440 



NATURE 



[March 6, 1884 



to the nerves and the bones, we have gone beyond the subject I 

 proposed to speak upon. My subject belongs to physical 

 science ; — what is called in Scotland, Natural Philosophy. 

 Physical science refers to dead mailer, and I have gone beyond 

 the range whenever I speak of a living body ; but we must speak 

 of a living body in dealing with the senses as the means of 

 perceiving — as the means by which, in John Banyan's language, 

 the soul in its citadel acquires a knowledge of external matter. 

 The physicist has to think of the organs of sense, merely as he 

 thinks of the microscope ; he has nothing to do with pliyslology. 

 He has a great deal to do with his own eyes and hands, how- 

 ever, and mu^t think of them, if he would understand what he 

 is doing, and w ishes to get a reasonable view of the subject, 

 whatever it may be, which is before him in his own depirtment. 

 Now what is the external object uf this internal action of 

 hearing and perceiving sound ? The external object is a change 

 of pressure of air. Well, how are we to define a sound simply ? 

 It looks a little like a vicious circle, but indeed it is not so, to 

 say it is sound if we call it a sound— if we perceive it as .sound, 

 it is sound. Any change of pressure, whicli is so sudden as to 

 let us perceive it as sound is a sound. There [giving a sudden 

 clap of the hands]— that is a sound. There is no question about 

 it — nobody will ever ask, Is it a sound or not ? It is sound if 

 you hear it. If you do not hear it, it is not to you a sound. 

 Thai is all I can say to define sound. To explain what it is, I 

 can say, it is change of pressure, and it differs from a gradual 

 change of pressure as seen on the Ijarometer only in being more 

 rapid, so rapid that we perceive it as a sound. If you could 

 perceive by the ear, that the barometer has fallen two-tenths of 

 an inch to day, that would be sound. But nobody hears by his 

 ear that the barometer has fallen, and so he does not perceive 

 the fall as a sound. But the sa-ne difTerence of pressure co'.nin.; 

 on us suddenly — a fall of the barometer, if by any mems it could 

 happen, amounting to a tenth of an inch, and taking place in a 

 thousandth of a second, — would affect us quite like sound. A 

 sudden rise of the barometer would produce a sound analogous 

 to what happened when I clapped my hands. What is the 

 difference between a noise and a musical sound ? Musical sound 

 is a regular and periodic change of ]iressure. It is an alternate 

 augmentation and diminution of air pressure, occurring rapidly 

 enough to be perceived as a sound, and taking place with perfect 

 regularity, period after period. Noises and musical sounds 

 merge into one another. Musical sounds have a possibility at 

 least of sometimes ending in a noise, or tending too much to a 

 noise, to altogether please a fastidious musical ear. All rough- 

 ness, irregularity, want of regular, smooth periodicity, has the 

 effect of playing out of tune, or of music that is so complicated 

 that it is Impossible to say whether it is in tune or not. 



But now, with reference to this sense of sound, there is some- 

 thing I should like to say as to the practical lesson to be drawn 

 from the great mathematical treatises which were placed before 

 the British Association, in the addresses of its president. Prof. 

 Cayley, and of the president of the mathematical and physical 

 section, Prof. Henrici. B jth of these professors dwelt on the 

 importance of graphical illustration, and one graphical illustra- 

 tion of Prof. Cayley's address miy be adduced in respect of this 

 very quality of sound. In the language of mathematics we have 

 just "one independent variable" to deal with in sound, and that 

 is air pres ure. We have not a complication of motions in 

 various directions. We have not the complication that we shall 

 have to thinic of presently, in connecti n\ with the sense of 

 force ; complication as to the place of application, and the 

 direction, of the force. We have not the infinite complications 

 we have in some of the other senses, notably smell and taste. 

 We have distinctly only one thing to consider, and that is air 

 pressure or the variation of air pressure. Now when we have 

 one thing that varies, that, in the language of mathematics, is 

 " one independent variable." Do not imagine that mathematics 

 is harsh, and crabbed, and repulsive to common sense. It is 

 merely the etherealisali m of common .-ense. The function of 

 one independent variable that you have here to deal with is the 

 pressure of air on the tympanum. Well now in a thousand 

 counting houses and business offices in Birmingham and London, 

 and Glasgow, and Manchester, a curve, as Prof. Cayley pointed 

 out, is regularly used to show to the eye a function of one inde- 

 pendent variable. The function of one inde|)endent variable 

 most important in Liverpool perhaps may be the price of cotton. 

 A curve showing the price of cotton, rising when the price of 

 cotton is high, and sinking when the price of cotton is low, 

 shows all the complicated changes of that independent variable 



to the eye. And so in the Registrar-General's tables of mortality, 

 we have curves showing the number of deaths from day to day — 

 the painful history of an epidemic, shown in a rising branch, 

 and the long gradual lalus in a falling branch of the curve, when 

 the epidemic is overcome, and the normal state of health is 

 again approached. All that is shown to the eye ; and one of 

 the most beautiful results of mathematics is the means of show- 

 ing to the eye the law of variation, however complicated, of one 

 independendeni variable. But now for what really to me seems 

 a marvel of marvels : think what a complicated thing is the 

 result of an orchestra playing — a hundred instruments and two 

 hundred voices singing in chorus accompanied by the orchestra. 

 Think of the condition of the air, how it is lacerated sometimes 

 in a complicated effect. Think of the smooth gradual increase 

 and diminution of pressure — smooth and gradual, though taking 

 place several hundred times in a second — when a piece of beauti- 

 ful harmony is heard ! Whether, however, it be the single note 

 of the most delicate sound of a flute, or the purest piece of 

 harmony of two voices singing perfectly in tu e ; or whether it 

 be the crash of an orchestra, and the high notes, soaietimes even 

 screechings and tearings of the air, which you may hear fluttering 

 above the sound of the chorus— think of all that, and yet that is 

 not too complicated to be represented by Prof. Cayley, with a 

 piece of chalk in his hand, drawing on the blackboard a single 

 line. A single curve, drawn in the manner of the curve of prices 

 of cotton, describes all that the ear can possibly hear, as the 

 result of the most complicated musical performance. How is 

 one sound more complicated thin another? It is simply that in 

 the complicated sound the variations of our one independent 

 variable, jjressure of air, are more abrupt, more sudden, less 

 smooth, and less distinctly periodic, than they are in the softer, 

 and purer, and simpler sound. But the superposition of the 

 different effects is really a marvel of marvels ; and to think that 

 all the different effects of all the diflferent instruments can be so 

 represented ! Think of it in this way. I suppose everybody 

 present knows what a musical score is — you know, at all events, 

 what the notes of a hymn tune look like, and can understand 

 the like for a chorus of voices, and accompanying orchestra — a 

 "score" of a whole page with a line for each instrument, 

 and with perhaps four different lines for four voice parts. 

 Think of how much you have to jjut down on a page of manu- 

 script or print, to show what the different performers are to do. 

 Think, too, how much more there is to be done than anything 

 the composer can put on the page. Think of the expression 

 which each player is able to give, and of the diflference between 

 a great player on the violin and a person who simply grinds suc- 

 cessfully through his part ; think, too, of the difference in 

 singing, and of all the expression put into a note or a sequence 

 of notes in singing that cannot be written down. There is, on 

 the written or printed page, a little wedge showing a diminuendo, 

 and a wedge turned the other way showing a crescendo, and 

 that is all that the musician can put on paper to mark the 

 difference of expression which is to be given. Well now, all 

 that can be represented by a whole page or two pages of 

 orchestral score, as the specification of the sound to be produced 

 in say ten seconds of time, is shown to the eye with perfect 

 clearness by a single curve on a riband of paper a hundred 

 inches lorg. That to my mind is a wonderful proof of the 

 pjtency of mathematics. Do nat let any student in this Insti- 

 tute be deterred for a moment from the pursuit of mathematical 

 studies by thinking that the great mathematicians get into the 

 realm of four dimensions, where you cannot follow them. Take 

 what Prof. Cayley himself, in his admirable address, which I 

 have already referred to, told us of the beautiful and splendid 

 power of mathematics for etherealising and illustrating common 

 sense, and you need not be disheartened in your study of 

 mathematics, but may rather be reinvigorated when you think of 

 the power which mathematicians, devoting their whole lives to 

 the study of mathematics, have succeeded in giving to that 

 marvellous science. 



{ To be contiuned. ) 



THE GEOLOGICAL POSITION OF THE 

 HUMAN SKELETON FOUND AT TILBURY 

 TN a paper on this subject read by Mr. T. V. Holmes, F.G.S., 

 -'■ at the meeting of the Essex Field Club on Saturday, 

 February 23, at Buckhurst Hill, the author pointed out that the 

 Tilbury skeleton was found in recent .alluvium. The section at 



