NATURE 



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LORD RAYLEIGH'S ''SOUND." 

 The Theory of Sound. By J. W. Strutt, Baron Rayleigh, 

 Sc.D., F.R.S. Second edition, revised and enlarged. 

 Two volumes. Pp. xiv + 480, and xvi + 504. (London : 

 Macmillan and Co., 1894 and 1896.) 



IT was neither to be expected nor to be desired that 

 any alteration of the general plan of Lord Rayleigh's 

 " Sound " should be introduced in a new edition. A few 

 errors have been detected and corrected (they are very 

 few indeed), and the book has been considerably en- 

 larged ; but the characteristic features of the new portions 

 are those of the old, and our admiration is again aroused 

 by the skilful interweaving of theory and experiment, each 

 supporting and adorning the other. 



We are grateful, too, that there is a continuance of the 

 help which we have received from the author in " clear- 

 ing our minds of cant," or rather of that unquestioning 

 employment of conventional explanations which is its 

 equivalent in physical science. For example, many 

 would even now be contentedly repeating the ordinary 

 text-book theory of the maintenance of vibrations in an 

 electric bell had he not awakened them to the knowledge 

 that it was wholly beside the mark ; and the statement 

 that "a simple vibration involves i?tfinite continuance, 

 and does not admit of variations of phase or amplitude " 

 should be very useful to many more. 



The first important addition is an investigation of the 

 resultant of a large number of vibrations whose phases 

 are accidentally distributed. An expression is found for 

 the probability of a resultant intensity of any specified 

 magnitude, and the mean intensity is shown to be the 

 sum of the intensities of the components. 



Under the head of intermittent vibrations, the differ- 

 ence between intermittence artificially imposed upon a 

 simple vibration and the intermittence of beats is pointed 

 out and employed to explain some experimental results 

 obtained by Prof. A. M, Mayer. 



A section is added dealing with unstable systems 

 with one degree of freedom, and we are reminded that 

 the possibility of periodic motion under the operation of 

 impressed periodic force is no proof of stability. 



The maintenance of vibrations is then discussed, and 

 it is shown that if impulses are given to a vibrating 

 system whenever it passes through its equilibrium 

 position their effect is mainly upon the amplitude and 

 the period is sensibly unaltered ; while if they are given 

 at the moments when the system is at rest the effect is 

 mainly upon the period, the vibrations being neither 

 encouraged nor discouraged. An investigation is also 

 given of the theory of the maintenance of vibrations by a 

 periodic force whose frequency is double that of the 

 maintained system, as in one form of Melde's well- 

 known experiment and in the crispations of a liquid 

 observed by Faraday. 



Next we come to a description of some of the principal 

 methods for the accurate determination of absolute 

 pitch, including, of course, the author's excellent com- 

 parison of a fork with a clock pendulum by the use 

 of the phonic wheel. An account of this instrument has 

 NO. 1493, VOL. 58] 



been given earlier in the book, and its use with a counting 

 apparatus certainly brings a fairly good determination 

 within the reach of experimentalists of very moderate 

 skill. Another interesting method which is described 

 is that of counting the two sets of beats of overtones 

 which are heard when two notes 'whose interval is 

 an equal temperament-whole tone are sounded on a 

 harmonium. The method depends, of course, on the fact 

 that in Jtiaintained vibrations the frequencies of overtones 

 must be accurately multiples of that of the fundamental. 

 The necessity of this correspondence is proved later, but 

 a hint of it might have been given here with advantage 

 to the student ; for in acoustics, as in other matters, the 

 progress of the human mind is from the vulgar credulity 

 of accepting all overtones as accurately harmonic through 

 the vulgar incredulity of doubting whether any can be so. 



In the general treatment of vibrating systems an in- 

 vestigation of the effects of imposed constraints upon the 

 periods is given, also the theorems of Routh relating 

 to the roots of the equation defining the periods, with 

 an extension to unstable systems ; a section dealing with 

 the reaction upon the driving-point of a system thrown 

 into forced vibration is also added. Under the head of 

 transverse vibrations of strings the propagation of 

 progressive waves along a string whose mass is supposed 

 to be concentrated at equidistant points is considered, 

 and it is shown that there will be no such propagation if 

 the frequency is above a certain critical value. The 

 reflection of waves at the junction of two strings is 

 treated, also reflection produced by gradual change of 

 density, and it is shown how the analogue of dispersion 

 in optics is introduced if the string is considered to 

 possess finite stiffness, and that in this case the ordinary 

 formula for the intensity of the reflection must be 

 modified. Reflection at a junction is also discussed in 

 the case of longitudinal vibrations of bars, and the 

 weakness of the transmitted intensity when the change 

 of velocity at the junction is considerable is pointed out. 



A summary is given of the experiments of Elsas on 

 forced vibrations of membranes, and the march of the 

 nodal lines with varying frequency is described. In the 

 chapter on vibrations of plates an account is given of the 

 author's interesting observations on the notes of bells, 

 and his ingenious method of obtaining the nodal lines 

 corresponding to each note by utilising the beats 

 produced by asymmetry. 



The first volume ends with two new chapters, one on 

 the vibrations of thin cylindrical and spherical shells, 

 and one on electrical vibrations. In the latter the 

 theory of oscillatory currents in circuits with capacity and 

 induction is given, and applications to Hughes' induction 

 balance and Wheatstone's bridge are discussed. The 

 concentration of currents of high frequency on the out- 

 side of a conductor is also worked out, and the propaga- 

 tion of current waves along cables is treated, justice 

 being done to Heaviside's work on the effect of in- 

 ductance in diminishing distortion in telephony. The 

 mode of action of the telephone is also discussed, and 

 the author's results as to the minimum audible current 

 are given. 



In the chapter on aerial vibrations, which opens the 

 second volume, some interesting phenomena depending 

 upon the second order of small quantities are explained, 



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