512 Prof. Arthur Schuster on 



theorem be resolved into a series of disturbances each of 

 which corresponds to homogeneous light. It is the object of 

 a spectroscope to separate laterally these homogeneous vibra- 

 tions, and no matter what the nature of the original light, the 

 greater the resolving power of the spectroscope, the more 

 nearly will it give us homogeneous light. 



4. The argument is at once seen to be conclusive in one 

 direction. However irregular the original light, interference 

 bands with large difference of path may always be produced, 

 if a spectroscope of sufficiently high resolving power is used. 

 But there is another side to the question. In order that 

 Fourier's series should correctly represent a given disturb- 

 ance, there must be a definite phase relation between the 

 different terms of the series. If a spectroscope of small 

 resolving power is used, and if it is required to calculate the 

 disturbance at the focus, we are not allowed to consider the 

 different components of Fourier's series as independent, but 

 must take account of this relation of phase. An example 

 will show that in special cases altogether incorrect results 

 will be obtained if this is neglected. Thus, let the light 

 falling on the slit of a spectroscope be screened off until a 

 given time, when the screen is removed but replaced subse- 

 quently after a short interval. The disturbance may by 

 Fourier's series be decomposed into a series of simple * 

 vibrations lasting through an infinity of time ; and if each 

 component could be treated independently of another, it 

 would follow that an eye examining the spectrum would 

 continue to see light for any length of time after the incident 

 beam has been cut off. This of course is absurd. The 

 analysis by Fourier's series leads to results which are per- 

 fectly correct, if, when finite resolving powers are used, we 

 take account of the phase relations between the component 

 vibrations. 



It seems therefore advisable to consider the effects of 

 finite resolving powers a little more in detail, although it will 

 appear that even then the effects produced can give us no 



* Is it too late to abolish tlie term "harmonic " vibration to express the 

 projection of a uniform circular motion? The term " harmonic" seems 

 to me to imply a relation between two things, and is very useful when we 

 want to distinguish between, say, harmonic and inharmonic overtones. 

 It is quite correct to speak of the expansion in a Fourier's series as an 

 harmonic expansion, because the different terms are harmonically related, 

 but each of them taken separately is not harmonic. Much confusion 

 has been caused by a series of lines in a spectrum being called harmonics, 

 because their distribution suggested some definite connexion between their 

 periods, independently of the question whether that connexion was of 

 the harmonic character. The term " simple " vibration seems to me to 

 be well adapted to express a sine vibration. 



