Definition of Intensity in the Theories of Light and Sound. 39 



But this alternative definition, just as much as the former, 

 stands in need of correction. For, any claim which the maxi- 

 mum velocity can have to be regarded as the test of the intensity 

 of a note or ray must rest on the assumption of its correctly 

 representing the effect of a single undulation on the organ 

 operated upon ; and, admitting this to be the case, the true 

 measure of intensity must be the square of the maximum velo- 

 city divided by the periodic time ; so that instead of the measure 

 of intensity being some constant multiple of the ratio of the 

 squares of the amplitude and periodic time, it must be a constant 

 multiple of the ratio of the square of the amplitude to the cube of 

 the periodic time. 



My reason for considering that the square of the amplitude 

 cannot enter as a factor into the expression for the intensity is 

 very simple. 



If we have two series of waves superposed, each of which is 

 represented by 



y = a sin — (vt—%), 



A 



the resultant vibration will be represented by 

 2/ = 2«sin^- (vt—w) ; 



A. 



from which it follows, if the square of the amplitude enters into 

 the expression for the intensity, that the two systems of vibra- 

 tions combined will produce four times the amount of illumina- 

 tion (supposing light to be referred to) which either would 

 produce separately- — a conclusion which appears absolutely fatal 

 to this mode of estimating the intensity*. 



That the data upon which Mr. Bosanquet founds his experi- 

 mental determination of the measure of intensity are precarious, 

 must, I conceive, strike every one. That the result he obtains 

 is inadmissible, appears to follow from the following considera- 

 tions. 



Let a, a l be the amplitudes of two notes at opposite extremi- 

 ties of the musical scale; separated, say, by seven octaves. 

 Then, if t be the periodic time of the one, 2 7 . t will be that of 



hension, inasmuch as the particles of air in contact with the tympanal 

 membrane must necessarily have the same velocity as the latter. 



If I remember rightly, Fresnel distinguishes between the intensity of the 

 vibration itself and that of the sensation resulting from it — expressing the 

 former by the simple power, the latter by the square of the maximum 

 velocity. 



* The only attempt to prove that the square of the amplitude and not 

 its simple power should be taken, with which I am acquainted, assumes as 

 a postulate that two candles will give twice the illumination of one ! See 

 Airy's * Tract on the Undulatory Theory ' in loco. 



