92 



NA TURE 



[Nov. 27, 1884 



able with the splendid and instructive experiments which many 

 of you have already seen. It is satisfactory to m : i" know that 

 so many of you, now present, are so thoroughly prepar 

 understand anything I can say, that those wh 1 have seen the 

 1 ., iriments will not feel their absence at this time. At the same 

 time I wish to make them intelligible to those who have nut had 

 the advantages to be gained by a systematic course of lectures. 

 I must say in the first place, without further preface, as time is 

 short and the subject is long, simply that sound and light are both 

 due to vibrations propagated in the manner of waves ; and 1 

 shall endeavour in the first place to define the manner of propaga- 

 tion and mode of motion that constitute those two subjects of our 

 senses, the sense of sound and the sense of light. 



Each is due to vibrations. The vibrations of light differ widely 

 from the vibrations of sound. Something that I can tell you 

 more easily than anything in the way of dynamics or mathematics 

 respecting the two classes of vibrations is, that there is a great 

 difference in the frequency of the vibrations of light when com- 

 pared with the frequency of the vibrations of sound. The term 

 "frequency " applied to vibrations is a convenient term, applied 

 by Lord Rayleigh in his book on sound to a definite number of 

 full vibrations of a vibrating body per unit of time. Consider, 

 then, in respect to sound, the frequency of the vibrations of notes, 

 which you all know in music represented by letters, and by the 

 syllables for singing, the do, re, mi, etc. The notes of the 

 modern scale correspond to different frequencies of vibrations. 

 A certain note and the octave above it correspond to a certain 

 number of vibrations per second and double that number. 



I may explain in the first place conveniently the note called 

 "C" ; I mean the middle "C" ; I believe it is the C of the 

 tenor voice, that most nearly approaches the tones used in 

 speaking. That note corresponds to two hundred and fifty-six 

 full vibrations per second, two hundred and fifty-six times to and 

 fro per second of time. 



Think of one vibration per second of time. The seconds 

 pendulum of the clock performs one vibration in two seconds, or 

 a half vibration in one direction per second. Take a ten-inch 

 pendulum of a drawing-room clock, which vibrates twice as fast 

 as the pendulum of an ordinary eight-day clock, and it gives a 

 vibration of one per second, a full period of one per second to 

 and fro. Now think of three vibrations per second. I can 

 move my hand three times per second easily, and by a violent 

 effort I can move it to and fro five times per second. With four 

 times as great force, if I could apply it, I could move it twice 

 five time; per second. 



Let us think, then, of an exceedingly muscular arm that would 

 cause it to vibrate ten times per second, that is ten times to the 

 left and ten times to the right. Think of twice ten times, that 

 is, twenty times per second, which would require four times as 

 much force ; three times ten, or thirty times a second, would 

 require nine times as much force. If a person were nine times 

 as strong as the most muscular arm can be, he could vibrate his 

 hand to and fro thirty times per second, and without any other 

 musical instrument could make a musical note by the movement 

 of his hand which would correspond to one of the pedal notes of 

 an organ. 



If you want to know the length of a pedal pipe, you can cal- 

 culate it in this way. There are some numbers you must 

 remember, and one of them is this. You, in this country, are 

 subjected to the British insularity in weights and measures ; you 

 use the foot and inch and yard. I am obliged to use that system, 

 but I apologise to you for doing so, because it is so inconvenient, 

 and I hope all Americans will do everything in their power to 

 introduce the French metrical system. I hope the evil action 

 performed by an Engli-h Minister, whose name I need not 

 mention, because I do not wish to throw obloquy on any one, 

 may be remedied. He abrogated a useful rule, which for a short 

 time was followed, and which I hope will soon be again en- 

 joined, that the French metrical system be taught in a 1 our 

 national schools. I do not know how it is in America. The 

 school system seems to be very admirable, and I hope tin- 

 teaching of the metrical system will not be let slip in tin 

 American schools any more than the u-e of the globes. 



I say this seriously. I do not think any one knows how 

 seriously I speak of it. I look upon our English system as a 

 wickedly brain-destroying piece of bondage under which we 

 suffer. The reason why we continue to use it is the imaginary 

 difficulty of making a change, and nothing else ; but I do not 

 think in America that any such difficulty should stand in the way 

 of adopting so splendidly useful a reform. 



I know the velocity of sound in foe; per second. If I remem- 

 ber rightly, it is 10S9 feet per second in dry air at the freezing- 

 point, and 1 1 15 feet per second in air of what we call moderate 

 temperature, 59° or 6o° — (I do not know whether that tem- 

 perature is ever attained in Philadelphia or not ; I have had 

 no experience of it, but people tell me it is sometimes 59 or 

 6o° in Philadelphia, and I believe them) — in round numbers 

 let us call it 1000 feet per second. Sometimes we call it a 

 thousand musical feet per second, it saves trouble in calculating 

 the length of organ pipes -, the time of vibration in an organ 

 pipe is the time it takes a vibration to run from one end to the 

 other and back. In an organ pipe 500 feet long the period 

 would be one per second ; in an organ pipe ten feet long, the 

 period would be fifty per second ; in an organ pipe twenty feel 

 long, the period would be twenty-five per second at the same 

 rate. Thus twenty-five per second, and fifty per second of 

 frequencies, corresponds to the periods of organ pipes of twenty 

 feet and ten feet. 



The period of vibration of an organ pipe, open at both ends, 

 is approximately the time it takes sound to travel from one end 

 to the other and back. You remember that the velocity in dry 

 air in a pipe ten feet long is a little more than fifty periods per 

 second ; going up to 256 periods per second, the vibrations cor- 

 respond to those of a pipe two feet long. Let us take 5 12 

 periods per second; that corresponds to a pipe about a fo it 

 long. In a flute, open at both ends, the holes are so arranged 

 that the length of the sound-wave is about one foot, for one of 

 the chief " open notes." Higher musical notes correspond to 

 greater and greater frequency of vibration, viz., 1000, 2000, 

 4000 vibrations pei second ; 4000 vibrations per second corre- 

 spond to a piccolo flute of exceedingly small length ; it would 

 be but one and a half inches long. Think of a note from a little 

 dog-call, or other whistle, one and a half inches long, open at 

 both ends, or from a little key having a tube three-quarters of an 

 inch long, closed at one end ; you will then have 4000 vibrations 

 per second. 



A wave length of sound is the distance traversed in the period 

 of vibration. I will illustrate what the vibrations of sound are 

 by this condensation travelling along our picture on the screen. 

 Alternate condensations and rarefactions of the air are made 

 continuously by a sounding body. When I pass my hand 

 vigorously in one direction, the air before it become^ dense, 

 and the air on the other side becomes rarefied. When I move 

 it in the other direction, these things become reversed ; there is 

 a spreading out of condensation from the place where my hand 

 moves in one direction and then in the reverse. Each condens- 

 ation is succeeded by a rarefaction. Rarefaction succeeds 

 condensation at an interval of one-half what we call "wave 

 lengths." Condensation succeeds condensation at the full interval 

 of what we call wave lengths. 



We have here these luminous particles on this scale, 1 repre- 

 senting portions of the air close together, dense ; a little higher 

 up, portions of air less dense. I now slowdy turn the handle of 

 the apparatus in the lantern, and you will see the luminous 

 sectors showing condensation travelling slowly upwards on the 

 screen ; now you have another condensation ; making one wave 

 length. 



This picture or chart represents a wave length of four feet. It 

 represents a wave of sound four feet long. The fourth part of a 

 thousand is 250. What we see now of the actual scale represents 

 the lower note C of the tenor voice. The air from the mouth of 

 a singer is alternately condensed and rarefied just as you see 

 here. 



But that process shoots forward at the rate of one thousand 

 feet per second ; the exact period of the motion is 256 vibrations 

 per second for the actual case before you. Follow one particle 

 of the air forming part of a sound wave, as represented by these 

 moving spots of light on the screen; now it goes down, then 

 another portion goes down rapidly ; now it stops going down ; 

 now it begins to go up ; now it goes down and up again. 



As the maximum of condensation is approached, it is going up 

 with diminishing maximum velocity, 'the maximum of rare- 

 faction has now reached it, and the particle stops going up and 

 begins to move down. When it is of mean density the particles 

 are moving with maximum velocity, one way or the other. You 

 can easily follow these motions, and you will see that each 

 particle moves to and fro, and the thing that we call condensation 

 travels along. 



1 Alluding to a moving diagram of \v:i 

 yorking slide for lantern proji ' 



nd produced by a 



