter 
 one be intercepted, heat takes the place of cold. 
 
 Y. Quenching the Sound of one Prong of a Tuning- 
 fork "by that of the other. 
 
 You have remarked the almost total absence of sound 
 on the part of a vibrating tuning-fork when held free in 
 the hand. The feebleness of the fork as a sounding body 
 arises in part from interference. The prongs always vi- 
 
372 
 
 SOUND. 
 
 brate in opposite directions, one producing a condensation 
 where the other produces a rarefaction, a destruction of 
 sound being the consequence. By simply passing a paste- 
 board tube over one of the prongs of the fork, its vibrations 
 are in part intercepted, and an augmentation of the sound 
 is the result. The single prong is' thus proved to be more 
 effectual than the two prongs. There are positions in 
 which the destruction of the sound of one prong by that 
 of the other is total. These positions are easily found by 
 
 striking the fork 
 
 V N. .X and turning it 
 
 round before the 
 ear. When the 
 back of the prong 
 is parallel to the 
 ear, the sound is 
 heard ; when the 
 side surfaces of 
 both prongs are 
 parallel to the 
 ear, the sound is 
 also heard; but 
 when the corner 
 
 of a prong is carefully presented to the ear, the sound is 
 utterly destroyed. During one complete rotation of the 
 fork we find four positions where the sound is thus ob- 
 literated. 
 
 Let ss (Fig. 160) represent the two ends of the tuning- 
 fork, looked down upon it as it stands upright. When the ear 
 is placed at a or J, or at c or d, the sound is heard. Along 
 the four dotted lines, on the contrary, the waves generated 
 by the two prongs completely neutralize each other, and 
 nothing is there heard. These lines have been proved by 
 Weber to be hyperbolic curves; and this must be theii 
 character according to the principle of interference. 
 
 / 
 
 
 
 / 
 
 / 
 
 
INTERFERENCE OF WAVES OF TUNING-FORK. 373 
 
 This remarkable case of interference, which was first 
 noticed by Dr. Thomas Young, and thoroughly investi- 
 gated by the brothers "Weber, may be rendered audible 
 by means of resonance. Bringing a vibrating fork over 
 a jar which resounds to it, and causing the fork to ro- 
 tate slowly, in four positions we have a loud resonance ; 
 in four others absolute silence, alternate risings and fall- 
 ings of the sound accompanying the fork's rotation. While 
 the fork is over the jar with its corner downward and 
 the sound entirely extinguished, let a pasteboard tube be 
 passed over one of its prongs, as in Fig. 161, a loud 
 resonance announces ^ FlQ 161 
 
 the withdrawal of 
 the vibrations of 
 that prong. To ob- 
 tain this effect, the 
 fork must be held 
 over the centre of 
 the jar, so that the 
 air shall be symmet- 
 rically distributed on 
 both sides of it. Mov- 
 ing the fork from 
 the centre toward 
 one of the sides, without altering its inclination in the 
 least, we obtain a forcible sound. Interference, however, 
 is also possible near the side of the jar. Holding the 
 fork, not with its corner downward, but with both its 
 prongs in the same horizontal plane, a position is soon 
 found near the side of the jar where the sound is extin- 
 guished. In passing completely from side to side over 
 the mouth of the jar, two such places of interference are 
 discoverable. 
 
 A variety of experiments will suggest themselves to 
 the reflecting mind, by which the effect of interference 
 
374 
 
 SOUND. 
 
 may be illustrated. It is easy, for example, to find a jar 
 which resounds to a vibrating plate. Such a jar, placed 
 over a vibrating segment of the plate, produces a powerful 
 resonance. Placed over a nodal line, the resonance is 
 entirely absent ; but if a piece of pasteboard be interposed 
 between the jar and plate, so as to cut off the vibrations 
 on one side of the nodal line, the jar instantly resounds 
 to the vibrations of the other. Again, holding two forks, 
 which vibrate with the same rapidity, over two resonant 
 jars, the sound of both flows forth in unison. "When a 
 bit of wax is attached to one of the forks, powerful beats 
 are heard. Removing the wax, the unison is restored. 
 When one of these unisonant forks is placed in the flame 
 of a spirit-lamp its elasticity is changed, and it produces 
 long loud beats with its unwarmed fellow. 1 If while one 
 of the forks is sounding on its resonant case the other be 
 excited and brought near the mouth of the case, as in Fig. 
 162, loud beats declare the absence of unison. Dividing 
 
 FIG. 162. 
 
 a jar by a vertical diaphragm, and bringing one of the 
 
 1 In his admirable experiments on tuning, Scheibler found in the beats a 
 test of differences of temperature of exceeding delicacy. 
 
RESULTANT TONES, 375 
 
 forks over one of its halves, and the other fork over 
 the other; the two semi-cylinders of air produce beats 
 by their interference. But the diaphragm is not neces- 
 sary; on removing it, the beats continue as before, one 
 half of the same column of air interfering with the 
 other. 1 
 
 The intermittent sound of certain bells, heard more 
 especially when their tones are subsiding, is an effect of 
 interference. The bell, through lack of symmetry, as ex- 
 plained in the fourth chapter, vibrates in one direction a 
 little more rapidly than in the other, and beats are the 
 consequence of the coalescence of the two different rates 
 of vibration. 
 
 RESULTANT TONES. 
 
 We have now to turn from this question of interference 
 to the consideration of a new class of musical sounds, of 
 which the beats were long considered to be the progeni- 
 tors. The sounds here referred to require for their pro- 
 duction the union of two distinct musical tones. Where 
 such union is effected, under the proper conditions, result- 
 ant tones are generated, which are quite distinct from 
 the primaries concerned in their production. They were 
 discovered in 1745, by a German organist, named Sorge, 
 but the publication of the fact attracted little attention. 
 They were discovered independently in 1Y54, by the cele- 
 brated Italian violinist Tartini, and after him have been 
 called Tartini's tones. 
 
 To produce them it is desirable, if not necessary, to 
 have the two primary tones of considerable intensity. 
 Helmholtz prefers the siren to all other means of exciting 
 
 1 Sir John Herschel and Sir C. Wheatstone, I believe, made this expert 
 ment independently. 
 
376 SOUND. 
 
 them, and with this instrument they are very readily 
 obtained. It requires some attention at first, on the part 
 of the listener, to single out the resultant tone from the 
 general mass of sound ; but, with a little practice, this is 
 readily accomplished ; and though the unpractised ear may 
 fail, in the first instance, thus to analyze the sound, the 
 clang-tint is influenced in an unmistakable manner by the 
 admixture of resultant tones. I set Dove's siren in rota- 
 tion, and open two series of holes at the same time ; with 
 the utmost strain of attention, I am as yet unable to hear 
 the least symptom of a resultant tone. Urging the in- 
 strument to greater rapidity, a dull, low droning mingles 
 with the two primary sounds. Raising the speed of rota- 
 tion, the low, resultant tone rises rapidly in pitch, and 
 now, to those who stand close to the instrument, it is very 
 audible. The two series of holes here open number 8 
 and 12 respectively. The resultant tone is in this case an 
 octave below the deepest of the two primaries. Opening 
 two other series of orifices, numbering 12 and 16 respec- 
 tively, the resultant tone is quite audible. Its rate of 
 vibration is one-third of the rate of the deepest of the two 
 primaries. In all cases, the resultant tone is that which 
 corresponds to a rate of vibration equal to the difference 
 of the rates of the two primaries. 
 
 The resultant tone here spoken of is that actually 
 heard in the experiment. But with finer methods of 
 experiment other resultant tones are proved to exist. 
 Those on which we have now fixed our attention are, 
 however, the most important. They are called difference- 
 tones by Helmholtz, in consequence of the law just men- 
 tioned. 
 
 To bring these resultant tones audibly forth, the pri- 
 maries must, as already stated, be forcible. When they 
 are feeble the resultants are unheard. I am acquainted 
 with no method of exciting these tones more simple and 
 
EXPERIMENTAL ILLUSTRATIONS. 377 
 
 effectual than a pair of suitable singing-flames. Two such 
 flames may be caused to emit powerful notes self-created, 
 self-sustained, and requiring no muscular effort on the 
 part of the observer to keep them going. Here are two 
 of them. The length of the shorter of the two tubes 
 surrounding these flames is lOf inches, that of the other 
 is 11 '4 inches. I hearken to the sound, and in the midst 
 of the shrillness detect a very deep resultant tone. The 
 reason of its depth is manifest : the two tubes being so 
 nearly alike in length, the difference between their vi- 
 brations is small, and the note corresponding to this dif- 
 ference, therefore, low in pitch. Lengthening one of the 
 tubes by means of its slider, the resultant tone rises 
 gradually, and now it swells surprisingly. When the tube 
 is shortened the resultant tone falls, and thus by alter- 
 nately raising and lowering the slider, the resultant tone 
 is caused to rise and sink in accordance with the law which 
 makes the number of its vibrations the difference between 
 the number of its two primaries. 
 
 We can determine, with ease, the actual number of vi- 
 brations corresponding to any one of those resultant tones. 
 The sound of the flame is that of the open tube which 
 surrounds it, and we have already learned (Chapter III.) 
 that the length of such a tube is half that of the sonorous 
 wave it produces. The wave-length, therefore, correspond- 
 ing to our 10f-inch tube is 20f inches. The velocity of 
 sound in air of the present temperature is 1,120 feet a 
 second. Bringing these feet to inches, and dividing by 
 20f, we find the number of vibrations corresponding to a 
 length of lOf inches to be 648 per second. 
 
 But it must not be forgotten here that the air in 
 which the vibrations are actually executed is much more 
 elastic than the surrounding air. The flame heats the 
 air of the tube, and the vibrations must, therefore, be 
 executed more rapidly than they would be in an ordinary 
 
378 SOUND. 
 
 organ-pipe of the same length. To determine the actual 
 number of vibrations, we must fall back upon our siren ; 
 and with this instrument it is found that the air within 
 the lOf-inch tube executes 717 vibrations in a second. 
 The difference of 69 vibrations a second is due to the 
 heating of the aerial column. Carbonic acid and aqueous 
 vapor are, moreover, the product of the name's combus- 
 tion, and their presence must also affect the rapidity of the 
 vibration. 
 
 Determining in the same way the rate of vibration of 
 the 11-4-inch tube, we find it to be 667 per second ; the 
 difference between this number and 717 is 50, which ex- 
 presses the rate of vibration corresponding to the first deep 
 resultant tone. 
 
 But this number does not mark the limit of audibility. 
 Permitting the 11 -4-inch tube to remain as before, 
 and lengthening its neighbor, the resultant tone sinks 
 near the limit of hearing. When the shorter tube meas 
 ures 11 inches, the deep sound of the resultant tone is still 
 heard. The number of vibrations per second executed 
 in this 11-inch tube is 700. We have already found the 
 number executed in the 11 -4-inch tube to be 667; hence 
 700667=33, which is the number of vibrations corre- 
 sponding to the resultant tone now plainly heard when the 
 attention is converged upon it. We here come very near 
 the limit which Helmholtz has fixed as that of musical 
 audibility. Combining the sound of a tube 17-f inches in 
 length with that of a 1 Of -inch tube, we obtain a resultant 
 tone of higher pitch than any previously heard. Now the 
 actual number of vibrations executed in the longer tube 
 is 459 ; and we have already found the vibrations of our 
 lOfinch tube to be 717; hence 717-459=258, which 
 is the number corresponding to the resultant tone now 
 audible. This note is almost exactly that of one of our 
 
RESULTANT TONES OF HARMONIC INTERVALS. 379 
 
 series of tuning-forks, which vibrates 256 times in a 
 second. 
 
 And now we will avail ourselves of a beautiful check 
 which this result suggests to us. The well-known fork 
 which vibrates at the rate just mentioned is here, mounted 
 on its case, and I touch it with the bow so lightly that the 
 sound alone could hardly be heard ; but it instantly coa- 
 lesces with the resultant tone, and the beats produced by 
 their combination are clearly audible. By loading the 
 fork, and thus altering its pitch, or by drawing up the 
 paper slider, and thus altering the pitch of the flame, the 
 rate of these beats can be altered, exactly as when we 
 compare two primary tones together. By slightly varying 
 the size of the flame, the same effect is produced We 
 cannot fail to observe how beautifully these results har- 
 monize with each other. 
 
 Standing midway between the siren and a shrill sing- 
 ing-flame, and gradually raising the pitch of the siren, the 
 resultant tone soon makes itself heard, sometimes swell- 
 ing out with extraordinary power. "When a pitch-pipe is 
 blown near the flame, the resultant tone is also heard, 
 seeming, in this case, to originate in the ear itself, or 
 rather in the brain. By gradually drawing out the stopper 
 of the pipe, the pitch of the resultant tone is caused to 
 vary in accordance with the law already enunciated. 
 
 The resultant tones produced by the combination of 
 the ordinary harmonic intervals l are given in the following 
 table : 
 
 1 A subject to be dealt with in Chapter IX. 
 
380 
 
 SOUND. 
 
 Interval 
 
 Katio of 
 vibrations. 
 
 Difference. 
 
 The resultant tone is 
 deeper than the lowest 
 primary tone by 
 
 Octave . 
 
 1 : 2 
 
 1 
 
 
 
 Fifth 
 
 2 : 3 
 
 ' 1 
 
 an octave. 
 
 Fourth 
 
 3 :4 
 
 1 
 
 a twelfth. 
 
 Major third 
 
 4: 5 
 
 1 
 
 two octaves. 
 
 Minor third 
 
 5: 6 
 
 1 
 
 two octaves and a 
 
 
 
 
 major third. 
 
 Major sixth 
 
 3 : 5 
 
 2 
 
 a fifth. 
 
 Micor sixth 
 
 5 : 8 
 
 3 
 
 major sixth. 
 
 The celebrated Thomas young thought that these re- 
 sultant tones were due to the coalescence of rapid beats, 
 which linked themselves together like the periodic im- 
 pulses of an ordinary musical note. This explanation 
 harmonized with the fact that the number of the beats, 
 like that of the vibrations of the resultant tone, is equal 
 to the difference between the two sets of vibrations. This 
 explanation, however, is insufficient. The beats tell more 
 forcibly upon the ear than any continuous sound. They 
 can be plainly heard when each of the two sounds that 
 produce them has ceased to be audible. This depends in 
 part upon the sense of hearing, but it also depends upon 
 the fact that when two notes of the same intensity pro- 
 duce beats, the amplitude of the vibrating air-particles 
 is at times destroyed, and at times doubled. But by 
 doubling the amplitude we quadruple the intensity of the 
 sound. Hence, when two notes of the same intensity pro- 
 duce beats, the sound incessantly varies between silence and 
 a tone of four times the intensity of either of the interfer- 
 ing ones. 
 
 If, therefore, the resultant tones were due to the beats 
 of their primaries, they ought to be heard, even when the 
 primaries are feeble. But they are not heard under these 
 circumstances. When several sounds traverse the same 
 air, each particular sound passes through the air as if it 
 
THEORIES OF YOUNG AND HELMHOLTZ. 381 
 
 alone were present, each particular element of a composite 
 sound asserting its own individuality. Now, this is in 
 strictness true only when the amplitudes of the oscillating 
 particles are infinitely small. Guided by pure reasoning, 
 the mathematician arrives at this result. The law is also 
 practically true when the disturbances are extremely 
 small ; but it is not true after they have passed a certain 
 limit. Yibrations which produce a large amount of dis- 
 turbance give birth to secondary waves, which appeal to 
 the ear as resultant tones. This has been proved by Helm- 
 holtz, and, having proved this, he inferred further that 
 there are also resultant tones formed by the sum of the 
 primaries, as well as by their difference. He thus discov- 
 ered the summation-tones before he had heard them ; and 
 bringing his result to the test of experiment, he found 
 that these tones had a real physical existence. They are 
 not at all to be explained by Young's theory. 
 
 Another consequence of this departure from the law of 
 superposition is, that a single sounding body, which dis- 
 turbs the air beyond the limits of the law of superposition, 
 also produces secondary waves, which correspond to the 
 harmonic tones of the vibrating body. For example, the 
 rate of vibration of the first overtone of a tuning-fork, 
 as stated in the fourth chapter, is 6J times the rate of the 
 fundamental tone. But Helmholtz shows that a tuning- 
 fork, not excited by a bow, but vigorously struck against a 
 pad, emits the octave of its fundamental note, this octave 
 being due to the secondary waves set up when the limits of 
 the law of superposition have been exceeded. 
 
 These considerations make it probably evident to you 
 that a coalescence of musical sounds is a far more com- 
 plicated dynamical condition than you have hitherto sup- 
 posed it to be. In the music of an orchestra, not only 
 have we the fundamental tones of every pipe and of every 
 string, but we have the overtones of each, sometimes 
 
382 SOUND. 
 
 audible as far as the sixteenth in the series. "We have 
 also resultant tones ; both difference-tones and summation- 
 tones ; all trembling through the same air, all knocking 
 at the self-same tympanic membrane. We have funda- 
 mental tone interfering with fundamental tone ; overtone 
 with overtone; resultant tone with resultant tone. And, 
 besides this, we have the members of each class interfering 
 with the members of every other class. The imagination 
 retires baffled from any attempt to realize the physical 
 condition of the atmosphere through which these sounds 
 are passing. And, as we shall immediately learn, the 
 aim of music, through the centuries during which it has 
 ministered to the pleasure of man, has been to arrange 
 matters empirically, so that the ear shall not suffer from 
 the discordance produced by this multitudinous interfer- 
 ence. The musicians engaged in this work knew nothing 
 of the physical facts and principles involved in their ef- 
 forts ; they knew no more about it than the inventors of 
 gunpowder knew about the law of atomic proportions. 
 They tried and tried till they obtained a satisfactory result ; 
 and now, when the scientific mind is brought to bear upon 
 the subject, order is seen rising through the confusion, 
 and the results of pure empiricism are found to be in har- 
 mony with natural law. 
 
SUMMARY, 383 
 
 SUMMARY OF CHAPTEK VIII. 
 
 several . systems of waves proceeding from dis- 
 tinct centres of disturbance pass through water or air, the 
 motion of every particle is the algebraic sum of the several 
 motions impressed upon it. 
 
 In the case of water, when the crests of one system of 
 waves coincide with the crests of another system, higher 
 waves will be the result of the coalescence of the two sys- 
 tems. But when the crests of one system coincide with 
 the sinuses, or furrows, of the other system, the two sys- 
 tems, in whole or in part, destroy each other. 
 
 This coalescence and destruction of two systems of 
 waves is called interference. 
 
 Similar remarks apply to sonorous waves. If in two 
 systems of sonorous waves condensation coincides with 
 condensation, and rarefaction with rarefaction, the sound 
 produced by such coincidence is louder than that produced 
 by either system taken singly. But if the condensations 
 of the one system coincide with the rarefactions of the 
 other, a destruction, total or partial, of both systems is the 
 consequence. 
 
 Thus, when two organ-pipes of the same pitch are 
 placed near each other on the same wind-chest and thrown 
 into vibration, they so influence each other, that as the air 
 enters the embouchure of the one it quits that of the other. 
 At the moment, therefore, the one pipe produces a con- 
 densation the other produces a rarefaction. The sounds of 
 two such pipes mutually destroy each other. 
 
 When two musical sounds of nearly the same pitch 
 are sounded together the flow of the sound is disturbed by 
 beats. 
 
 These beats are due to the alternate coincidence and 
 17 
 
384 SOUND. 
 
 interference of the two systems of sonorous waves. If the 
 two sounds be of the same intensity, their coincidence pro- 
 duces a sound of four times the intensity of either ; while 
 their opposition produces absolute silence. 
 
 The effect, then, of two such sounds, in combination, is 
 a series of shocks, which we have called " beats," separated 
 from each other by a series of " pauses." 
 
 The rate at which the beats succeed each other is equal 
 to the difference between the two rates of vibration. 
 
 When a bell or disk sounds, the vibrations on opposite 
 sides of the same nodal line partially neutralize each 
 other; when a tuning-fork sounds, the vibrations of its 
 two prongs in part neutralize each other. By cutting off 
 a portion of the vibrations in these cases the sound may 
 be intensified. 
 
 When a luminous beam, reflected on to a screen from 
 two tuning-forks producing beats, is acted upon by the vi- 
 brations of both, the intermittence of the sound is an- 
 nounced by the alternate lengthening and shortening of 
 the band of light upon the screen. 
 
 The law of the superposition of vibrations above enun- 
 ciated is strictly true only when the amplitudes are exceed- 
 ingly small. When the disturbance of the air by a sound- 
 ing body is so violent that the law no longer holds good, 
 secondary waves are formed, which correspond to the har 
 monic tones of the sounding body. 
 
 When two tones are rendered so intense as to exceed 
 the limits of the law of superposition, their secondary waves 
 combine to produce resultant tones. 
 
 Resultant tones are of two kinds ; the one class corre- 
 sponding to rates of vibration equal to the difference of 
 the rates of the two primaries ; the other class correspond- 
 ing to rates of vibration equal to the sum of the two pri 
 maries. The former are called difference-tones, the latter 
 .9 umination-tones. 
 
385 
 
 CHAPTEK IX. 
 
 Combination of Musical Sounds. The smaller the Two Numbers which ex- 
 press the Ratio of their Rates of Vibration, the more perfect is the 
 Harmony of Two Sounds. Notions of the Pythagoreans regarding Musi- 
 cal Consonance. Euler's Theory of Consonance. Theory of Helm- 
 holtz. Dissonance due to Beats. Interference of Primary Tones and 
 of Overtones. Mechanism of Hearing. Shultze's Bristles. The Oto- 
 liths. Corti's Fibres. Graphic Representation of Consonance and 
 Dissonance. Musical Chords. The Diatonic Scale. Optical Illustra- 
 tion of Musical Intervals. Lissajous's Figures. Sympathetic Vibra- 
 tions. Various Modes of illustrating the Composition of Vibrations. 
 
 1. The Facts of Musical Consonance. 
 
 THE subject of this day's lecture has two sides, a physi- 
 cal and an aesthetical. We have to-day to study the ques- 
 tion of musical consonance to examine musical sounds in 
 definite combination with each other, and to unfold the 
 reason why some combinations are pleasant and others un- 
 pleasant to the ear. 
 
 Pythagoras made the first step toward the physical ex- 
 planation of the musical intervals. This great philosopher 
 stretched a string, and then divided it into three equal 
 parts. At one of its points of division he fixed it firmly, 
 thus converting it into two, one of which was twice the 
 length of the other. He sounded the two sections of 
 the string simultaneously, and found the note emitted 
 by the short section to be the higher octave of that emitted 
 by the long one. He then divided his string into two 
 parts, bearing to each other the proportion of 2:3, and 
 found that the notes were separated by an interval of a 
 fifth. Thus, dividing his string at different points, Py- 
 
386 SOUND. 
 
 thagoras found the so-called consonant intervals in music 
 to correspond with certain lengths of his string ; and he 
 made the extremely important discovery that the simpler 
 the ratio of the two parts into which the string was di- 
 vided, the more perfect was the harmony of the two 
 sounds. Pythagoras went no further than this, and it 
 remained for the investigators of a subsequent age to 
 show that the strings act in this way in virtue of the 
 relation of their lengths to the number of their vibra- 
 tions. Why simplicity should give pleasure remained 
 long an enigma, the only pretence of a solution being 
 that of Euler, which, briefly expressed, is, that the human 
 soul takes a constitutional delight in simple calculations. 
 
 The double siren (Fig. 163) enables us to obtain a great 
 variety of combinations of musical sounds. And this in- 
 strument possesses over all others the advantange that, by 
 simply counting the number of orifices corresponding re- 
 spectively to any two notes, we obtain immediately the 
 ratio of their rates of vibration. Before proceeding to 
 these combinations I will enter a little more fully into the 
 action of the double siren than has been hitherto deemed 
 necessary or desirable. 
 
 The instrument, as already stated, consists of two of 
 Dove's sirens, o' and c, connected by a common *axis, the 
 upper one being turned upside down. Each siren is 
 provided with four series of apertures, numbering as 
 follows : 
 
 Upper siren. Lower siren. 
 
 Number of apertures. Number of apertures. 
 1st Series 16 18 
 
 2d Series .... 15 12 
 
 3d Series .... 12 10 
 
 4th Series ... 9 8 
 
 The number 12, it will be observed, is common to both 
 sirens. I open the two series of 12 orifices each, and 
 urge air through the instrument ; both sounds flow to- 
 
THE DOUBLE SIREN. 
 
 Fro. 163. 
 
 387 
 
388 SOUND. 
 
 gether in perfect unison ; the unison being maintained, 
 however the pitch may be exalted. We have, however, 
 already learned (Chapter II.) that by turning the handle 
 of the upper siren the orifices in its wind-chest c' are 
 caused either to meet those of its rotating disk, or to re- 
 treat from them, the pitch of the upper siren being 
 thereby raised or lowered. This change of pitch instantly 
 announces itself by beats. The more rapidly the handle 
 is turned, the more is the tone of the upper siren raised 
 above or depressed below that of the lower one, and, as a 
 consequence, the more rapid are the beats. 
 
 Now the rotation of the handle is so related to the 
 rotation of the wind-chest </ that when the handle turns 
 through half a right angle the wind-chest turns through 
 J-th.of,. a right angle, or through the ^th of its whole cir- 
 cumference. But in the case now before us, where the 
 circle is perforated by 12 orifices, the rotation through 
 ^ th of its circumference causes the apertures of the 
 upper wind-chest to be closed at the precise moments 
 when those of the lower one are opened, and vice versa. 
 It is plain, therefore, that the intervals between the puffs 
 of the lower siren, which correspond to the rarefactions of 
 its sonorous waves, are here filled by the puffs, or con- 
 densations, of the upper siren. In fact, the condensations 
 of the one coincide with the rarefactions of the other, and 
 the absolute extinction of the sounds of both sirens is the 
 consequence. 
 
 I may seem to you to have exceeded the truth here ; for 
 when the handle is placed in the position which corresponds 
 to absolute extinction, you still hear a distinct sound. And, 
 when the handle is turned continuously, though alternate 
 swellings and sinkings of the tone occur, the sinkings by 
 no means amount to absolute silence. The reason is this : 
 The sound of the siren is a highly composite one. By 
 the suddenness and violence of its shocks, not only does it 
 
INTERFERENCE AND BEATS OF THE DOUBLE SIREN. 389 
 
 produce waves corresponding to the' number of its orifices, 
 but the aerial disturbance breaks up into secondary waves, 
 which associate themselves with the primary waves of the 
 instrument, exactly as the harmonics of a string, or of an 
 open organ-pipe, mix with their fundamental tone. When 
 the siren sounds, therefore, it emits, besides the funda- 
 mental tone, its octave, its twelfth, its double octave, and 
 so on. That is to say, it breaks the air up into vibrations 
 which have twice, three times, four times, etc., the ra- 
 pidity of the fundamental one. Now, by turning the 
 upper siren through ^th of its circumference, we extin- 
 guish utterly the fundamental tone. But we do not ex- 
 tinguish its octave. 1 Hence, when the handle is in the 
 position which corresponds to the extinction of the funda- 
 jnental tone, instead of silence, we have the full first har- 
 monic of the instrument. 
 
 Helmholtz has surrounded both his upper and his lower 
 siren with circular brass boxes, B, B', each composed of 
 two halves, which can be readily separated (one half of 
 each box is removed in the figure). These boxes exalt 
 by their resonance the fundamental tone of the instru- 
 ment, and enable us to follow its variations much more 
 easily than if it were not thus reenforced. It requires a 
 certain rapidity of rotation to reach the maximum reso- 
 nance of the brass boxes ; but when this speed is attained, 
 the fundamental tone swells out with greatly augmented 
 force, and, if the handle be then turned, the beats succeed 
 each other with extraordinary power. 
 
 Still, as already stated, the pauses between the beats 
 of the fundamental tone are not intervals of absolute 
 silence, but are filled by the higher octave; and this 
 renders caution necessary when the instrument is em- 
 ployed to determine rates of vibration. It is not without 
 
 1 Nor indeed any of those tones whose rates of vibration are even multi 
 pies of the rate of the fundamental. 
 
390 SOUND. 
 
 reason that I say so. Wishing to determine the rate of 
 vibration of a small singing-flame, I once placed a siren 
 at some distance from it, sounded the instrument, and 
 after a little time observed the flame dancing in syn- 
 chronism with audible beats. I took it for granted that 
 unison was nearly attained, and, under this assumption, 
 determined the rate of vibration. The number obtained 
 was surprisingly low indeed not more than half what 
 it ought to be. "What was the reason ? Simply this : 
 I was dealing, not with the fundamental tone of the 
 siren, but with its higher octave. This octave and the 
 flame produced beats by their coalescence ; and hence the 
 counter of the instrument, which recorded the rate, not of 
 the octave, but of the fundamental, gave a number which 
 was only half the true one. The fundamental tone was 
 afterward raised to unison with the flame. On approach- 
 ing unison beats were again heard, and the jumping of 
 the flame proceeded with an energy greater than that 
 observed in the case of the octave. The counter of the in- 
 strument then recorded the accurate rate of the flame's 
 vibration. 
 
 The tones first heard in the case of the siren are al- 
 ways overtones. These attain sonorous continuity sooner 
 than the fundamental, flowing as smooth musical sounds 
 while the fundamental tone is still in a state of intermit- 
 tence. The siren is, however, so delicately constructed 
 that a rate of rotation which raises the fundamental tone 
 above its fellows is almost immediately attained. And 
 if we seek, by making the blast feeble, to keep the speed 
 of rotation low, it is at the expense of intensity. Hence 
 the desirability, if we wish to examine the overtones, of 
 devising some means by which a strong blast and slow 
 rotation shall be possible. 
 
 Helmholtz caused a spring to press as a light brake 
 against the disk of the siren. Thus raising by slow de- 
 
BEATS OF OVERTONES OF SIREN. 391 
 
 greets the speed of rotation, he was able deliberately to 
 notice the predominance of the overtones at the commence- 
 ment, and the final triumph of the fundamental tone. He 
 did not trust to the direct observation of pitch, but deter- 
 mined the tone by the number of beats corresponding to 
 one revolution of the handle of the upper siren. Suppos- 
 ing 12 orifices to be opened above and 12 below, the mo- 
 tion of the handle through 45 produces interference, and 
 extinguishes the fundamental tone. The coincidences of 
 that tone occur at the end of every rotation of 90. Hence, 
 for the fundamental tone, there must be four beats for 
 every complete rotation of the handle. Now Helmholtz, 
 when he made the arrangement just described, found that 
 the first beats numbered, not 4, but 12, for every revolu- 
 tion. They were, in fact, the beats, not of the funda- 
 mental tone, not even of the first overtone, but of the 
 second overtone, whose rate of vibration is three times 
 that of the fundamental. These beats continued as long 
 as the number of air-shocks did not exceed 30 or 40 per 
 second. "When the shocks were between 40 and 80 per 
 second, the beats fell from 12 to 8 for every revolution of 
 the handle. Within this interval the first overtone, or 
 the octave of the fundamental tone, was the most power- 
 ful, and made the beats its own. Not until the impulses 
 exceeded 80 per second did the beats sink to 4 per revo- 
 lution. In other words, not until the speed of rotation 
 had passed this limit was the fundamental tone able to 
 assert its superiority over its companions. 
 
 This premised, we will combine the tones in defi- 
 nite order, while the cultivated ears here present shall 
 judge of their musical relationship. The flow of perfect 
 unison when the two series of 12 orifices each are opened 
 has been already heard. I now open a series of 8 holes 
 in the upper, and of 16 in the lower siren. The interval 
 you judge at once to be an octave. If a series of 9 holes 
 
392 SOUND. 
 
 in the upper and of 18 holes in the lower siren be opened, 
 the interval is still an octave. This proves that the inter- 
 val is not disturbed by altering the absolute rates of vi- 
 bration, so long as the ratio of the two rates remains the 
 same. The same truth is more strikingly illustrated by 
 commencing with a low speed of rotation, and urging the 
 siren to its highest pitch ; as long as the orifices are in the 
 ratio of 1 : 2, we retain the constant interval of an octave. 
 Opening a series of 10 holes in the upper, and of 15 in the 
 lower siren, the ratio is as 2 : 3, and every musician present 
 knows that this is the interval of a fifth. Opening 12 
 holes in the upper, and 18 in the lower siren, does not 
 change the interval. Opening two series of 9 and 12, or 
 of 12 and 16, we obtain an interval of a fourth ; the ratio 
 in both these cases being as 3 : 4. In like manner two 
 series of 8 and 10, or of 12 and 15, give us the interval of a 
 major third ; the ratio in this case being as 4 : 5. Finally, 
 two series of 10 and 12, or of 15 and 18, yield the inter- 
 val of a minor third, which corresponds to the ratio 5 : 6. 
 
 These experiments amply illustrate two things : First- 
 ly, that a musical interval is determined, not by the ab- 
 solute number of vibrations of the two combining notes, 
 but by the ratio of their vibrations. Secondly, and this 
 is of the utmost significance, that the smaller the two 
 numbers which express the ratio of the two rates of 
 vibration, the more perfect is the consonance of the 
 two sounds. The most perfect consonance is the unison 
 1:1; next comes the octave 1:2; after that the fifth 
 2:3; then the fourth 3:4; then the major third 4:5; 
 and finally the minor third 5 : 6. We can also open 
 two series numbering, respectively, 8 and 9 orifices : this 
 interval corresponds to a tone in music. It is a disso- 
 nant combination. Two series which number respectively 
 15 and 16 orifices make the interval of a semi-tone: it is 
 a very sharp and grating dissonance. 
 
EULEK'S THEORY OF CONSONANCE. 393 
 
 2. The Theory of Musical Consonance. Pythagoras 
 and Eider. 
 
 Whence, then, does this arise? Why should the 
 smaller ratio express the more perfect consonance ? The 
 ancients attempted to solve this question. The Pythago- 
 reans found intellectual repose in the answer " All is num- 
 ber and harmony." The numerical relations of the seven 
 notes of the musical scale were also thought by them to 
 express the distances of the planets from their central fire ; 
 hence the choral dance of the worlds, the " music of the 
 spheres," which, according to his followers, Pythagoras 
 alone was privileged to hear. And might we not in pass- 
 ing contrast this glorious superstition with the groveling 
 delusion which has taken hold of the fantasy of our day ? 
 Were the character which superstition assumes in different 
 ages an indication of man's advance or retrogression, as- 
 suredly the nineteenth century would have no reason to 
 plume itself, in comparison with the sixth, B. c. A more 
 earnest attempt to account for the more perfect conso- 
 nance of the smaller ratios was made by the celebrated 
 mathematician, Euler, and his explanation, if such it 
 could be called, long silenced, if it did not satisfy, in- 
 quirers. Euler analyzes the cause of pleasure. We take 
 delight in order ; it is pleasant to us to observe means 
 " cooperant to an end." But then, the effort to discern 
 order must not be so great as to weary us. If the rela- 
 tions to be disentangled are too complicated, though we 
 may see the order, we cannot enjoy it. The simpler the 
 terms in which the order expresses itself, the greater is 
 our delight. Hence the superiority of the simpler ratios 
 in music over the more complex ones. Consonance, then, 
 according to Euler, was the satisfaction derived from the 
 perception of order without weariness of mind. 
 
 But in this theory it was overlooked that Pythagoras 
 
394 SOUND. 
 
 himself, who first experimented on the musical intervals, 
 knew nothing about rates of vibration. It was forgotten 
 that the vast majority of those who take delight in music, 
 and who have the sharpest ears for the detection of a dis- 
 sonance, are in the condition of Pythagoras, knowing 
 nothing whatever about rates or ratios. And it may also 
 be added that the scientific man, who is fully informed 
 upon these points, has his pleasure in no way enhanced 
 by his knowledge. Euler's explanation, therefore, does 
 not satisfy the mind, and it was reserved for an eminent 
 German investigator of our own day, after a profound 
 analysis of the entire question, to assign the physical 
 cause of consonance and dissonance a cause which, when 
 once clearly stated, is so simple and satisfactory as to 
 excite surprise that it remained so long without a dis- 
 coverer. 
 
 Yarious expressions employed in our previous lectures 
 have already, in part, forestalled Helmholtz's explanation 
 of consonance and dissonance. Let me here repeat an 
 experiment which will, almost of itself, force this ex- 
 planation upon your attention. Before you are two jets 
 of burning gas, which can be converted into singing- 
 flames by inclosing them within two tubes (represented 
 in Fig. 117). The tubes are of the same length, and the 
 flames are now singing in unison. By means of a tele- 
 scopic slider I lengthen slightly one of the tubes; you 
 hear deliberate beats, which succeed each other so slowly 
 that they can readily be counted. I augment still further 
 the length of the tube. The beats are now more rapid 
 than before : they can barely be counted. It is perfectly 
 manifest that the shocks of which you are now sensible 
 differ only in point of rapidity from the slow beats which 
 you heard a moment ago. There is no breach of con- 
 tinuity here. "We begin slowly, we gradually increase the 
 rapidity, until finally the succession of the beats is so 
 
BEATS A POSSIBLE CAUSE OF DISSONANCE. 395 
 
 rapid as to produce that particular grating effect which 
 every musician that hears it would call dissonance. Let 
 us now reverse the process, and pass from these quick 
 beats to slow ones. The same continuity of the phe- 
 nomenon is noticed. By degrees the beats separate from 
 each other more and more, until finally they are slow 
 enough to be counted. Thus these singing-flames enable 
 us to follow the beats with certainty, until they cease to 
 be beats, and are converted into dissonance. 
 
 This experiment proves conclusively that dissonance 
 may be produced by a rapid succession of beats ; and I 
 imagine this cause of dissonance would have been pointed 
 out earlier, had not men's minds been thrown off the prop- 
 er track by the theory of " resultant tones " enunciated by 
 Thomas Young. Young imagined that, when they were 
 quick enough, the beats ran together to form a resultant 
 tone. He imagined the linking together of the beats to 
 be precisely analogous to the linking together of simple 
 musical impulses ; and he was strengthened in this notion 
 by the fact already adverted to, that the first difference- 
 tone, that is to say, the loudest resultant tone, corresponded, 
 as the beats do, to a rate of vibration equal to the differ- 
 ence of the rates of the two primaries. The fact, how- 
 ever, is, that the effect of beats upon the ear is altogether 
 different from that of the successive impulses of an ordi- 
 nary musical tone. 
 
 3. Sympathetic Vibrations. 
 
 But to grasp, in all its fullness, the new theory of musi- 
 cal consonance some preliminary studies will be necessary. 
 And here I would ask you to call to mind the experi- 
 ments (in Chapter III.) by which the division of a string 
 into its harmonic segments was illustrated. This was 
 done by means of little paper riders, which were un- 
 
396 SOUND. 
 
 horsed, or not, according as they occupied a ventral seg- 
 ment or a node upon the string. Before you at present 
 is the sonometer, employed in the experiments just re- 
 ferred to. Along it, instead of one, are stretched two 
 strings, about three inches asunder. By means of a key 
 these strings are brought into unison. And now I place 
 a little paper rider upon the middle of one of them, and 
 agitate the other. What occurs ? The vibrations of the 
 sounding string are communicated to the bridges on 
 which it rests, and through the bridges to the other 
 string. The individual impulses are very feeble, but, 
 because the two strings are in unison, the impulses can 
 so accumulate as finally to toss the rider off the untouched 
 string. 
 
 Every experiment executed with the riders and a sin- 
 gle string may be repeated with these two unisonant 
 strings. Damping, for instance, one of the strings, at a 
 point one-fourth of its length from one of its ends, and 
 placing the red and blue riders formerly employed, not on 
 the nodes and ventral segments of the damped string, 
 but at points upon the second string exactly opposite to 
 those nodes and segments, when the bow is passed across 
 the shorter segment of the damped string, the five red 
 riders on the adjacent string are unhorsed, while the four 
 blue ones remain tranquilly in their places. By relaxing 
 one of the strings, it is thrown out of unison with the 
 other, and then all efforts to unhorse the riders are un- 
 availing. That accumulation of impulses, which unison 
 alone renders possible, cannot here take place, and the 
 consequence is, that however great the agitation of the 
 one string may be, it fails to produce any sensible effect 
 upon the other. 
 
 The influence of synchronism may be illustrated in a 
 still more striking manner, by means of two tuning-forks 
 which sound the same note. Two such forks mounted on 
 
SYMPATHETIC VIBRATIONS. 397 
 
 their resonant supports are placed upon the table. I draw 
 the bow vigorously across one of them, permitting the 
 other fork to remain untouched. On stopping the agi- 
 tated fork, the sound is enfeebled, but by no means 
 quenched. Through the air and through the wood the 
 vibrations have been conveyed from fork to fork, and the 
 untouched fork is the one you now hear. When, by means 
 of a morsel of wax, a small coin is attached to one of the 
 forks, its power of influencing the other ceases ; the change 
 in the rate of vibration, if not very small, so destroys the 
 sympathy between the two forks as to render a response 
 impossible. On removing the coin the untouched fork 
 responds as before. 
 
 This communication of vibrations through wood and 
 air may be obtained when the forks, mounted on their 
 cases, stand several feet apart. But the vibrations may 
 also be communicated through the air alone. Holding the 
 resonant case of a vigorously vibrating fork in my hand, I 
 bring one of its prongs near an unvibrating one, placing 
 the prongs back to back, but allowing a space of air to 
 exist between them. Light as is the vehicle, the accu- 
 mulation of impulses, secured by the perfect unison of 
 the two forks, enables the one to set the other in vibra- 
 tion. Extinguishing the sound of the agitated fork, that 
 which a moment ago was silent continues sounding, 
 having taken up the vibrations of its neighbor. Re- 
 moving one of the forks from its resonant case, and 
 striking it against a pad, it is thrown into strong vibra- 
 tion. Held free in the air, its sound is audible. But, 
 on bringing it close to the silent mounted fork, out of 
 the silence rises a full mellow sound, which is due, not 
 to the fork originally agitated, but to its sympathetic 
 neighbor. 
 
 Various other examples of the influence of synchro- 
 nism, already brought forward, will occur to you here ; and 
 
398 SOUND. 
 
 cases of the kind might be indefinitely multiplied. If 
 two clocks, for example, with pendulums of the same 
 period of vibration, be placed against the same wall, and 
 if one of the clocks is set going and the other not, the 
 ticks of the moving clock, transmitted through the wall, 
 will act upon its neighbor. The quiescent pendulum, 
 moved by a single tick, swings through an extremely mi- 
 nute arc ; but it returns to the limit of its swing just in 
 time to receive another impulse. By the continuance of 
 this process, the impulses so add themselves together as 
 finally to set the clock a-going. It is by this timing of 
 impulses that a properly-pitched voice can cause a glass 
 to ring, and that the sound of an organ can break a partic- 
 ular window-pane. 
 
 4. Sympathetic Vibration in Relation to the Human 
 
 Ear. 
 
 If I dwell so fully upon this subject, it is for the pur- 
 .pose of rendering intelligible the manner in which sono- 
 rous motion is communicated to the auditory nerve. In 
 the organ of hearing, in man, we have first of all the 
 external orifice of the ear, closed at the bottom by the 
 circular tympanic membrane. Behind that membrane is 
 the drum of the ear, this cavity being separated from the 
 space between it and the brain by a bony partition, in 
 which there are two orifices, the one round and the other 
 oval. These orifices are also closed by fine membranes. 
 Across the drum stretches a series of four little bones. 
 The first, called the hammer, is attached to the tympanic 
 membrane ; the second, called the anvil, is connected by 
 a joint with the hammer ; a third little round bone con- 
 nects the anvil with the stirrup-bone, the base of which 
 is planted against the membrane of the oval orifice just 
 referred to. This oval membrane is almost covered by 
 
ACOUSTIC ARRANGEMENTS WITHIN THE EAR. 399 
 
 the stirrup-bone, a narrow rim only of the membrane 
 surrounding the bone being left uncovered. Behind the 
 bony partition, and between it and the brain, we have the 
 extraordinary organ called the labyrinth, filled with water, 
 over the lining membrane of which are distributed the 
 terminal fibres of the auditory nerve. When the tympanic 
 membrane receives a shock, it is transmitted through the 
 series of bones above referred to, being concentrated 
 on the membrane against which the base of the stirrup- 
 bone is fixed. The membrane transfers the shock to the 
 water of the labyrinth, which, in its turn, transfers it to 
 the nerves. 
 
 The transmission, however, is not direct. At a cer- 
 tain place within the labyrinth exceedingly fine elastic 
 bristles, terminating in sharp points, grow up between 
 the terminal nerve-fibres. These bristles, discovered by 
 Max Scnultze, are eminently calculated to sympathize 
 with such vibrations of the water as correspond to their 
 proper periods. Thrown thus into vibration, the bristles 
 stir the nerve-fibres which lie between their roots. At 
 another place in the labyrinth we have little crystalline 
 particles called otolites the Horsteine of the Germans 
 imbedded among the nervous filaments, which, when 
 they vibrate, exert an intermittent pressure upon the ad- 
 jacent nerve-fibres. The otolites probably serve a dif- 
 ferent purpose from that of the bristles of Schultze. 
 "They are fitted, by their weight, to accept and prolong 
 the vibrations of evanescent sounds, which might other- 
 wise escape attention, while the bristles of Scnultze, be- 
 cause of their extreme lightness, would instantly yield up 
 an evanescent motion. They are, on the other hand, emi- 
 nently fitted for the transmission of continuous vibrations. 
 
 Finally, there is in the labyrinth an organ, discovered 
 by the Marchese Corti, which is to all appearance a musi- 
 cal instrument, with its chords so stretched as to accept 
 
iOO SOUND. 
 
 vibrations of different periods, and transmit them to the 
 nerve-filaments which traverse the organ. Within the 
 ears of men, and without their knowledge or contrivance, 
 this lute of 3,000 strings x has 'existed for ages, accepting 
 the music of the outer world and rendering it fit for re- 
 ception by the brain. Each musical tremor which falls 
 upon this organ selects from the stretched fibres the one 
 appropriate to its own pitch, and throws it into unisonant 
 vibration. And thus, no matter how complicated the mo- 
 tion of the external air may be, these microscopic strings 
 can analyze it and reveal the constituents of which it is com- 
 posed. Surely, inability to feel the stupendous wonder of 
 what is here revealed would imply incompleteness of 
 mind; and surely those who practically ignore, or fear 
 them, must be ignorant of the ennobling influence which 
 such discoveries may be made to exercise upon both the 
 emotions and the understanding of man. 
 
 5. Consonant Intervals in Relation to the Human Ear. 
 
 This view of the use of Corti's fibres is theoretical; 
 but it comes to us commended by every appearance of 
 truth. It will enable us to tie together many things, 
 whose relations it would be otherwise difficult to discern. 
 When a musical note is sounded its corresponding Corti's 
 fibre resounds, being moved, as a string is moved by a 
 second unisonant string. And when two sounds coalesce 
 to produce beats, the intermittent motion is transferred 
 to the proper fibre within the ear. But here it is to be 
 noted that, for the same fibre to be affected simultaneously 
 by two different sounds, it must not be far removed in 
 pitch from either of them. Call to mind our repetition 
 of Melde's experiments (in Chapter III). You then had 
 frequent occasion to notice that even, before perfect syn- 
 chronism had been established between the string and the 
 
 1 According to Kolliker, this is the number of fibres in Corti's organ. 
 
RELATION OF BEATS TO CORTI'S ORGAN. 401 
 
 tuning-fork to which it was attached, the string began to 
 respond to the fork. But you also noticed how rapidly 
 the vibrating amplitude of the string increased, as it came 
 close to perfect synchronism with the vibrating fork. On 
 approaching unison the string would open out, say to 
 an amplitude of an inch ; and then a slight tightening or 
 slackening, as the case might be, would bring it up to uni- 
 son, and cause it to open out suddenly to an amplitude of 
 six inches. 
 
 So also in reference to the experiment made a moment 
 ago with the sonometer ; you noticed that the unhorsing 
 of the paper riders was preceded by a fluttering of the 
 bits of paper ; showing that the sympathetic response of 
 the second string had begun, though feebly, prior to per- 
 fect synchronism. Instead of two strings, conceive three 
 strings, all nearly of the same pitch, to be stretched upon 
 the sonometer ; and suppose the vibrating period of the 
 middle string to lie midway between the periods of its 
 two neighbors, being a little higher than the one and a 
 little lower than the other. Each of the side strings, 
 sounded singly, would cause the middle string to respond. 
 Sounding the two side strings together they would pro- 
 duce beats ; the corresponding intermittence would be prop- 
 agated to the central string, which would beat in syn- 
 chronism with the beats of its neighbors. In this way 
 we make plain to our minds how a Corti's fibre may, to 
 some extent, take up the vibrations of a note, nearly, but 
 not exactly, in unison with its own ; and that when two 
 notes close to the pitch of the fibre act upon it together, 
 their beats are responded to by an intermittent motion 
 on the part of the fibre. This power of sympathetic 
 vibration would fall rapidly on both sides of the perfect 
 unison, so that on increasing the interval between the two 
 notes, a time would soon arrive when the same fibre would 
 refuse to be acted on simultaneously by both. Here the 
 
02 SOUND. 
 
 condition of the organ, necessary for the perception of 
 audible beats, would cease. 
 
 In the middle region of the piano-forte, with the in- 
 terval of a semitone, the beats are sharp and distinct, fall- 
 ing indeed upon the ear as a grating dissonance. Extend- 
 ing the interval to a whole tone, the beats become more 
 rapid, but less distinct. With the interval of a minor 
 third between the two notes, the beats in the middle region 
 of the scale cease to be sensible. But this smoothening 
 of the sound is not wholly due to the augmented rapidity 
 of the beats. It is due in part to the fact, for which the 
 foregoing considerations have prepared us, that the two 
 notes here sounded are too far removed from that of the 
 intermediate Corti's fibre to affect it powerfully. By 
 ascending to the higher regions of the scale we can pro- 
 duce, with a narrower interval than the minor third, the 
 same, or even a greater number of beats, which are sharply 
 distinguishable because of the closeness of their component 
 notes. In the very highest regions of the scale, however, 
 the beats, when they become very rapid, cease to appeal as 
 roughness to the ear. 
 
 Hence both the rapidity of the beats, and the width of 
 the interval, enter into the question of consonance. Helm- 
 holtz judges that in the middle and higher regions of the 
 musical scale, when the beats reach 33 per second, the dis- 
 sonance reaches its maximum. Both slower and quicker 
 beats have a less grating or dissonant effect. When the 
 beats are very slow, they may be of advantage to the mu- 
 sic ; and, when they reach 132 per second, their roughness 
 is no longer discernible. 
 
 Thanks to Helmholtz, whose views I have here sought 
 to express in the briefest possible language, we are now in 
 a condition to grapple with the question of musical inter- 
 vals, and to give the reason why some are consonant and 
 some dissonant to the ear. Circumstanced as we are upon 
 
RELATION OF CONSONANCE TO OVERTONES. 403 
 
 earth, all our feelings and emotions, from the lowest sensa- 
 tion to the highest sesthetic consciousness, have a me- 
 chanical cause : though it may be forever denied to us to 
 take the step from cause to effect ; or to understand why 
 the agitations of nervous matter can awaken the delights 
 which music imparts. Take, then, the case of a violin. 
 The fundamental tone of every string of this instrument 
 is demonstrably accompanied by a crowd of overtones ; so 
 that, when, two violins are sounded, we have not only to 
 take into account the consonance, or dissonance, of the 
 fundamental tones, but also those of the higher tones of 
 both. Supposing two strings sounded whose fundamental 
 tones, and all of whose partial tones, coincide, we have then 
 absolute unison; and this we actually have when the 
 ratio of vibration is 1:1. So also when the ratio of 
 vibration is accurately 1 : 2, each overtone of the funda- 
 mental finds itself in absolute coincidence with either 
 the fundamental tone or some higher tone of the octave. 
 There is no room for beats or dissonance. When we ex- 
 amine the interval of a fifth, with a ratio of 2 : 3, we find 
 the coincidence of the partial tones of the two strings 
 so perfect as almost, though not wholly, to exclude every 
 trace of dissonance. Passing on to the other intervals, we 
 find the coincidence of the partial tones less perfect, as 
 the numbers expressing the ratio of the vibrations become 
 more large. Thus, the dissonance of intervals whose rates 
 of vibration can only be expressed by large numbers, is 
 not to be ascribed to any mystic quality of the numbers 
 themselves, but to the fact that the fundamental tones 
 which require such numbers are inexorably accompanied 
 by partial tones whose coalescence produces beats, these 
 producing the grating effect known as dissonance. 
 
 6. Graphic Representation of Consonance and Dissonance. 
 
 Helmholtz has attempted to represent this result 
 graphically, and from his work I copy, with some modi 
 
4:04 SOUND. 
 
 fi cation, the next two diagrams. He assumes, as already 
 stated, the maximum dissonance to correspond to 33 beats 
 per second; and he seeks to express different degrees of 
 dissonance by lines of different lengths. The horizontal 
 line G' G" , Fig. 164, represents a range of the musical scale 
 in which G" is our middle c, with 528 vibratious, and c' 
 the lower octave of G". The distance from any point of 
 this line to the curve above it represents the dissonance 
 corresponding to that point. The pitch here is supposed 
 to ascend continuously, and not by jumps. Supposing, for 
 example, two performers on the violin to start with the 
 same note 0', and that, while one of them continues to 
 sound that note, the other gradually and continuously 
 shortens his string, thus gradually raising its pitch up to 
 the octave G". The effect upon the ear would be repre- 
 
 FTG. 164. 
 
 sented by the irregular curved line in Fig. 164. Soon after 
 the unison, which is represented by contact at c' , is de- 
 parted from, the curve suddenly rises, showing the disso- 
 nance here to be the sharpest of all. At e' , the curve 
 approaches the straight line G' c", and this point corre- 
 sponds to the major third. At/' the approach is still 
 nearer, and this point corresponds to the fourth. At g f 
 the curve almost touches the straight line, indicating that 
 at this point, which corresponds to the fifth, the disso- 
 
CONSONANCE AND DISSONANCE SHOWN GRAPHICALLY. 
 
 nance almost vanishes. At a 1 we have the major sixth ; 
 while at G" , where the one note is an octave above the 
 other, the dissonance entirely vanishes. The e s' and the 
 a s', of this diagram, are the German names of a flat third 
 and a flat sixth. 
 
 Maintaining the same fundamental note </, and passing 
 through the octave above c f ' ', the various degrees of conso- 
 nance and dissonance are those shown in Fig. 165. That is 
 
 FIG. 165. 
 
 to say, beginning with the octave c f c" , and gradually ele- 
 vating the pitch of one of the strings, till it reaches c"' ', the 
 octave of c 1 ' ', the curved line represents the effect upon the 
 ear. We see, from both these curves, that dissonance is the 
 general rule, and that only at certain definite points does 
 the dissonance vanish, or become so decidedly enfeebled 
 as not to destroy the harmony. These points correspond 
 to the places where the numbers expressing the ratio of the 
 two rates of vibration are small whole numbers. It must 
 be remembered that these curves are constructed on 
 the supposition that the beats are the cause of the 
 dissonance ; and the agreement between calculation and 
 experience sufficiently demonstrates the truth of the 
 assumption. 1 
 
 1 The comparison employed by Mr. Sedley Taylor appeals with graphic 
 truth to a mountaineer. Considering the above curve to represent a moun- 
 tain-chain, he calls the discords peaks, and the concords passes. 
 
406 SOUND. 
 
 You have thus accompanied me to the verge of the 
 Physical portion of the science of Acoustics, and through 
 the aesthetic portion I have not the knowledge of music nec- 
 essary to lead you. I will only add that, in comparing three 
 or more sounds together, that is to say, in choosing them 
 for chords, we are guided by the principles just mentioned. 
 We choose sounds which are in harmony with the funda- 
 mental sound and with each other. In choosing a series of 
 sounds for combination two by two, the simplicity alone of 
 the ratios would lead us to fix on those expressed by the 
 numbers 1, , f , f , f, 2 ; these being the simplest ratios 
 that we can have within an octave. But, when the notes 
 represented by these ratios are sounded in succession, it is 
 found that the intervals between 1 and , and between \ 
 and 2, are wider than the others, and require the interpo- 
 lation of a note in each case. The notes chosen are such 
 as form chords, not with the fundamental tone, but with 
 the note f regarded as a fundamental tone. The ratios of 
 these two notes with the fundamental are $ and ^. In- 
 terpolating these, we have the eight notes of the natural 
 or diatonic scale, expressed by the following names and 
 ratios : 
 
 Names. C. D. E. F. G. A. B. C'. 
 Intervals 1st. 2d. 3d. 4th. 5th. 6th. 7th. 8th. 
 Rates of vibration. 1, f, f, , f, f, -^, 2. 
 
 Multiplying these ratios by 24, to avoid fractions, we 
 obtain the following series of whole numbers, which ex- 
 press the relative rates of vibration of the notes of the 
 diatonic scale : 
 
 24, 27, 30, 32, 30, 40, 45, 48. 
 
 The meaning of the terms third, fourth, fifth, etc., 
 which we have so often applied to the musical intervals, 
 is now apparent ; the term has reference to the position of 
 the note in the scale. 
 
MECHANICAL STUDIES. 4-07 
 
 Y. Composition of Vibrations. 
 
 In our second lecture I referred to, and in part illus- 
 trated, a method devised by M. Lissajous for studying 
 musical vibrations. By means of a beam of light reflected 
 from a mirror attached to a tuning-fork, the fork was 
 made to write the story of its own motion. In our last 
 lecture the same method was employed to illustrate opti- 
 cally the phenomenon of beats. I now propose to apply it 
 to the study of the composition of the vibrations which con- 
 stitute the principal intervals of the diatonic scale. We 
 must, however, prepare ourselves for the thorough com- 
 prehension of this subject by a brief preliminary examina- 
 tion of the vibrations of a common pendulum. 
 
 Such a pendulum hangs before you. It consists of a 
 wire carefully fastened to a plate of iron at the roof of the 
 house, and bearing a copper ball weighing 10 Ibs. I draw 
 the pendulum aside and let it go ; it oscillates to and fro 
 almost in the same plane. 
 
 I say "almost," because it is practically impossible to 
 suspend a pendulum without some little departure from 
 perfect symmetry around its point of attachment. In 
 consequence of this, the weight deviates sooner or later 
 from a straight line, and describes an oval more or less 
 elongated. Some years ago this circumstance presented a 
 serious difficulty to those who wished to repeat M. Fou- 
 cault's celebrated experiment, demonstrating the rotation 
 of the earth. 
 
 Nevertheless, in the case now before us, the pendu- 
 lum is so carefully suspended that its deviation from a 
 straight line is not at first perceptible. Let us suppose 
 the amplitude of its oscillation to be represented by the 
 dotted line a 5, Fig. 166. The point d, midway between 
 a and 5, is the pendulum's point of rest. When drawn 
 aside from this point to 5, and let go, it will return to d, 
 and in virtue of its momentum will pass on to a. There 
 
 18 
 
408 
 
 SOUND. 
 
 it comes momentarily to rest, and returns through d to I. 
 FIG. 166. And thus it will continue to oscillate 
 
 until its motion is expended. 
 
 The pendulum having first reached 
 the limit of its swing at &, let us sup- 
 pose a push in a direction perpen- 
 dicular to a b imparted to it ; that is 
 to say, in the direction b c. Suppos- 
 ing the time required by the pen- 
 dulum to swing from 5 to a to be 
 one second, 1 then the time required to swing from b to 
 FIG. let. d will be half a second. Suppose, fur 
 ther, the force applied at b to be such as 
 would carry the bob, if free to move in 
 that direction alone, to c in half a second, 
 and that the distance b c is equal to b d, 
 the question then occurs, where will the 
 bob really find itself at the end of half 
 a second ? It is perfectly manifest that 
 both forces are satisfied by the pendulum 
 reaching the point e, exactly opposite the 
 centre d, in half a second. To reach 
 this point, it can be shown that it must 
 describe the circular arc b e, and it will 
 pursue its way along the continuation of 
 the same arc, to #, and then pass round 
 to b. Thus, by the rectangular impulse 
 the rectilinear oscillation is converted into 
 a rotation, the pendulum describing a cir 
 cle, as shown in Fig. 167. 
 
 If the force applied at b be sufficient 
 to urge the weight in half a second 
 through a greater distance than b <?, the 
 
 1 This supposition is of course made for the sake of simplicity, the rea. 
 period of oscillation of a pendulum 28 feet long being between two and 
 three seconds. 
 
THE PENDULUM. 
 
 409 
 
 pendulum will describe an ellipse, with the lines a b for 
 its smaller axis ; if, on the contrary, the force applied at ~b 
 urge the pendulum in half a second through a distance -less 
 than ~b c, the weight will describe an ellipse, with the line 
 a b for its greater axis. 
 
 Let us now inquire what occurs when the rectangular 
 impulse is applied at the moment the ball is passing 
 through its position of rest at d. 
 
 Supposing the pendulum to be moving from a to b, 
 Fig. 168, and that at d a shock is imparted to it sufficient 
 
 FIG. 168. 
 
 FIG. 169. 
 
 of itself to carry it in half a second to c / it is here mani- 
 fest that the resultant motion will be along the straight 
 line d g lying between b d and d c. The pendulum will 
 return along this line to d, and pass on to h. In this case, 
 therefore, the pendulum will describe a straight line, g A, 
 oblique to its original direction of oscillation. 
 
 Supposing the direction of motion at the moment the 
 push is applied to be from b to a, instead of from a to 5, 
 it is manifest that the resultant here will also be a straight 
 line oblique to the primitive direction of oscillation ; but 
 its obliquity will be that shown in Fig. 169. 
 
 When the impulse is imparted to the pendulum neither 
 at the centre nor at the limit of its swing, but at some 
 point between both, we obtain neither a circle nor a straight 
 line, but something between both. We have, in fact, a 
 more or less elongated ellipse with its axis oblique to a J, 
 the original direction of vibration. If, for example, the 
 
410 
 
 SOUND. 
 
 impulse be imparted at d' 9 Fig. 170, while the pendulum 
 is moving toward 5, the position of the ellipse will be that 
 shown in Fig. 170 ; but if the push at d' be given when 
 the motion is toward a, then the position of the ellipse 
 will be that represented in Fig. 171. 
 
 FIG. 1TO. 
 
 FIG. 171. 
 
 By the method of M. Lissajous we can combine the 
 rectangular vibrations of two tuning-forks, a subject 
 which I now wish to illustrate before you. In front of 
 
 FIG. 172. 
 
 an electric lamp, L, Fig. 172, is placed a large tuning-fork, 
 T', fixed in a stand horizontally, and provided with a 
 
COMPOSITION OF SONOROUS VIBRATIONS. 4H 
 
 mirror, on which a narrow beam of light, L T', is per- 
 mitted to fall. The beam is thrown back, by reflection. 
 In the path of the reflected beam is placed a second up- 
 right tuning-fork, T, also furnished with a mirror. By 
 the horizontal fork, when it vibrates, the beam is tilted 
 laterally ; by the vertical fork, vertically. At the pres- 
 ent moment both forks are motionless, the beam of light 
 being reflected from the mirror of the horizontal to that 
 of the vertical fork, and from the latter to the screen, on 
 which it prints a brilliant disk. I now agitate the up- 
 right fork, leaving the other motionless. The disk is 
 drawn out into a fine luminous band, 3 feet long. On 
 sounding the second fork, the straight band is instantly 
 transformed into a white ring o p. Fig. 172, 36 inches 
 in diameter. * What have we done here ? Exactly what 
 we did in our first experiment with the pendulum. We 
 have caused a beam of light to vibrate simultaneously in 
 two directions, and have accidentally hit upon the phase 
 when one fork has just reached the limit of its swing 
 and come momentarily to rest, while the beam is receiving 
 the maximum impulse from the other fork. 
 
 That the circle was obtained is, as stated, a mere 
 accident; but it was a fortunate accident, as it enables 
 us to see the exact similarity between the motion of the 
 beam and that of the pendulum. I stop both forks, and, 
 agitating them afresh, obtain an ellipse with its axis 
 oblique. After a few trials we obtain the straight line, 
 indicating that both the forks then pass simultaneously 
 through their positions of equilibrium. In this way, by 
 combining the vibrations of the two forks, we reproduce 
 all the figures obtained with the pendulum. 
 
 When the vibrations of the two forks are, in all re- 
 spects, absolutely alike, whatever the figure may be which 
 is first traced upon the screen, it remains unchanged in 
 form, diminishing only in size as the motion is expended. 
 But the slightest difference in the rates of vibration de- 
 
i!2 SOUND. 
 
 stroys this fixity of the image. I endeavored before the 
 lecture to render the unison between these two forks as 
 perfect as possible, and hence you have observed very 
 little alteration in the shape of the figure. But by 
 moving a small weight along the prong of either fork, or 
 by attaching to either of them a bit of wax, the unison is 
 impaired. The figure then obtained by the combination 
 of both passes slowly from a straight line into an oblique 
 ellipse, thence into a circle ; after which it narrows again 
 to an ellipse with an opposed obliquity ; it then passes again 
 into a straight line, the direction of which is at right 
 angles to the first direction. Finally, it passes, in the 
 reverse order, through the same series of figures to the 
 straight line with which we began. The interval be- 
 tween two successive identical figures is the time in 
 which one of the forks succeeds in executing one com- 
 plete vibration more than the other. Loading the fork 
 still more heavily, we have more rapid changes ; the 
 straight line, ellipse, and circle, being passed through in 
 quick succession. At times the luminous curve exhibits 
 a stereoscopic depth, which renders it difficult to believe 
 that we are not looking at a solid ring of white-hot metal. 
 By causing the mirror of the fork, T, to rotate through 
 a small arc, the steady circle first obtained is drawn out 
 into a luminous scroll stretching right across the screen, 
 Fig. 173. The same experiment made with the changing 
 
 FIG. 173. 
 
 figure, obtained by throwing the forks out of unison, 
 gives us a scroll of irregular amplitude, Fig. l?t, 
 
 "We have next to combine the vibrations of two forks, 
 
 1 This figure corresponds to the interval 15 : 16. For it and some other 
 fierures, I am indebted to that excellent mechanician, M. Konig, of Paris. 
 
MUSICAL INTERVALS OPTICALLY ILLUSTRATED. 413 
 
 one of which oscillates with twice the rapidity of the 
 other ; in other words, to determine the figure correspond- 
 
 FIG. 174. 
 
 ITB. 
 
 ing to the combination of a note and its octave. To pre- 
 pare ourselves for the mechanics of the problem, we must 
 resort once more to our pendulum ; for it also can be 
 caused to oscillate in one direction twice as rapidly as in 
 another. By a complicated mechanical arrangement this 
 might be done in a very perfect manner, but at present 
 simplicity is preferable to completeness. The wire of our 
 pendulum is therefore permitted to 
 descend from its point of suspen- 
 sion, A, Fig. 175, midway between 
 two horizontal glass rods, a b, a' b', 
 supported firmly at their ends, and 
 about an inch asunder. The rods 
 cross the wire at a height of 7 feet 
 above the bob of the pendulum. 
 The whole length of the pendulum 
 being 28 feet, the glass rods inter- 
 cept one-fourth of this length. On 
 drawing the pendulum aside in the 
 direction of the rods, a 5, a! b', and 
 letting it go, it oscillates freely be- 
 tween them. I bring it to rest and 
 draw it aside in a direction perpen- a'I 
 dicular to the last ; a length of 7 
 feet only can now oscillate, and by 
 the laws of oscillation a pendulum 7 
 feet long vibrates with twice the 
 rapidity of a pendulum 28 feet long. 
 I wish to show you the figure 
 
SOUND. 
 
 described by the combination of these two rates of vibra- 
 tion. Attached to the copper ball,^?, is a camel' s-hair pencil, 
 intended to rub lightly upon a glass plate placed on black 
 paper, and over which is strewed white sand. Allowing 
 the pendulum to oscillate as a whole, the sand is rubbed 
 away along a straight line which represents the amplitude 
 of the vibration. Let a Z>, Fig. 1T6, represent this line, 
 which, as before, we will assume to be described in one 
 FIG. ire. second. When the pendulum is at the 
 
 limit, , of its swing, let a rectangular 
 impulse be imparted to it sufficient 
 to carry it to c in one-fourth of a 
 V / \ j second. If this were the only impulse 
 acting on the pendulum, the bob would 
 reach G and return to 5 in half a second. But under the 
 actual circumstances it is also urged toward d, which 
 point, through the vibration of the whole pendulum, it 
 ought also to reach in half a second. Both vibrations, 
 therefore, require that the bob shall reach d at the same 
 moment ; and to do this it will have to describe the curve 
 b c f d. Again, in the time required by the long pen- 
 dulum to pass from d to &, the short pendulum will pass 
 to and fro over the half of its excursion ; both vibrations 
 must therefore reach a at the same moment, and to ac- 
 complish this the pendulum describes the lower curve 
 between d and a. It is manifest that these two curves 
 will repeat themselves at the opposite sides of a 5, the 
 combination of both vibrations producing finally a figure 
 of 8, which you now see fairly drawn upon the sand 
 before you. 
 
 The same figure is obtained if the rectangular impulse 
 be imparted when the pendulum is passing its position of 
 rest, d. 
 
 I have here supposed the time occupied by the pen- 
 dulum in describing the line a l> to be one second. Let 
 
COMBINATION OF A NOTE AND ITS OCTAVE. 415 
 
 us suppose three-fourths of the second exhausted, and 
 the pendulum at d', Fig. ITT, in its excursion toward I ; 
 let the rectangular impulse then be FIG. 177. 
 
 imparted to it, sufficient to carry it to 
 c in one-fourth of a second. JS"ow the 
 long pendulum requires that it should 
 move from d' to 5 in one-fourth of a 
 second ; both impulses are therefore 
 satisfied by the pendulum taking up 
 the position c' at the end of a quarter of a second. To 
 reach this position it must describe the curve d' c' . It 
 will manifestly return along the same curve, and at the 
 end of another quarter of a second find itself again at d f . 
 From d' to d the long pendulum requires a quarter of a 
 second. But at the end of this time the short pendulum 
 must be at the lower limit of its swing : both require- 
 ments are satisfied by the pendulum being at e. We 
 thus obtain one arm, c' e, of a curve which repeats itself 
 to the left of e ; so that the entire curve, due to the 
 combination of the two vibrations, is that represented in 
 Fig. 165. This figure is a parabola, whereas the figure of 
 8 before obtained is a lemniscata. 
 
 We have here supposed that, at the moment when 
 the rectangular impulse was appiied, the motion of the 
 pendulum was toward I; if it were FIG. ITS. 
 
 toward a, we should obtain the in- 
 verted parabola, as shown in Fig. ITS. 
 
 Supposing, finally, the impulse to a 
 be applied, not when the pendulum is 
 passing through its position of equi- 
 librium, nor when it is passing a point 
 corresponding to three-fourths or one-fourth of the time 
 of its excursion, but at some other point in the line, a 5, 
 between its end and centre. Under these circumstances 
 we should have neither the parabola nor the perfectly 
 symmetrical figure of 8. but a distorted 8. 
 
16 SOUND. 
 
 And now we are prepared to witness with profit the 
 combined vibration of our two tuning-forks, one of which 
 sounds the octave of the other. Permitting the vertical 
 fork, T, Fig. 172, to remain undisturbed in front of the 
 lamp, we can oppose to it an horizontal fork, which 
 vibrates with twice the rapidity. The first passage of 
 the bow across the two forks reveals the exact simi- 
 larity of this combination, and that of our pendulum. A 
 very perfect figure of 8 is described upon the screen. 
 Before the lecture the vibrations of these two forks were 
 fixed as nearly as possible to the ratio of 1:2, and the 
 steadiness of the figure indicates the perfection of the 
 tuning. Stopping both forks, and again agitating them, 
 we have the distorted 8 upon the screen. A few trials 
 enable me to bring out the parabola. In all these cases 
 the figure remains fixed upon the screen. But if a 
 morsel of wax be attached to one of the forks, the 
 figure is steady no longer, but passes from the perfect 8 
 into the distorted one, thence into the parabola, from 
 which it afterward opens out to an 8 once more. By 
 augmenting the discord, we can render those changes as 
 rapid as we please. 
 
 When the 8 is steady on the screen, a rotation of the 
 mirror of the fork, T, produces the scroll shown in 
 Fig. 179. 
 
 PIG. 179. 
 
 Our next combination will be that of two forks vibrat- 
 ing in the ratio of 2:3. Observe the admirable steadi- 
 ness of the figure produced by the compounding of these 
 two rates of vibration. On attaching a fourpenny-piece 
 with wax to one of the forks the steadiness ceases, and we 
 
OTHER COMBINATIONS. 417 
 
 have an apparent rocking to and fro of the luminous 
 figure. Passing on to intervals of 3 : 4, 4 : 5, and 5 : 6, the 
 figures become more intricate as we proceed. The last 
 combination, 5 : 6, is so entangled, that to see the figure 
 plainly a very narrow band of light must be employed. 
 The distance existing between the forks and the screen also 
 helps us to unravel the complication. 
 
 And here it is worth noting that, when the figure is 
 fully developed, the loops along the vertical and horizontal 
 edges express the ratio of the combined vibrations. In the 
 octave, for example, we have two loops in one direction, 
 and one in another ; in the fifth, two loops in one direc- 
 tion, and three in another. When the combination is as 
 1 : 3, the luminous loops are also as 1 : 3. The changes 
 which some of these figures undergo, when the tuning is 
 not perfect, are extremely remarkable. In the case of 1 : 3, 
 for example, it is difficult at times not to believe that you 
 are looking at a solid link of white-hot metal. The figure 
 exhibits a depth, apparently incompatible with its being 
 traced upon a plane surface. 
 
 Fig. 181 is a diagram of these beautiful figures, includ- 
 ing combinations from 1 : 1 to 5 : 6. In each case, the 
 characteristic phases of the vibration are shown; and 
 through all of these each figure passes when the interval 
 between the two forks is not pure. I also add here, Fig. 
 180, two phases of the combination 8 : 9. 
 
 FIG. 180. 
 
 To these illustrations of rectangular vibrations I add 
 two others, Figs. 182 and 183, from a very beautiful series 
 
4:18 
 
RECTANGULAR VIBRATIONS. 
 
 419 
 
 Fie.182. 1:2. 
 
 FIG. 188. 1 : 8. 
 
 FIG. 184. 2:8. 
 
 FIG. 185. 8 : 4. 
 
20 SOUND. 
 
 obtained by Mr. Hubert Airy with a compound pendulum. 
 The experiments are described in Nature for August 17 
 and September 7, 1871. As their loops indicate, the 
 figures are those of an octave, and a twelfth. 
 
 But the most instructive apparatus for the compound- 
 ing of rectangular vibrations is that of Mr. Tisley. Figs. 
 J 84 and 185 are copies of figures obtained by him through 
 the joint action of two distinct pendulums ; the rates of 
 vibration corresponding to these particular figures being 
 2 : 3 and 3 : 4 respectively. The pen which traces the 
 figures is moved simultaneously by two rods attached to 
 the pendulums above their places of suspension. These 
 two rods lie in the two planes of vibration, being at right 
 angles to the pendulums, and to each other. At their 
 place of intersection is the pen. By means of a ball and 
 socket, of a special kind, the rods are enabled to move 
 with a minimum of friction in all directions, while the 
 rates of vibration are altered, in a moment, by the shift- 
 ing of movable weights. The figures are drawn either 
 with ink on paper, or, when projection on a screen is de- 
 sired, by a sharp point on smoked glass. When the pen- 
 dulums, having gone through the entire figure, return to 
 their starting-point, they have lost a little in amplitude. 
 The second excursion will, therefore, be smaller than the 
 first, and the third smaller than the second. Hence the 
 series of fine lines, inclosing gradually-diminishing areas, 
 shown in these exquisite figures. 1 Mr. Tisley's apparatus 
 reflects the highest credit upon its able constructor. 
 
 Sir Charles Wheatstone devised, many years ago, a 
 small and very efficient apparatus for the compounding of 
 rectangular vibrations. A drawing, Fig. 186, and a de- 
 scription of this beautiful little instrument, for both of 
 which I am indebted to its eminent inventor, may find a 
 
 1 For some beautiful figures of this description I arn indebted to Prof. 
 Lyman, of Yale College. 
 
WHEATSTONE'S APPARATUS. 
 
 421 
 
 place here : a is a steel rod polished at its upper end so 
 as to reflect a point of light ; this rod moves in a ball- 
 
 Fio. 186. 
 
 and-socket joint at 5, so that it may assume any position. 
 Its lower end is connected with two arms c and d, placed 
 at right angles to each other, the other ends of which 
 are respectively attached to the circumferences of the two 
 circular disks e and f. The axis of the disk e carries at 
 its opposite end another larger disk g, which gives motion 
 to the small disk A, placed on the axis which carries the 
 disk/*/ and, according as this small disk h is placed nearer 
 to or farther from the centre of the disk g, it communicates 
 a different relative motion to the disk f. The nut and 
 screw i enable the disk h to be placed in any position 
 between the centre and circumference of the larger disk g 
 and by means of the 1'ork^' the disk f is caused to revolve, 
 whatever may be the position of the disk h. By this 
 arrangement, while the wheel ~k is turned regularly, the rod 
 a is moved backward and forward by the disk e in one 
 direction, and by the disk /, with any relative oscillatory 
 
122 SOUND. 
 
 motion, in the rectangular direction. The end of the rod 
 is thus made to describe and to exhibit optically all the 
 beautiful acoustical figures produced by the composition 
 of vibrations of different periods in directions rectangular 
 to each other. A lever Z, bearing against the nut ?', indi- 
 cates, on a scale j, the numerical ratio of the two vibra- 
 tions. 1 
 
 I close these remarks on the combination of rectan- 
 gular vibrations with a brief reference to an apparatus 
 constructed by Mr. A. E. Donkin, of Exeter College, 
 Oxford, and described in the " Proceedings of the Koyal 
 Society," vol. xxii., p. 196. In its construction great 
 mechanical knowledge is associated with consummate 
 skill. I saw the apparatus as a wooden model, before 
 it quitted the hands of its inventor, and was charmed 
 with its performance. It is now constructed by Messrs. 
 Tisley and Spiller. 
 
 1 Mr. Sang, of Edinburgh was, I believe, the first to treat this subject 
 aualvticallv 
 
SUMMARY 423 
 
 SUMMARY OF CHAPTER IX. 
 
 BY the division of a string Pythagoras determined 
 the consonant intervals in mnsic, proving that, the simpler 
 the ratio of the two parts into which the string was divided, 
 the more perfect is the harmony of the sounds emitted 
 by the two parts of the string. Subsequent investigators 
 showed that the strings act thus because of the relation of 
 their lengths to their rates of vibration. 
 
 With the double siren this law of consonance is readily 
 illustrated. Here the most perfect harmony is the unison, 
 where the vibrations are in the ratio of 1 : 1. ISText comes 
 the octave, where the vibrations are in the ratio of 1 : 2. 
 Afterward follow in succession the fifth, with a ratio of 
 2:3; the fourth, with a ratio of 3:4; the major third, 
 with a ratio of 4:5; and the minor third, with a ratio of 
 5 : 6. The interval of a tone, represented by the ratio 
 8 : 9, is dissonant, while that of a semi-tone, with a ratio 
 of 15 : 16, is a harsh and grating dissonance. 
 
 The musical interval is independent of the absolute 
 number of the vibrations of the two notes, depending only 
 on the ratio of the two rates of vibration. 
 
 The Pythagoreans referred the pleasing effect of the 
 consonant intervals to number and harmony, and con- 
 nected them with " the music of the spheres." Euler ex- 
 plained the consonant intervals by reference to the consti- 
 tution of the mind, which, he affirmed, took pleasure in 
 simple calculations. The mind was fond of order, but 
 of such order as involved no weariness in its contempla- 
 
SOUND. 
 
 tion. This pleasure was afforded by the simpler ratios in 
 the case of music. 
 
 The researches of Helmholtz prove the rapid succes- 
 sion of beats to be the real cause of dissonance in music. 
 
 By means of two singing-flames, the pitch of one of 
 them being changeable by the telescopic lengthening of 
 its tube, beats of any degree of slowness or rapidity 
 may be produced. Commencing with beats slow enough 
 to be counted, and gradually increasing their rapidity, we 
 reach, without breach of continuity, downright disso- 
 nance. 
 
 But, to grasp this theory in all its completeness, we 
 must refer to the constitution of the human ear. We 
 have first the tympanic membrane, which is the anterior 
 boundary of the drum of the ear. Across the drum 
 stretches a series of little bones, called" respectively the 
 hammer, the anvil, and the stirrup-'bone the latter 
 abutting against a second membrane, which forms part of 
 the posterior boundary of the drum. Beyond this mem- 
 brane is the labyrinth filled with water, and having its 
 lining membrane covered with the filaments of the audi- 
 tory nerve. 
 
 Every shock received by the tympanic membrane is 
 transmitted through the series of bones to the opposite 
 membrane ; thence to the water of the labyrinth, and 
 thence to the auditory nerve. 
 
 The transmission is not direct. The vibrations are in 
 the first place taken up by certain bodies, which can swing 
 sympathetically with them. These bodies are of three 
 kinds : the otolites, which are little crystalline particles ; 
 the bristles of Max Schultze ; and the fibres of Corti's 
 organ. This latter is to all intents and purposes a stringed 
 instrument, of extraordinary complexity and perfection, 
 placed within the ear. 
 
 As regards our present subject, the strings of Corti's 
 
SUMMARY. 425 
 
 organ probably play an especially important part. That 
 one string should respond, in some measure, to another, it 
 is not necessary that the unison should be perfect ; a cer- 
 tain degree of response occurs in the immediate neighbor- 
 hood of unison. 
 
 Hence each of two strings, not far removed from each 
 other in pitch, can cause a third string, of intermediate 
 pitch, to respond sympathetically. And if the two strings 
 be sounded together, the beats which they produce. are 
 propagated to the intermediate string. 
 
 So, as regards Corti's organ, when single sounds of 
 various pitches, or rather when vibrations of various ra- 
 pidities, fall upon its strings, the vibrations are responded 
 to by the particular string whose period coincides with 
 theirs. And when two sounds, close to each other in pitch, 
 produce beats, the intermediate Corti's fibre is acted on by 
 both, and responds to the beats. 
 
 In the middle and upper portions of the musical scaie 
 the beats are most grating and harsh when they succeed 
 each other at the rate of 33 per second. "When they 
 occur at the rate of 132 per second, they cease to be 
 sensible. 
 
 The perfect consonance of certain musical intervals 
 is due to the absence of beats. The imperfect consonance 
 of other intervals is due to their existence. And here 
 the overtones play a part of the utmost importance. For, 
 though the primaries may sound together without any 
 perceptible roughness, the overtones may be so related to 
 each other as to produce harsh and grating beats. A 
 strict analysis of the subject proves that intervals which 
 require large numbers to express them, are invariably 
 accompanied by overtones which produce beats ; while in 
 intervals expressed by small numbers the beats are prac- 
 tically absent. 
 
 The graphic representation of the consonances and dis- 
 
4:26 SOUND. 
 
 sonances of the musical scale, by Helmholtz, furnishes a 
 striking proof of this explanation. 
 
 The optical illustration of the musical intervals has 
 been effected in a very beautiful manner by Lissajous. 
 Corresponding to each interval is a definite figure, pro- 
 duced by the combination of its vibrations. 
 
 The compounding of vibrations has, of late years, been 
 beautifully illustrated by apparatus constructed by Sir C. 
 Wheatstone, Mr. Herbert Airy, and Mr. A. E. Donkin ; 
 and by the beautiful pendulum apparatus of Mr. Tisley, 
 of the firm of Tisley and Spiller. 
 
 The pressure which, on a former occasion, prevented 
 me from adding a " summary " to this chapter, was also 
 the cause of hastiness, and partial inaccuracy, in its sketch 
 of the theory of Helinholtz. That the sketch needed 
 emendation I have long known, but I did not think it 
 worth while to anticipate the correction here made; as 
 the chapter, imperfect as it was, had been published, with- 
 out comment, in Germany, by Helinholtz himself. 
 
APPE.N DICES. 
 
 APPENDIX I. 
 
 ON THE INFLUENCE OF MUSICAL SOUNDS ON THE FLAME OF A JET OF 
 COAL-GAS. BY JOHN LE CONTE, M. D. 1 
 
 A SHORT time after reading Prof. John TyndalTs excellent article 
 44 On the Sounds produced by the Combustion of Gases in Tubes," 8 
 I happened to be one of a party of eight persons assembled after tea 
 for the purpose of enjoying a private musical entertainment. Three 
 instruments were employed in the performance of several of the 
 grand trios of Beethoven, namely, the piano, violin, and violoncello. 
 Two "jfeh-tail" gas-burners projected from the brick wall near the 
 piano. Both of them burned with remarkable steadiness, the win- 
 dows being closed and the air of the room being very calm. Never- 
 theless, it was evident that one of them was under a pressure nearly 
 sufficient to make it flare. 
 
 Soon after the music commenced, I observed that the flame of 
 the last-mentioned burner exhibited pulsations in height which were 
 exactly synchronous with the audible beats. This phenomenon was 
 very striking to every one in the room, and especially so when the 
 strong notes of the violoncello came in. It was exceedingly inter- 
 esting to observe how perfectly even the trills of this instrument 
 were reflected on the sheet of flame. A deaf man might have seen the 
 harmony. As the evening advanced, and the diminished consump- 
 tion of gas in the city increased the pressure, the phenomenon became 
 more conspicuous. The jumping of the flame gradually increased, 
 became somewhat irregular, and finally it began to flare continuous- 
 ly, emitting the characteristic sound indicating the escape of a greater 
 
 1 This able paper was the starting-point of the experiments on sensitive 
 flames, recorded in Chapters VI. and VII. ; the researches of Thomas Young 
 and Savart being the starting-point of the experiments on smoke-jets and 
 water-jets. J. T. 
 
 a Philosophical Magazine, section 4, vol. xiii., p. 473, 1857 
 
i28 APPENDIX. 
 
 amount of gas than could be properly consumed. I then ascertained 
 by experiment that the phenomenon did not take place unless the 
 discharge of gas was so regulated that the flame approximated to the 
 condition of flaring. I likewise determined by experiment that the 
 effects were not produced by jarring or shaking the floor and walls of 
 the room by means of repeated concussions. Hence it is obvious 
 that the pulsations of the flame were not owing to indirect vibrations 
 propagated through the medium of the walls of the room to the 
 burning apparatus, but must have been produced by the direct influ- 
 ence of the aerial sonorous pulses on the burning jet. 
 
 In the experiments of M. Schaffgotsch and Prof. J. Tyndall, it is 
 evident that "the shaking of the singing-flame within the glass 
 tube," produced by the voice or the siren, was a phenomenon per- 
 fectly analogous to what took place under my observation without 
 the intervention of a tube. In my case the discharge of gas was so 
 regulated that there was a tendency in the flame to flare, or to emit 
 a " singing-sound." Under these circumstances, strong aerial pulsa- 
 tions occurring at regular intervals were sufficient to develop syn- 
 chronous fluctuations in the height of the flame. It is probable that 
 the effects would be more striking when the tones of the musical 
 instrument are nearly in unison with the sounds which would be 
 produced by the flame under the slight increase in the rapidity of 
 discharge of gas required to manifest the phenomenon of flaring. 
 This point might be submitted to an experimental test. 
 
 As in Prof. Tyndall's experiments on the jet of gas burning within 
 a tube, clapping of the hands, shouting, etc., were ineffectual in con- 
 verting the "silent" into the " singing-flame," so in the case under 
 consideration, irregular sounds did not produce any perceptible influ- 
 ence. It seems to be necessary that the impulses should accumulate, 
 in order to exercise an appreciable effect. 
 
 With regard to the mode in which the sounds are produced by 
 the combustion of gases in tubes, it is universally admitted that the 
 explanation given by Prof. Faraday in 1818 is essentially correct. 
 It is well known that he referred these sounds to the successive 
 explosions produced by the periodic combination of the atmospheric 
 oxygen with the issuing jet of gas. While reading Prof. J. Plateau's 
 admirable researches (third series) on the " Theory of the Modifica- 
 tions experienced by Jets of Liquid issuing from Circular Orifices 
 when exposed to the Influence of Vibratory Motions," 1 the idea 
 flashed across my mind that the phenomenon which had fallen under 
 
 1 Philosophical Magazine, section 4, vol. xiv., p. 1, d seq., July, 1887. 
 
APPENDIX. 429 
 
 my observation was nothing more than a particular case of the 
 effects of sounds on all kinds of fluid jets. Subsequent reflection 
 has only served to fortify this first impression. 
 
 The beautiful investigations of Felix Savart on- the influence of 
 sounds on jets of water afford results presenting so many points of 
 analogy with their effects on the jet of burning gas, that it may be 
 well to inquire whether both of them may be referred to a common 
 cause. In order to place this in a striking light, I shall subjoin some 
 of the results of Savart's experiments. Vertically-descending jets of 
 water receive the following modifications under the influence of 
 vibrations : 
 
 1. The continuous portions become shortened ; the vein resolves 
 itself into separate drops nearer the orifice than when not under the 
 influence of vibrations. 
 
 2. Each of the masses, as they detach themselves from the ex- 
 tremity of the continuous part, becomes flattened alternately in a 
 vertical and horizontal direction, presenting to the eye, under the 
 influence of their translatory motion, regularly-disposed series of 
 maxima and minima of thickness, or ventral segments and nodes. 
 
 3. The foregoing modifications become much more developed and 
 regular when a note, in unison with that which would be produced 
 by the shock of the discontinuous part of the jet against a stretched 
 membrane, is sounded in its neighborhood. The continuous part 
 becomes considerably shortened, and the ventral segments are en- 
 larged. 
 
 4. When the note of the instrument is almost in unison, the con- 
 tinuous part of the jet is alternately lengthened and shortened, and 
 the beats which coincide with these variations in length can be rec- 
 ognized ly the ear. 
 
 5. Other tones act with less energy on the jet, and some produce 
 no sensible effect. 
 
 When a jet is made to ascend obliquely, so that the discontinuous 
 part appears scattered into a kind of sheaf in the same vertical 
 plane, M. Savart found : 
 
 a. That, under the influence of vibrations of a determinate 
 period, this sheaf may form itself into two distinct jets, each possess- 
 ing regularly-disposed ventral segments and nodes ; sometimes with 
 a different node, the sheaf becomes replaced by three jets. 
 
 I). The note which produces the greatest shortening of the con- 
 tinuous part always reduces the whole to a single jet, presenting a 
 perfectly regular system of ventral segments and nodes. 
 
4:30 APPENDIX. 
 
 In the last memoir of M. Savart a posthumous one, presented to 
 the Academy of Sciences of Paris, by M. Arago, in 1853 J several 
 remarkable acoustic phenomena are noticed in relation to the musical 
 tones produced by the efflux of liquids through short tubes. When 
 certain precautions and conditions are observed (which are minutely 
 detailed by this able experimentalist), the discharge of the liquid 
 gives rise to a succession of musical tones of great intensity and of a 
 peculiar quality, somewhat analogous to that of the human voice. 
 That these notes were not produced by the descending drops of the 
 liquid vein, was proved by permitting it to discharge itself into a 
 vessel of water, while the orifice was below the surface of the latter. 
 In this case the jet of liquid must have been continuous, but never- 
 theless the notes were produced. These unexpected results have 
 been entirely confirmed by the more recent experiments of Prof. 
 Tyndall. 9 
 
 According to the researches of M. Plateau, all the phenomena of 
 the influence of vibrations on jets of liquid are referable to the con- 
 flict between the vibrations and the forces of figure (" forces figu- 
 ratrices " ). If the physical fact is admitted and it seems to be 
 indisputable that a liquid cylinder attains a limit of stability when 
 the proportion between its length and its diameter is in the ratio of 
 twenty-two to seven, it is almost a physical necessity that the jet 
 should assume the constitution indicated by the observations of 
 Savart. It likewise seems highly probable that a liquid jet, while in 
 a transition stage to discontinuous drops, should be exceedingly sen- 
 sitive to the influence of all kinds of vibrations. It must be con- 
 fessed, however, that Plateau's beautiful and coherent theory does 
 not appear to embrace Savart's last experiment, in which the musical 
 tones were produced by a jet of water issuing under the surface of 
 the same liquid. It is rather difficult to imagine what agency the 
 "forces of figure " could have, under such circumstances, in the pro- 
 duction of the phenomenon. This curious experiment tends to cor- 
 roborate Savart's original idea, that the vibrations which produce 
 the sounds must take place in the glass reservoir itself, and that the 
 cause must be inherent in the phenomenon of the flow. 
 
 To apply the principles of Plateau's theory to gaseous jets, we 
 are compelled to abandon the idea of the non-existence of molecular 
 cohesion in gases. But is there not abundant evidence to show that 
 
 1 Comptes Eendus for August, 1853. Also Philosophical Magazine, section 
 4, vol. vii., p. 186, 1854. 
 
 2 Philosophical Magazine, section 4, vol. viii., p. 74, 1854. 
 
APPENDIX. 
 
 cohesion does exist among the particles of gaseous masses ? Does not 
 the deviation from rigorous accuracy, both in the law of Mariotte 
 and Gay-Lussac especially in the case of condensable gases, as 
 shown by the admirable experiments of M. Regnault clearly prove 
 that the hypothesis of the non-existence of cohesion in aeriform 
 bodies is fallacious? Do not the expanding rings which ascend 
 when a bubble of phosphuretted hydrogen takes fire in the air, 
 indicate the existence of some cohesive force in the gaseous product 
 of combustion (aqueous vapor), whose outlines are marked by the 
 opaque phosphoric acid ? In short, does not the very form of the 
 flame of a "fish-tail" burner demonstrate that cohesion must exist 
 among the particles of the issuing gas? It is well known that in this 
 burner the single jet which issues is formed by the union of two 
 oblique jets immediately before the gas is emitted. The result is a 
 perpendicular sheet of flame. How is such a result produced by the 
 mutual action of two jets, unless the force of cohesion is brought 
 into play? Is it not obvious that such a fan-like flame must be 
 produced by the same causes as those varied and beautiful forms of 
 aqueous sheets, developed by the mutual action of jets of water, so 
 strikingly exhibited in the experiments of Savart and of Magnus ? 
 
 If it be granted that gases possess molecular cohesion, it seems to 
 be physically certain that jets of gas must be subject to the same 
 laws as those of liquid. Vibratory movements excited in the neigh- 
 borhood ought, therefore, to produce modifications in them analogous 
 to those recorded by M. Savart in relation to jets of water. Flame 
 or incandescent gas presents gaseous matter in a visible form, admi- 
 rably adapted for experimental investigation ; and, when produced ly 
 a jet, should be amenable to the principles of Plateau's theory. Ac- 
 cording to this view, the pulsations or beats which I observed in the 
 gas-flame when under the influence of musical sounds, are produced 
 by the conflict between the aerial vibrations and the "forces of 
 figure" (as Plateau calls them) giving origin to periodical fluctua- 
 tions of intensity, depending on the sonorous pulses. 
 
 If this view is correct, will it not be necessary for us to modify 
 our ideas in relation to the agency of tubes in developing musical 
 sounds by means of burning jets of gas ? Must we not look upon 
 all burning jets as in the case of water-jets as musically inclined ; 
 and that the use of tubes merely places them in a condition favor- 
 able for developing the tones ? It is well known that burning jets 
 frequently emit a singing-sound when they are perfectly free. Are 
 these sounds produced by successive explosions analogous to those 
 19 
 
432 APPENDIX. 
 
 which take place in glass tubes? It is very certain that, under the. 
 influence of molecular forces, any cause which tends to elongate the 
 flame, without affecting the velocity of discharge, must tend to 
 render it discontinuous, and thus bring about that mixture of gas 
 and air which is essential to the production of the explosions. The 
 influence of tubes, as well as of aerial vibrations, in establishing this 
 condition of things, is sufficiently obvious. Was not the " beaded 
 line" with its succession of "luminous stars," which Prof. Tyndall 
 observed when a flame of olefiant gas, burning in a tube, was ex- 
 amined by means of a moving mirror, an indication that the flame 
 became discontinuous, precisely as the continuous part of a jet of 
 water becomes shortened, and resolved into isolated drops, under the 
 influence of sonorous pulsations? But I forbear enlarging on this 
 very interesting subject, inasmuch as the accomplished physicist last 
 named has promised to examine it at a future period. In the hands 
 of so sagacious a philosopher, we may anticipate a most searching 
 investigation of the phenomena in all their relations. In the mean 
 time I wish to call the attention of men of science to the view pre- 
 sented in this article, in so far as it groups together several classes 
 of phenomena under one head, and may be considered a partial gen- 
 eralization. From SILLIMAN'S American Journal for January, 1858. 
 
 APPENDIX II. 
 
 ON ACOUSTIC KEVEESIBILITY. 1 
 
 Off the 21st and 22d of June, 1822, a commission, appointed by 
 the Bureau des Longitudes of France, executed a celebrated series 
 of experiments on the velocity of sound. Two stations had bee& 
 chosen, the one at Villejuif, the other at Montlhery, both lying south 
 of Paris, and 11*6 miles distant from each other. Prony, Mathieu, 
 and Arago, were the observers at Villejuif, while Humboldt, Bouvard, 
 and Gay-Lussac were at Montlhery. Guns, charged sometimes with 
 two pounds and sometimes with three pounds of powder, were fired 
 at both stations, and the velocity was deduced from the interval 
 between the appearance of the flash and the arrival of the sound. 
 
 On this memorable occasion an observation was made which, as 
 far as I know, has remained a scientific enigma to the present hour. 
 
 i " Proceedings of the Royal Institution," January 15, 1876. 
 
APPENDIX. 433 
 
 It was noticed that while every report of the cannon fired at Mont- 
 lhe>y was heard with the greatest distinctness at Villejuif, by far 
 the greater number of the reports from Villejuif failed to reach 
 Hontlhe'ry. Had wind existed, and had it blown from Montlhe'ry to 
 Villejuif, it would have been recognized as the cause of the observed 
 difference ; but the air at the time was calm, the slight motion of 
 translation actually existing being from Villejuif toward Montlhe'ry, 
 or against the direction in which the sound was best heard. 
 
 So marked was the difference in transmissive power between the 
 two directions, that on June 22d, while every shot fired at Montlhe'ry 
 was heard d merveille at Villejuif, but one shot out of twelve fired at 
 Villejuif was heard, and that feebly, at the other station. 
 
 With the caution which characterized him on other occasions, 
 and which has been referred to admiringly by Faraday, 1 Arago made 
 no attempt to explain this anomaly. His words are: "Quant aux 
 differences si remarquables d'intensite" que le bruit du canon a tou- 
 jours pr6sentes suivant qu'il se propageait du nord au sud entre 
 Villejuif et Montlhe'ry, ou du sud au nord entre cette seconde station 
 et la premiere, nous ne chercherons pas aujourd'hui a 1'expliquer, 
 parce que nous ne pourrions offrir au lecteur que des conjectures 
 denudes de preuves." 2 
 
 I have tried, after much perplexity of thought, to bring this sub- 
 ject within the range of experiment, and have now to submit the 
 following solution of the enigma : The first step was to ascertain 
 whether the sensitive flame, referred to in my recent paper in the 
 "Philosophical Transactions," could be safely employed in experi- 
 ments on the mutual reversibility of a source of sound and an object 
 on which the sound impinges. Now, the sensitive flame usually em- 
 ployed by me measures from eighteen to twenty-four inches in 
 height, while the reed employed as a source of sound is less than a 
 square quarter of an inch in area. If, therefore, the whole flame, or 
 the pipe which fed it, were sensitive to sonorous vibrations, strict 
 experiments on reversibility with the reed and flame might be diffi- 
 cult, if not impossible. Hence my desire to learn whether the seat 
 of sensitiveness was so localized in the flame as to render the con- 
 templated interchange of flame and reed permissible. 
 
 The flame being placed behind a cardboard screen, the shank of 
 a funnel passed through a hole in the cardboard was directed upon 
 the middle of the flame. The sound-waves issuing from the vibrntiny 
 
 1 " Researches in Chemistry and Physics," p. 484. 
 a " Connaissance des Temps," 1825, p. 370. 
 
434 APPENDIX. 
 
 reed, placed within the funnel, produced no sensible effect upon the 
 flame. Shifting the funnel so as to direct its shank upon the root of 
 the flame, the action was violent. 
 
 To augment the precision of the experiment, the funnel was con- 
 nected with a glass tube three feet long and half an inch in diameter, 
 the object being to weaken, by distance, the effect of the waves dif- 
 fracted round the edge of the funnel, and to permit those only which 
 passed through the glass tube to act upon the flame. 
 
 Presenting the end of the tube to the orifice of the burner 
 (&, Fig. 1), or the orifice to the end of the tube, the flame was vio- 
 lently agitated by the sounding-reed, E. On shifting the tube, or the 
 burner, so as to concentrate the sound on a portion of the flame about 
 half an inch above the orifice, the action was nil. Concentrating the 
 sound upon the burner itself, about half an inch below its orifice, 
 there was no action. 
 
 These experiments demonstrate the localization of " the seat of 
 sensitiveness," and they prove the flame to be an appropriate instru- 
 ment for the contemplated experiments on reversibility. 
 
 FIG. i. 
 
 The experiments then proceeded thus : The sensitive flame 
 being placed close behind a screen of cardboard 18 inches high by 
 12 inches wide, a vibrating reed, standing at -the same height as the 
 root of the flame, was placed at a distance of 6 feet on the other 
 side of the screen. The sound of the reed, in this position, pro- 
 duced a strong agitation of the flame. 
 
 The whole upper half of the flame was here visible from the 
 reed ; hence the necessity of the foregoing experiments 1o prove 
 the action of the sound on the upper portion of the flame to be 
 nil, and that the waves had really to bend round the edge of the 
 screen, so as to reach the seat of sensitiveness in the neighborhood 
 of the burner. 
 
APPENDIX. 435 
 
 The positions of the flame and reed were reversed, the latter 
 being now close behind the screen, and the former at a distance 
 of 6 feet from it. The sonorous vibrations were without sensible 
 action upon the flame. 
 
 The experiment was repeated and varied in many ways. 
 Screens of various sizes were employed ; and, instead of reversing 
 the positions of the flame and reed, the screen itself was moved, 
 so as to bring, in some experiments the flame, and in other experi- 
 ments the reed, close behind it. Care was also taken that no 
 reflected sound from the walls or ceiling of the laboratory, or 
 from the body of the experimenter, should have anything to do 
 with the effect. In all cases it was shown that the sound was ef- 
 fective when the reed was at a distance from the screen, and the 
 flame close behind it ; while the action was insensible when these 
 positions were reversed. 
 
 Thus, let s e, Fig. 2, be a vertical section of the screen. When 
 the reed was at A and. the flame at B there was no action ; when 
 the reed was at B and the flame at A the action was decided. It 
 may be added that the vibrations communicated to the screen 
 
 FIG. 2. 
 
 itself, and from it to the air beyond it, were without effect ; for 
 when the reed, which at B was effectual, was shifted to 0, where 
 its action on the screen was greatly augmented, it ceased to have 
 any action on the flame at A. 
 
 We are now, I think, prepared to consider the failure of re- 
 versibility in the larger experiments of 1822. Happily an inci- 
 dental observation of great significance comes here to our aid. 
 It was observed and recorded at the time that, while the reports 
 of the guns at Villejuif were without echoes, a roll of echoes, 
 lasting from 20 to 25 seconds, accompanied every shot at 
 Montlhery, being heard by the observers there. Arago, the 
 writer of the report, referred these echoes to reflection from the 
 
36 APPENDIX. 
 
 clouds, an explanation which I think we are now entitled to regard 
 as problematical. The report says that "tons les coups tires a 
 Montlh6ry y 6taient accompagnes d'un roulement seuiblable a 
 celui du tonnerre." I have italicized a very significant word 
 a word which fairly applies to our experiments on gun-sounds 
 at the South Foreland, where there was no sensible interval be- 
 tween explosion and echo, but which could hardly apply to echoes 
 coming from the clouds. For, supposing the clouds to be only a 
 mile distant, the sound and its echo would have been separated by 
 an interval of nearly ten seconds. But there is no mention of 
 any interval; and, had such existed, surely the word "followed," 
 instead of " accompanied," would have been the one employed. 
 The echoes, moreover, appear to have been continuous, while the 
 clouds observed seem to have been separate. " Ces ph6nomenes," 
 says Arago, " n'ont jamais eu lieu qu'au moment de 1'apparition de 
 quelques nuages." But from separate clouds a continuous roll of 
 echoes could hardly come. "When to this is added the experi- 
 mental fact that clouds far denser than any ever formed in the 
 atmosphere are demonstrably incapable of sensibly reflecting sound, 
 while cloudless air, which Arago pronounced echoless has been 
 proved capable of powerfully reflecting it, I think we have strong 
 reason to question the hypothesis of the illustrious French philosopher. 1 
 
 And, considering the hundreds of shots fired at the South 
 Foreland, with the attention especially directed to the aerial 
 echoes, when no single case occurred in which echoes of measu- 
 rable duration did not accompany the report of the gun, I think 
 Arago's statement, that at Yillejuif no echoes were heard when 
 the sky was clear, must simply mean that they vanished with great 
 rapidity. Unless the attention was specially directed to the point, 
 a slight prolongation of the cannon-sound might well escape ob- 
 servation ; and it would be all the more likely to do so if the echoes 
 were so loud and prompt as to form apparently part and parcel of 
 the direct sound. 
 
 I should be very loath to transgress here the limits of fair criti- 
 cism, or to throw doubt, without good reason, on the recorded obser- 
 vations of illustrious men. Still, taking into account what has been 
 just stated, and remembering that the minds of Arago and his col- 
 leagues were occupied by a totally different problem (that the 
 echoes were an incident rather than an object of observation), I 
 think we may justly consider the sound which he called "install- 
 
 See Chapter VII., Part II. 
 
APPENDIX. 4.37 
 
 taneous " as one whose aerial echoes did not differentiate them- 
 selves from the direct sound by any noticeable fall of intensity, and 
 which rapidly died into silence. 
 
 Turning now to the observations at Montlhery, we are struck 
 by the extraordinary duration of the echoes heard at that station. 
 At the South Foreland the charge habitually fired was equal to 
 the largest of those employed by the French philosophers; but 
 on no occasion did the gun-sounds produce echoes approaching 
 to 20 or 25 seconds' duration. The time rarely reached half this 
 amount. Even the siren-echoes, which were more remarkable 
 and more long continued than those of the gun, never reached 
 the duration of the Montlhery echoes. The nearest approach to it 
 was on October 17, 18Y3, when the siren-echoes required 15 seconds 
 to subside into silence. 
 
 On this same day, moreover (and this is a point of marked 
 significance), the transmitted sound reached its maximum range, 
 the gun-sounds being heard at the Quenocs buoy, 16^ nautical 
 miles from the South Foreland. I have stated in another place 
 that the duration of the air-echoes indicates "the atmospheric 
 depths " from which they came. An optical analogy may help 
 us here. Let light fall upon chalk, the light is wholly scattered 
 by the superficial particles ; let the chalk be powdered and 
 mixed with water, light reaches the observer from a far greater 
 depth of the turbid liquid. The solid chalk typifies the action of 
 exceedingly dense acoustic clouds; the chalk and water that of 
 clouds of more moderate density. In the one case we have echoes 
 of short, in the other echoes of long duration. These considera- 
 tions prepare us for the inference that Montlhery, on the occasion 
 referred to, must have been surrounded by a highly-diacoustic 
 atmosphere ; while the shortness of the echoes at Villejuif shows 
 that the atmosphere surrounding that station must have been, in 
 a high degree, acoustically opaque. 
 
 Have we any clew to the cause of the opacity ? I think we 
 have. Villejuif is close to Paris, and over it, with the observed 
 light wind, was slowly wafted the air from the city. Thousands 
 of chimneys to windward of Villejuif were discharging their 
 heated currents ; so that an exceedingly non-homogeneous at- 
 mosphere must have surrounded that station. 1 At no great 
 height in the atmosphere the equilibrium of temperature would 
 be established. This non-homogeneous air surrounding Villejuif 
 
 1 The effect of the air of London is sometimes strikingly evident. 
 
38 APPENDIX. 
 
 is experimentally typified by our screen, with the source of sound 
 close behind it, the upper edge of the screen representing the 
 place where equilibrium of temperature was established in the 
 atmosphere above the station. In virtue of its proximity to the 
 screen, the echoes from our sounding-reed would, in the case 
 here supposed, so blend with the direct sound as to be practically 
 indistinguishable from it, as the echoes at Villejuif followed the 
 direct sound so hotly, and vanished so rapidly, that they escaped 
 observation. And as our sensitive flame, at a distance, failed to be 
 affected by the sounding body placed close behind the cardboard 
 screen, so, I take it, did the observers at Montlhery fail to hear the 
 sounds of the Villejuif gun. 
 
 Something further may be done toward the experimental 
 elucidation of this subject. The facility with which sounds pass 
 through textile fabrics has been already illustrated, 1 a layer of 
 cambric or calico, or even of thick flannel or baize, being found 
 competent to intercept but a small fraction of the sound from a 
 vibrating reed. Such a layer of calico may be taken to represent 
 a layer of air, differentiated from its neighbors by temperature 
 or moisture; while a succession of such sheets of calico may be 
 taken to represent successive layers of non-homogeneous air. 
 
 Two tin tubes (M N and O P, Fig. 3) with open ends were 
 
 FIG. 3. 
 
 placed so as to form an accute angle with each other. At the end 
 of one was the vibrating reed r ; opposite the end of the other, 
 and in the prolongation of P O, the sensitive flame /, a second 
 sensitive flame (f) being placed in the continuation of the axis 
 of M N. On sounding the reed, the direct sound through M N 
 agitated the flame f. Introducing the square of calico a 5 at the 
 
 i "Philosophical Transactions," 18Y4, Part I., p. 208, and chapter vii. of 
 this volume. 
 
APPENDIX. 439 
 
 proper angle, a slight decrease of the action on f was noticed, and 
 the feeble echo from a I produced a barely perceptible agitation of 
 the flame/. Adding another square, c d, the sound transmitted 
 by a I impinged on c d; it was partially echoed, returned through 
 a 5, passed along P O, and still further agitated the flame /. 
 Adding a third square, e /, the reflected sound was still further 
 augmented, every accession to the echo being accompanied by a 
 corresponding withdrawal of the vibrations from /', and a con- 
 sequent stilling of that flame. 
 
 With thinner calico or cambric it would require a greater num- 
 ber of layers to intercept the entire sound ; hence with such cam- 
 bric we should have echoes returned from a greater distance, and 
 therefore of greater duration. Eight layers of the calico employed 
 in these experiments, stretched on a wire frame and placed close 
 together as a kind of pad, may be taken to represent a dense 
 acoustic cloud. Such a pad, placed at the proper angle beyond N, 
 cuts off the sound, which in its absence reaches /', to such an ex- 
 tent that the flame /', when not too sensitive, is thereby stilled, 
 while / is far more powerfully agitated than by the reflection from 
 a single layer. With the source of sound close at hand, the echoes 
 from such a pad would be of insensible duration. Thus close at 
 hand do I suppose the acoustic clouds surrounding^Villejuif to have 
 been, a similar shortness of echo being the consequence. 
 
 A further step is here taken in the illustration of the analogy 
 between light and sound. Our pad acts chiefly by internal reflec- 
 tion. The sound from the reed is a composite one, made up of par- 
 tial sounds differing in pitch. If these sounds be ejected from the 
 pad in their pristine proportions, the pad is acoustically white ; if 
 they return with their proportions altered, the pad is acoustically 
 colored. 
 
 In these experiments my assistant, Mr. Oottrell, has rendered 
 me material assistance. 1 
 
 June 3^. I annex here a sketch of an apparatus 2 devised 
 by my assistant, Mr. Oottrell, and constructed by Tisley and Spil- 
 
 1 Since this was written I have sent the sound through fifteen layers of 
 calico, and echoed it back through the same layers, in strength sufficient to 
 ngitate the flame. Thirty layers were here crossed by the sound. The sound 
 was subsequently found able to penetrate two hundred layers of cotton net; 
 a single layer of wetted calico being competent to stop it. 
 
 9 The cut reached me too late for introduction at the proper place. 
 
APPENDIX. 
 
 ler, for the demonstration of the law of reflection of sound. It 
 consists of two tubes (A F, B E), with a source of sound at the end 
 E of one of them, and a sensitive flame at the end F of the other. 
 The axes of the tuhe converge upon the mirror, M, and they are 
 capable of being placed so as to inclose any required angle. The 
 angles of incidence and reflection are read off on the graduated 
 semicircle. The mirror M is also movable round a vertical axis. 
 
INDEX. 
 
 AGO 
 
 A (JOUSTIC clouds, echoes from, 
 O. 306 
 
 reversibility, 433-441 
 
 transparency, great change of, 302 
 Air, process of the propagation of 
 
 sound through the, 33 
 propagation of sound through air 
 of varying density, 40 
 
 elasticity and density of air, 52 
 
 influence of temperature on the ve- 
 locity of sound, 53 
 
 thermal changes produced by the 
 sonorous wave, 57 
 
 ratio of specific heats at constant 
 pressure and at constant volume, 
 deduced from velocities of sound, 
 59 
 
 mechanical equivalent of heat de- 
 duced from this ratio, 61 
 
 inference that atmospheric air pos- 
 sesses no sensible power to radiate 
 heat, 63 
 
 velocity of sound in, 66 
 
 musical sounds produced by puffs 
 of air, 83 
 
 other modes of throwing the air in- 
 to a state of periodic motion, 86 
 
 reflection from heated air, 317 
 A.lbans, St., echo in the Abbey .Church 
 
 of, 48 
 
 Amplitude of the vibration of a sound- 
 wave, 41 
 
 Arago, his report on the velocity of 
 sound, 308 
 
 Atmosphere, reflection from atmos- 
 pheric air, 315 
 
 its effect on sound, 342 
 Auditory nerve, office of the, 32 
 
 manner in which sonorous motion 
 is communicated to the, 353 
 
 OLA 
 
 BARS, heated, musical sounds pro- 
 duced by, 81 
 
 examination of vibrating bars by 
 polarized light, 197 
 
 Beats, theory of, 362 
 
 action of, on flame, 353 
 
 optical illustration of, 366 
 
 various illustrations of, 373 
 
 dissonance due to beats, 325, 402 
 Bell, experiments on a, placed in vacuo, 
 
 36 
 
 Bells, analysis of vibrations of, 178, 
 187 
 
 fluctuations of, 329-331 
 Bourse, at Paris, echoes of the gallery 
 
 of the, 47 
 
 Burners, fish-tail and bat's-wing, ex- 
 periments with, 260 
 
 /CARBONIC acid, velocity of sound 
 \J in, 66 
 
 reflection from, 313 
 
 Carbonic oxide, velocity of sound in, 
 
 66 
 Chladni, his tonometer, 160 
 
 his experiments on the modes of 
 vibration possible to rods free at 
 both ends, 164 
 
 his analysis of the vibrations of a 
 tuning-fork, 166 
 
 . his device for rendering the vibra- 
 tions visible, 168 
 
 illustrations of his experiments, 
 169 
 
 Chords, musical, 406 
 Clang, definition of, 144 
 Claque-bois, formation of the, 165, 
 
 186 
 Clarionet, tones of the, 223 
 
INDEX. 
 
 CLO 
 
 Clouds, sounds reflected from the, 48 
 Corti's fibres, in the mechanism of the 
 
 ear, 399 
 Cottrell, Mr., his experiment of an echo 
 
 from flame, 318 
 
 DERHAM, Dr., on fog-signals, 
 288 
 
 Diatonic scale, 347 
 Difference-tones, 380 
 Diffraction of sound, 72, note, 18 
 Disks, analysis of vibrations of, 17G, 
 
 187 
 
 Dissonance, cause of, 402 
 graphic representations of, 404 
 Doppler, his theory of the colored 
 
 stars, 106 
 
 EAR, limits of the range of hearing 
 of the, 99, 111 
 
 causes of artificial deafness, 101, 
 112 
 
 mechanism of the ear, 398 
 
 consonant intervals in relation to, 
 400 
 
 Echoes, 47 
 
 instances of, 47, 48 
 
 aerial, production of, 309 
 
 from flame, 318 
 
 reputed cloud echoes. 309 
 Eolian harp, formation of the, 160 
 Erith, effects of the explosion of 1864 
 
 on the village and church of, 5] 
 Eustachian tube, the, 101 
 
 mode of equalizing the air on each 
 side of the tympanic membrane, 
 102, 112 
 
 FALSETTO voice, causes of the, 
 225 
 
 Faraday, Mr., his experiment on sono- 
 rous ripples, 184 
 Fiddle, formation of the, 116 
 
 sound-board of the, 116 
 
 the iron fiddle, 160, 185 
 
 the straw-fiddle, 166, 186 
 Flames, sounding, 244, 284 
 
 rhythmic character of friction, 244, 
 284 
 
 influence of the tube surrounding 
 the flame, 247, 284 
 
 HAB 
 
 Flames continued. 
 
 singing-flames, 249, 284 
 
 effect of unisonant notes on sing- 
 ing-flames, 258 
 
 action of sound on naked flames, 
 258, 285 
 
 influence of pitch, 267 
 
 extraordinary delicacy of flames as 
 acoustic reagents, 257 
 
 the vowel-flame, 269 
 
 discovery of a new sensitive flame 
 by Philip Barry, 270 
 
 echo from, 318 
 
 action of beats on flame, 363 
 Flute, tones of the, 223 
 
 Fog, its want of power to obstruct 
 sound, 326 
 
 observations in London, 327 
 
 fog-signals in, 333 
 
 artificial, experiments on, 335 
 Fog-signals, researches on the acous- 
 tic transparency of the atmosphere 
 in relation to the question of, 287 
 
 station at South Foreland, 290 
 
 instruments and observations, 290 
 
 variations of range, 296, 297 
 
 contradictory results, 298 
 
 solution of contradictions, 298 
 
 extraordinary case of acoustic opac- 
 ity, 299 
 
 in fogs, 333 
 
 minimum range of, 347 
 
 its position, 347 
 
 disadvantages of the gun, 348 
 Foreland, South, fog-signal station at, 
 
 290 
 fog at, 332 
 
 /RAINES'S FARM, account of the 
 \J battle of, 304 
 Gases, velocity of sound in, 66 
 Gun, range of, for fog-signals, 294 
 
 inferiority to the siren, 345 
 
 its disadvantages as a signal, 345 
 
 HAIL, doubt as to its power to ob- 
 struct sound, 321 
 
 Harmonic tones of strings, 143, 144 
 Harmony, 385 
 
 notions of the Pythagoreans, 386 
 
 Euler's theory, 393 
 
 conditions of harmony, 386 
 
INDEX. 
 
 443 
 
 HA.K 
 
 Ha rraony continued. 
 
 influence of overtones on harmony, 
 403 
 
 graphic representations of conso- 
 nance and dissonance, 405 
 
 Harmonica, the glass, 166 
 
 Hawksbee, his experiment on sound- 
 ing bodies placed in vacua, 36 
 
 Hearing, mechanism of, 398 
 
 Heat, thermal changes in the air pro- 
 duced by the sonorous wave, 57 
 
 ratio of specific heats at constant 
 pressure and at constant volume 
 deduced from velocities of sound, 
 59 
 
 mechanical equivalent of heat de- 
 duced from this ratio, 61 
 
 inference that atmospheric air 
 possesses no sensible power to 
 radiate heat, 63 
 
 musical sounds produced by heated 
 bars, 81 
 
 Helmholtz, his theory of resultant 
 
 tones, 380, 382 
 
 consonance, 389, 393 
 
 Herschel, Sir John, his article on 
 
 " Sound " quoted, 48 
 
 his account of Arago's observation 
 on velocity of sound, 308 
 
 Hooke, Dr. Robert, his anticipation 
 of the stethoscope, 71 
 
 his production of musical sounds 
 by the teeth of a rotating wheel, 
 80 
 
 Horn, as an instrument for fog-sig- 
 naling, 293 
 Hydrogen, action of, upon the voice, 39 
 
 deadening of sound by, 38 
 
 velocity of sound in, 53, 66 
 
 TNFLECTION of sound, 51 
 J. case of the Erith explosion, 51 
 Interference of sonorous waves, 358, 
 383 
 
 extinction of sound by sound, 360, 
 383 
 
 theory of beats, 362, 383 
 Intervals, optical illustration of, 413 
 
 JOULE'S equivalent, 64 
 Jungfrau, echoes of the, 47 
 
 MU8 
 
 TTALEIDOPHONE, Wheatstone's, 
 l\ formation of, 160, 185, 186 
 Kundt, M., his experiments, 229 
 
 T APLACE, his correction of New. 
 JJ ton's formula for the velocity oi 
 
 sound, 56 
 Le Conte, Professor, his observation 
 
 upon sensitive naked flames, 258 
 
 on the influence of musical sounds 
 on the flame of a jet of coal-gas, 
 427, 432 
 
 Lenses, refraction of sound by, 49 
 Light, analogy between sound niid, 
 43, 49 
 
 analogy of, 300 
 
 Liquids, velocity of sound in, 66 
 
 transmission of musical rounds 
 through, 106 
 
 constitution of liquid veins, 273 
 
 action of sound on liquid veins, 
 276 
 
 Plateau's theory of the resolution 
 of a liquid vein into drops, 277, 
 286 
 
 delicacy of liquid veins, 282 
 Lissajous, M., his method of giving 
 
 optical expression to the vibrations 
 of a tuning-fork, 88 
 
 MAYER, his formula of the equiva- 
 lent of heat, 63 
 
 Melde, M., his experiments with vi- 
 brating strings, 133, 400 
 and with sonorous rip- 
 ples, 183 
 
 Metals, velocity of sound transmitted 
 through, 68 
 
 determination of velocity in, 199 
 Molecular structure, influence of, oc 
 
 the velocity of sound, 69 
 Monochord or sonometer, the, 113 
 Motion, conveyed to the brain by the 
 
 nerves, 31 
 
 sonorous motion. (See SOUND.) 
 Mouth, resonance of the, 226 
 Music, physical difference between 
 
 noise and, 77, 110 
 
 a musical tone produced by peri- 
 odic, noise by unperiodic, impulses, 
 78, 110 
 
 production of musical sounds by 
 taps, 80, 110 
 
INDEX. 
 
 MUS 
 
 Music continued. 
 by puffs of air, 83, 1 10 
 
 pitch and intensity of musical 
 sounds, 85, 87, 110 
 
 description of the siren, 90 
 
 definition of an octave, 98 
 description of the double siren 103 
 
 transmission of musical sounds 
 through liquids and solids, 106 
 
 musical chords, 406 
 
 the diatonic scale, 406 
 
 See also HARMONY. 
 Musical-box, formation of the, 160, 
 
 186 
 
 NERVES of the human body, mo- 
 tion conveyed by the, to the 
 brain, 31 
 
 rapidity of impressions conveyed 
 by, 32, note 
 
 Newton, Sir Isaac, his calculation of 
 
 the velocity of sound, 56 
 Nodes, 124 
 
 the nodes not points of absolute 
 rest, 127 
 
 nodes of a tuning-foi-k, 165, 167 
 
 rendered visible, 167, 169 
 
 a node the origin of vibration, 236 
 Noise, physical difference between 
 
 music and, 77 
 
 OCTAVE, definition of an, 98 
 Organ-pipes, 206, 240 
 
 vibrations of stopped pipes, 208, 
 240 
 
 the Pandean pipes, 210 
 
 open pipes, 211, 241, 244 
 
 state of the air in sounding-pipes, 
 213, 241 
 
 reeds and reed-pipes, 220 
 Otolites of the ear, 399 
 Overtones, definition of, 144 
 
 relation of the point plucked to the, 
 146 
 
 overtones corresponding to the vi- 
 brations of a rod fixed at both 
 ends, 156 
 
 of a tuning-fork, 165, 167 
 
 rendered visible, 167, 169 
 
 of rods vibrating longitudinally, 
 
 195 
 of the siren, 390 
 
 'influence of overtones on harmony, 
 403 
 
 8CH 
 
 "PANDEAN pipes, the, 210 
 
 Ji Piano-wires, clang of, 148 
 
 curves described by vibrating, 150 
 Pipes. (See ORGAN-PIPES.) 
 
 Pitch of musical sounds, 85 
 
 illustration of the dependence of 
 pitch on rapidity of vibration, 94 
 
 relation of velocity to pitch, 199 
 
 velocity deduced from pitch, 219 
 Plateau, his theory of the resolution 
 
 of a liquid vein into drops, 277, 
 286 
 
 Pythagoreans, notions of the, regard- 
 ing musical consonance, 385 
 
 T) A IN, reputed power of obstruct- 
 j\i ing sound, 321 
 
 artificial, passage of sound through, 
 324 
 
 Reeds and reed-pipes, 220 
 
 the clarionet and flute, 223 
 Reflection of sound, 43 
 
 from gases, 312 
 
 aerial, proved experimentally, 242 
 Refraction of sound, 49 
 Resonance, 200 
 
 of the air, 201, 240 
 
 of coal-gas, 203 
 
 of the mouth, 227 
 Resonators, 205 
 
 Resultant tones, discovery of, 375 
 
 conditions of their production, 375 
 
 experimental illustrations, 377 
 
 theories of Young and Helmholtz, 
 380, 382 
 
 Reversibility, acoustic, 433, 441 
 
 Robinson, Dr., his summary of exist- 
 ing knowledge of fog-signals, 288 
 
 Robinson, Professor, his production 
 of musical sounds by puffs of air, 
 83 
 
 Rod, vibrations of a, fixed at both 
 ends ; its subdivisions and corre- 
 sponding overtones, 156, 186 
 
 vibrations of a rod fixed at one 
 end, 157, 186 
 
 of rods free at both ends, 164, 
 
 186 
 
 SAV ART'S experiments on the in- 
 fluence of sounds on jets of 
 water, 429. 
 
 Schultze's bristles in the mechanism 
 of hearing, 399 
 
INDEX. 
 
 Sea-water, velocity of sound in, 67 
 
 Sensitive flames, 257 
 
 Smoke-jets, action of musical sounds 
 
 on, 272 
 Snow, its reputed power to obstruct 
 
 sound, 323 
 Solids, velocity of sound transmitted 
 
 through, 66, 67 
 
 musical sounds transmitted 
 through, 107 
 
 determination of velocity in, 199 
 Sonometer, or monochord, the, 113 
 Sorge, his discovery of resultant 
 
 tones, 375 
 
 Sound, production and propagation 
 of, 32, 73 
 
 experiments on sounding bodies 
 placed in vacuo, 36, 73 
 
 deadened by hydrogen, 38 
 
 action of hydrogen upon the voice, 
 39 
 
 propagation of sound through air 
 of varying density, 40 
 
 amplitude of the vibration of a 
 sound-wave, 41, 73 
 
 the action of sound compared with 
 that of light and radiant heat, 43 
 
 reflection of, 44, 73 
 
 echoes, 47, 48, 73 
 
 sounds reflected from the clouds, 
 48 
 
 refraction of sound, 49, 73 
 
 inflection of sound, 61, 73 
 
 influence of temperature on veloci- 
 ty of sound, 52, 74 
 
 influence of density and elasticity 
 on velocity, 63, 74 
 
 determination of velocity, 54, 74 
 Newton's calculation, 56, 75 
 
 Laplace's correction of Newton's 
 formula, 56, 76 
 
 thermal changes produced by the 
 sonorous wave, 56, 75 
 
 velocity of sound in different gases, 
 66, 76, 77 
 
 in liquids and solids, 
 
 66-69, 76 
 
 influence of molecular structure 
 on the velocity of sound, 69, 76 
 
 velocity of sound transmitted 
 through wood, 70, 76, 77 
 
 diffraction of, 72, note, 73 
 
 physical distinction between noise 
 and music, 77 
 
 SOU 
 
 Sound continued. 
 
 musical sounds periodic, noise un- 
 periodic, impulses, 78 
 
 produced by taps, 80 
 
 by puffs of air, 83 
 
 pitch and intensity of musical 
 sounds, 85 
 
 vibrations of a tuning-fork, 86 
 
 M. Lissajous's method of giving 
 optical expression to the vibrations 
 of a tuning-fork, 88 
 
 description of the siren, and defi- 
 nition of the wave-length, 90 
 
 determination of the rapidity of 
 vibration, 95 
 
 and of the length of the corre- 
 sponding sonorous wave, 96 
 
 various definitions of vibration and 
 of sound-wave, 97 
 
 limits of range of hearing of the 
 ear : highest and deepest tones, 99 
 
 double siren, 103 
 
 transmission of musical sounds 
 through liquids and solids, 106-109 
 
 the sonometer, or monochord, 113 
 
 vibrations of strings, 113 
 
 influence of sound-boards, 116 
 
 laws of vibrating strings, 118 
 
 direct and reflected pulses, 121 
 
 stationary and progressive waves, 
 122 
 
 nodes and ventral segments, 124 
 
 application of the results to the 
 vibration of musical strings, 130 
 
 M. Melde's experiments, 133, 400 
 
 longitudinal and transverse im- 
 pulses, 136 
 
 laws of vibration thus demonstrat- 
 ed, 139, 152 
 
 harmonic tones of strings, 143, 
 154 
 
 definitions of timbre, or quality, 
 of overtones and clang, 144, 154 
 
 relation of the point of string 
 plucked to overtones, 146 
 
 vibrations of a rod fixed at both 
 ends ; its subdivisions and corre- 
 sponding overtones, 156 
 
 of a rod fixed at one end, 157 
 
 Chladni's tonometer, 159 
 
 Wheatstone's kaleidophone, 160, 
 185 
 
 vibrations of rods free at both ends, 
 164, 185 
 
INDEX. 
 
 SOU 
 
 Sound continued, 
 
 nodes and overtones of a tuning- 
 fork, 165-167, 186 
 
 rendered visible, 167-169, 
 
 186, 187 
 
 vibrations of squared plates, 173, 
 186 
 
 of disks and bells, 176, 179, 187 
 
 sonorous ripples in water, 181, 187 
 Faraday's and Melde's experi- 
 ments on sonorous ripples, 183, 
 184, 187 
 
 longitudinal vibrations of a wire, 
 188 
 
 relative velocities of sound in 
 brass and iron, 191 
 
 examination of vibrating bars by 
 polarized light, 197 
 
 determination of velocity in solids, 
 199 
 
 relation of velocity to pitch, 199 
 
 resonance, 200, 238, 240 
 of the air, 201, 240 
 
 resonance of coal-gas, 203, 240 
 
 description of vowel-sounds, 226 
 
 Kundt's experiments on sound- 
 figures within tubes, 229, 243 
 
 new methods of determining veloc- 
 ity of sound, 232, 233, 243 
 
 causes that obstruct the propaga- 
 tion of sound, 288 
 
 action of fog upon sound, 289 
 
 contradictory results of fog-signal- 
 ing, 298 
 
 solution of contradictions of fog- 
 signaling, 298 
 
 extraordinary case of acoustic 
 opacity, 299 
 
 great change of acoustic transpar- 
 ency, 312 
 
 noise of battle unheard, 304 
 
 echoes from invisible acoustic 
 clouds, 306, 352 
 
 report of Arago on the velocity of, 
 308 
 
 aerial echoes of, 310 
 
 demonstration of reflection from 
 gases, 312 
 
 reflection from vapors, 316 
 heated air, 317 
 
 echo from flame, 318 
 
 investigations of the transmission 
 of sound through the atmosphere, 
 320 
 
 SOL 
 
 Sound continued. 
 
 action of hail and rain, 320 
 
 action of snow, 323 
 
 passage through tissues, 324 
 
 passage through artificial showers, 
 324 
 
 action of fog, 326 
 
 fluctuations of bells, 329, 331 
 
 action of wind, 338 
 
 atmospheric selection, 342 
 
 law of vibratory motions in water 
 and air, 354, 383 
 
 superposition of vibrations, 357 
 
 interference and coincidence of 
 sonorous waves, 311, 358, 383 
 
 extinction of sound by sound, 360, 
 383 
 
 theory of beats, 362, 383 
 
 action of beats on flame, 363, 884 
 
 optical illustration of beats, 366, 
 384 
 
 various illustrations of beats, 373 
 
 resultant tones, 375, 384 
 conditions of their produc- 
 tion, 375 
 
 experimental illustrations, 
 
 377 
 
 theories of Young and Helm- 
 
 holtz, 381, 382 
 
 difference - tones and summa- 
 tion-tones, 387 
 
 combination of musical sounds, 
 385 
 
 sympathetic vibrations, 397 
 
 mode in which sonorous motion 
 is communicated to the auditory 
 nerve, 400 
 
 Sound-boards, influence of, 116, 117 
 
 Sound - figures within tubes, M. 
 Kundt's experiments with, 229, 
 235 
 
 Stars, Doppler's theory of the col- 
 ored, 106 
 
 Steam-siren, description of, 291 
 
 conclusive opinion as to its power 
 for a fog-signal, 346 
 
 Stethoscope, Dr. Hook's anticipations 
 
 of the, 71 
 Stokes, Professor, his explanation of 
 
 the action of sound-boards, 117 
 
 his explanation of the effect of 
 wind on sound, 340 
 
 Solids, transmission of musical sounds 
 through, 109, 116 
 
INDEX. 
 
 447 
 
 STR 
 Straw-fiddle, formation of the, 166, 
 
 186 
 Strings, vibration of, 113 
 
 laws of vibrating strings, 118 
 
 combination of direct and reflected 
 pulses, 121 
 
 stationary and progressive waves, 
 122 
 
 nodes and ventral segments, 124, 
 125 
 
 experiments of M. Melde, 133 
 
 longitudinal and transverse im- 
 pulses, 136 
 
 laws of vibration thus demon- 
 strated, 139, 152 
 
 harmonic tones of strings, 143, 153 
 
 timbre, or quality, and overtones 
 and clang, 146, 154 
 
 Dr. Young's experiments on the 
 curves described by vibrating 
 piano-wires, 150 
 
 longitudinal vibrations of a wire, 
 188 
 
 with one end fixed, 
 
 192 
 with both ends free, 
 
 193 
 
 Summation-tones, 381 
 Siren, description of the, 90 
 
 sounds, description of the, 91 
 
 its determination of the rate of 
 vibration, 96 
 
 the double siren, 103, 386 
 
 the echoes of the, 310 
 
 rnARTINFS tones, 375. (See RE- 
 
 JL SULTANT TONES.) 
 
 Timbre, or quality of sound, defini- 
 tion of, 144 
 
 Tisley, Mr., his apparatus for the com- 
 pounding of rectangular vibrations, 
 420 
 
 Toepler, M., his experiment on the 
 rate of vibration of the flame, 252 
 
 Trumpets, range of, for fog-signals, 
 294 
 
 Tonometer, Chladni's, 159 
 
 Tuning-fork, vibrations of a, 87 
 
 - M. Lissajous's method of giving 
 optical expression to the vibra- 
 tions, 88 
 
 strings set in motion by tuning- 
 forks, 130 
 
 VIB 
 
 T uning-fork continued. 
 
 vibrations of the tuning-forks as 
 analyzed by Chlailni, 166 
 
 nodes and overtones of a tuning- 
 fork, 167, 186 
 
 interference of waves of the, 371 
 
 T7APORS, reflection from, 315 
 V Velocity of sound, influence of 
 temperature on, 52 
 
 influence of density and elasticity 
 on, 53 
 
 determination of, 54 
 
 Newton's calculation, 56 
 
 velocity of sound in different 
 
 and transmitted through various 
 liquids and solids, 66, 69 
 
 relative velocities of sound in brass 
 and iron, 194 
 
 relation of velocity to pitch, 199 
 
 velocity deduced from pitch, 219 
 Ventral segments, 124 
 
 Vertical jets, action of sound on, 279 
 
 286 
 Vibrations of a tuning-fork, 87 
 
 method of giving optical expres- 
 sion to the vibrations of a tuning- 
 fork, 88 
 
 illustration of the dependence of 
 pitch on rapidity of vibration, 95 
 
 the rate of vibration determined 
 by the siren, 95 
 
 determination of tho length of the 
 sound-wave, 96, 111 
 
 various definitions of vibrations, 
 97, 111 
 
 vibrations of strings, 113 
 
 laws of vibrating strings, 118 
 
 direct and reflected pulses illus- 
 trated, 121 
 
 application of the result to the 
 vibration of musical strings, 130 
 
 M. Melde's experiments on the vi- 
 bration of strings, 133 
 
 longitudinal and transverse im- 
 pulses, 136 
 
 vibration of a red-hot wire, 138 
 
 laws of vibration thus demon- 
 strated, 139, 152 
 
 new mode of determining the law 
 of vibration, 141 
 
 harmonic tones of strings, 143, 154 
 
INDEX. 
 
 VIB 
 
 Vibrations continued. 
 
 vibrations of a rod fixed at both 
 ends; its subdivisions and corre 
 spending overtones, 156 
 
 vibrations of a rod fixed at one 
 end, 157 
 
 Chladni's tonometer, 159 
 
 Wheatstone's kaleidophone, 160 
 
 vibrations of rods free at both 
 ends, 164 
 
 nodes and overtones rendered visi- 
 ble, 167, 169 
 
 vibrations of square plates, 173 
 of disks and bells, 176 
 
 longitudinal vibrations of a wire, 
 188, 239 
 
 with one end fixed, 192 
 
 with both ends free, 
 
 193 
 
 divisions and overtones of rods, 
 vibrating longitudinally, 195 
 
 examination of vibrating bars by 
 polarized light, 198 
 
 vibrations of stopped pipes, 208 
 of open pipes, 211 
 
 a node the origin of vibration, 236 
 
 law of vibratory motions in water 
 and air, 354 
 
 superposition of vibrations, 357 
 
 theory of beats, 362 
 
 sympathetic vibrations, 397 
 
 M. Lissajous's method of studying 
 musical vibrations, 407 
 
 apparatus for the compounding of 
 rectangular vibrations, 420 
 
 Violin, formation of the, 116 
 
 sound-board of the, 116 
 
 the iron fiddle, 160, 185 
 
 Voice, human, action of hydrogen 
 upon the, 39 
 
 sonorous waves of the, 98 
 
 description of the organ of voice, 
 224 
 
 causes of the roughness of the 
 voice in colds, 225 
 
 causes of the squeaking falsetto 
 voice, 225 
 
 Muller's imitation of the action of 
 the vocal chords, 226 
 
 formation of the vowel-sounds, 226 
 
 synthesis of vowel-sounds, 228 
 
 YOU 
 
 Vowel-flame, the, 269 
 Vowel-sounds, formation of the, 228 
 
 synthesis of, 228 
 
 WATER-WAVES, stationary, phe- 
 nomena of, 128 
 Water, velocity of sound in, 66, 67 
 
 transmission of musical sounds 
 through, 105 
 
 effects of musical sounds on jets 
 of water, 274 
 
 delicacy of liquid veins, 276 
 
 theory of the resolution of u liquid 
 vein into drops, 277, 286 
 
 law of vibratory motions in water, 
 354 
 
 Wave-length, definition of, 90 
 
 determination of the length of the 
 sonorous wave, 96 
 
 definition of sonorous wave, 97 
 Wave-motion, illustration, 121-125 
 
 stationary waves, 125 
 
 law of, 354 
 
 Waves of the sea, causes of the roar 
 
 of the breaking, 83 note. 
 Weber, Messrs., their researches on 
 
 wave-motion, 125 
 Wetterhorn, echoes of the, 47 
 Wheatstone, Sir Charles, his kaleido- 
 
 phone, 160 
 
 his apparatus for the compound- 
 ing of rectangular vibrations, 420 
 
 Whistles, range of, for fog.-signals, 294 
 Wind, effect on sound, 338 
 Wires. (See STRINGS.) 
 Wood, velocity of sound transmitted 
 through, 70 
 
 musical sounds transmitted 
 through, 107 
 
 the claque-bois, 165 
 
 determination of velocitv in wood, 
 199 
 
 Woodstock Park, echoes fh, 48 
 
 , Dr. Thomas, his proof of 
 JL the relation of the point of a 
 string plucked to the overtones, 145 
 
 on the curves described by vibrat> 
 ing piano-wires, 150, 151 
 
 his theory of resultant tones, 380 
 
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