360 Dr. H. Hudson on the Intensity of Light fyc. 



only be regarded as an illustration." Sir George writes (p. 20), 

 " We shall assume the intensity of the light to be represented by 

 c?V ; an d (in a note) adds, " We must take some even power of c 

 to represent the intensity, since the undulation where the vibra- 

 tion is expressed by — csin^ — (pt— #)+Q r differs in no 

 respect from that whose vibration is expressed by 



/2tt \ 



-fcsinf — (irf-.r) + Cj, 



except that it is half the length of a wave before or behind it." 

 It would appear, therefore, that the Astronomer Royal was 

 influenced to adopt the ' ' square " of the amplitude as the mea- 

 sure of intensity chiefly because the even powers of positive and 

 negative quantities are {algebraically) identical. 



I would suggest, however, that the true physical interpretation 

 of the signs (+ and — ) prefixed respectively to two perfectly 

 similar vibrations is that " the coefficient (c) must be measured 

 in opposite directions from the point of rest of the disturbed par- 

 ticle," which in fact constitutes the difference, by half a wave- 

 length, of these two similar vibrations ; and it is evident (alge- 

 braically as well as physically) that the combination of any two 

 such vibrations must produce zero (i. e. darkness in the case of 

 light), or in optical language "interference." 



1 would now submit my view of Sir George Airy's argument 

 (in his note, p. 20) to the consideration of mathematicians. 

 First, let us assume (with Sir George, p. 7) that c is the " maxi- 

 mum vibration of the disturbed particle;" in this case (the 

 wave-length and amplitude being identical) it appears to me 

 that the only effect of introducing C and D into two perfectly 

 similar vibrations is (see 'Undulatory Theory/ p. 6) to "alter 

 the origin of the linear measure from which x is reckoned," and 

 that no conclusion as to the "influence of amplitude on inten- 

 sity" can be deduced from such a change. Secondly (c and X 

 being still alike in both the new forms), if we consider c to re- 

 present merely the "actual distance of the disturbed particle 

 from its place of rest," the introduction of C and D into the 

 vibration-formula may also represent a " change of phase of the 

 wave." But (inasmuch as c no longer represents the maximum 

 vibration) it will not 'be possible to deduce any "influence of 

 amplitude on intensity" from the formulae even in this case. 

 Musical men are aware that a "pizzicato note" from a stringed 

 instrument, even with very moderate amplitude of vibration, 

 can be heard at a considerable distance. Suppose now that such 

 a sound wave (with 1 inch amplitude) becomes insensible at 200 

 feet : if the amplitude be reduced to half an inch, the distance 



