May 11, 1900.] 



SCIENCE. 



733 



the appeal of music to tbe human mind and 

 heart that eluded his philosophy. 



Though this ancient question of the 

 physical basis of music is still a problem, 

 there is time here to note but two points, 

 and these have reference rather to the mode 

 of attack than to tbe problem itself: (1) 

 What scholarly musicians of to-day think 

 of as music differs to an important extent 

 from what was in Helmholtz's mind forty 

 years ago as truly, though not as widely, as 

 it differs from mediaeval music; (2) Ma- 

 terials available in recent years for the his- 

 torical study of European and Oriental scales 

 disclose several consciously-used principles 

 of scale-building which could not result in 

 the diatonic or harmonic scales for which 

 Helmholtz's overtone and resultant-tone 

 theory furnished- so strong a justification. 

 Perhaps the greatest value of the book has 

 been its stimulus to investigation in many 

 fields, especially in the psychology of 

 music ; yet in spite of all our modern prog- 

 ress the greater part of the work remains 

 as indispensable as ever. 



II. Since the publication of Hemholtz's 

 work the most noteworthy things in con- 

 nection with Acoustics have been : 



1. The multiplying and perfecting of 

 methods and instruments, especially by 

 Konig and Appunn ; the development of 

 the phonograph ; the application of photog- 

 raphy. 



2. The publication of Rayleigh's math- 

 ematical Theory of Sound ; of the ten volumes 

 of the Vierteljahrsschrift fur Musikiuissenschaft, 

 full of scholarly monographs on the musical 

 and historical side ; and of Ellis & Hopkins' 

 researches on musical scales. 



3. The developments in musical instru- 

 ments (especially the piano), so giving us 

 instruments of more accurate intonation 

 and of greater power, and unfortunately 

 driving out the older soft- toned instruments. 



4. The general introduction into the 

 household of the piano or reed organ, often 



leading psychologically to the conviction 

 that there can be no music without har- 

 mony. 



5. The building-up of several great col- 

 lections of musical instruments from vari- 

 ous lands and times, and the publication 

 of books and monographs based thereon. 



6. The accumulation of a vast amount of 

 observations and experiments in the field 

 of music- psychology. 



III. Confining our attention now to Phys- 

 ical Acoustics, we may consider a little 

 more in detail some of the recent advances 

 that can readily be grouped together. 



The Velocity of Sound in free air has been 

 shown to increase greatly for very intense 

 sounds, and has been measured in air com- 

 pressed up to 100 atmospheres ; the velocity 

 in air confined in tubes is found to be a 

 function of the diameter and nature of the 

 walls, and of the pitch. The velocity in 

 solids has been much studied, and meas- 

 ured even in such soft bodies as parafl&n 

 and rubber. 



The Frequency of Vibration in specially fa- 

 vorable cases is now measured to within a 

 few parts in a million ; so the writing tun- 

 ing-fork is now the usual means of dividing 

 a second, say into 100 parts ; but in ordi- 

 nary cases, especially where the pitch is 

 high, or the sound weak or of short dura- 

 tion, errors of some per cent, are frequent. 

 Quite recently the sets of high forks made 

 by Appunn for physiologists have been found 

 to be extravagantly in error ; but as partial 

 compensation for the disappointment the 

 science has been enriched by new experi- 

 mental methods. 



Of extreme importance to the modern 

 physicist is the question of the energy in- 

 volved in any movement. The experi- 

 mental study of Intensity of Vibration began, 

 I believe, with Topler and Boltzman's in- 

 genious optical determination, in 1870, of 

 the actual variations in density in the air 

 of a sounding organ pipe, and the distance 



