160 Intelligence and Miscellaneous Articles. 



space, and that the spectrum of the aurora is in reality the spec- 

 trum of that medium. 



Professor Harkness calls attention to the continual increase in 

 the wave-length of the light emitted by the brightest part of the 

 second band of the spectrum as a phenomenon hitherto unobserved. 

 He refers it to an increase of the temperature of the comet as it 

 approached the sun. 



ON THE INTENSITY OF SOUND AND LIGHT. 



To the Editors of the Philosophical Magazine and Journal. 



GrENTLEMEK", 



Glenville, Fermoy, Jan. 6, 1873. 



The subject of Mr. Moon's paper (Phil. Mag. vol. xlv.. p. 38) 

 deserves consideration physically as well as mathematically. The 

 formula for the intensity must necessarily embrace two factors, viz. 

 one representing the number of waves (of a given length), and the 

 other giving the amplitude of the vibration of the particle of aether 

 under consideration in each particular wave. 



In regard to the former, the Astronomer Royal's assumption as 

 to intensity of light from two candles (supposed perfectly alike) is 

 obviously legitimate ; at the same time I conceive (Mr. Moon's 

 view) that the " amplitude of the vibration " {not its square) truly 

 represents the other factor of the intensity formula. 

 . This point'can be easily tested experimentally as regards sound. 

 Thus a tense string with amplitude of vibration =1 ought to be- 

 come inaudible at twice the distance at which it ceases to be heard 

 with amplitude =0*70715, if the simple power of the amplitude 

 (not its square) be the correct assumption. 



As regards the mathematical formula for the displacement of a 



particle of the aether in a wave, viz. y=a sin — (vt—x), I believe a 



\ 



represents the distance of the disturbed particle from its place of 

 rest (not necessarily, therefore, the " maximum vibration" as stated 

 by the Astronomer Royal, ' Undulatory Theory,' p. 7), and conse- 

 quently that for an undulation comprising several waves of the 

 same period but varying amplitudes, the formula should be 



(a+a f + a" &c.) sin — (vt—x), not a 2 sin — . (vi— so). 

 A A 



Of course when there are waves of different periods, the expres- 

 sions for each undulation (or series of such waves) must be kept 

 distinct, and be added together to obtain the intensity. 



Hexky Hudson, M.D., M.R.I.A. 



