306 Definition of Intensity in the Theories of Light and Sound. 



considerable influence^ has indeed expressed to me his surprise 

 that I could suppose the doctrine of the intensity increasing with 

 the amplitude to be maintained independently of the restriction, 

 cceteris paribus. He further states that he knows no one who 

 maintains the doctrine I impugn, and that he is in the habit 

 in his lectures of pointing out formally and explicitly that it is 

 only in comparing sounds of the same pitch, or lights of the 

 same refrangibility, that it is asserted that greater intensity and 

 greater amplitude of vibration go together. 



I cannot help thinking that if the writers whom I have cited 

 had been as well aw^are as ray correspondent of the limited 

 application of the received definition of intensity in the theories 

 of light and sound, they would have been as careful as he ap- 

 pears to have been in formally and explicitly indicating the fact. 



To me it appears to be simply inconceivable that Sir John 

 Herschel and Dr. Lloyd should have contrasted note and colour 

 as depending on frequency of impulse, with loudness and bright- 

 ness as depending on amplitude of excursion, if they had been 

 familiar with the fact that loudness and brightness depend just 

 as much on frequency of impulse as on amplitude of excursion 

 ■ — or that Mr. Airy should have assumed the intensity of the 

 light represented by the above formula to be denoted by c^, and 

 the colour to depend upon X, all the while knowing that the in- 

 tensity depends upon X just as much as does the colour — or 

 that Professor Tyndall should have spoken of the intensity of 

 sound being proportional to the maximum velocity, keeping 

 silent as to the time of vibration, having the fact present to his 

 mind that the intensity depends on the time of vibration just as 

 much as on the maximum velocity*. 



But whatever may be the degree of illumination prevailing at 

 Cambridge in regard to this subject, none such has extended to 

 Heidelberg, as appears conclusively from the following 

 passage : — 



" Mecaniquement, Pintensite des vibrations, pour des sons de 

 differentes hauteurs, est proportionnelle a la force vive, c'est a dire 

 au carre de la plus grande vitesse des molecules vibrantes. Mais 

 Poreille a une sensibilite differente pour les sons de differentes 

 hauteurs, en sorte qu^on ne pent arriver ainsi au veritable 

 rapport (pour les differentes hauteurs) entre Pintensite et la sen- 

 sation.^^ — Theorie Physiologique de la Musique, par H. Helmholz. 

 Traduit de P Allemand par M. G. Gueroult. Paris, 1868,p. 15,n.t 



But while expressing his consciousness of the defective 



* If definitions after the fashion my correspondent would attribute to 

 the writers referred to are tolerated in the " exact sciences," it is clear that 

 they must speedily lose all claim to the appellation. 



t The passage of which the above is the translation is retained intact in 

 the German edition of 1870 (see p. 20)* 



