462 Lord Rayleigh on the Character of the 



which shows that in this case the intermittent vibration is 

 equivalent to three simple vibrations of frequencies n, n + in, 

 n — m. 



In order to distinojuish wave-frequencies, whose difference 

 is small, a correspond ingly long series of waves is necessary ; 

 and of no finite train of irregular vibrations can it be said 

 that waves of a certain frequency are present, and waves of a 

 frequency infinitely little different therefrom absent. Neither 

 can the, proportions, in which the two are present be assigned. 

 In professing to assign these proportions, (5) and similar 

 formulae make assertions not directly supported by experi- 

 ment. In a sense all the formulae of mathematical physics 

 are in this predicament ; but here the assertion is of such a 

 nature that it could not be tested otherwise than by experi- 

 ments prolonged over all time. 



In practice it is. not time that brings the limitation, but the 

 resolving power of our instruments. In gratings the resolv-, 

 ing power is measured by the product of the total number of 

 lines and the order of the spectrum under examination *. It 

 will be allowing a good deal for the progress of experiment if 

 we suppose that in measurements of energy it may be possible 

 to discriminate wave-lengths (or frequencies) which differ by 

 a millionth part. But a million wave-lengths of yellow light 

 would occupy only 60 centim., and the waves would pass in 

 2 X 10~^ seconds ! Waves whose frequencies differ by less 

 than this are inextricably blended, even though we are at 

 liberty to prolong our observations to all eternity. 



At any point in the spectrum of a hot body there are, 

 therefore, mingled waves of various frequencies lying within 

 narrow limits. The resultant for any very short interval of 

 time may be identified with a simple train, whose amplitude 

 and phase, depending as they do upon the relative phases of 

 the components, must be regarded as matters of chance. 

 The probability of various amplitudes depends upon the 

 principles explained in a former communication, " On the 

 Resultant of a large number of Vibrations of the same Pitch 

 and of Arbitrary Phase. '"f After an interval of time com- 

 parable with 10~^ second the amplitude is again practically a 

 matter of chance ; so that during the smallest interval of 

 time of which our senses or our instruments could take cog- 

 nizance, there are an immense number of independent com- 

 binations. But, under these circumstances, as was shown in 

 the place referred to, we have to do merely with the sum of 

 the individual intensities. 



* Phil. Mag. vol. xlvii. p. 200 (1874). 

 t Phil. Mag. Aug. 1880. 



