interference Phenomena. 523 



The maxima of light take place when q = /c, and the 

 amplitude of the principal maximum is 2?np/(q + fc). If this 

 is compared with the amplitude of the principal maximum 

 formed when an infinite train of waves falls on a finite 

 grating, it is easily seen that : The position of the principal 

 maximum and the amplitude at the principal maximum are the 

 same whether an infinite train of waves falls on a grating con- 

 taming 2N lines or whether the grating is considered infinite 

 and the train of waves is limited to 2N complete waves. If 

 we compare the time of vibration instead of the amplitude, we 

 must note an important difference in the two cases. With an 

 unlimited train of waves falling on a finite grating the period 

 is everywhere the same as in the incident light ; but when the 

 train of waves is limited, the period is that determined by the 

 position of the telescope. At the principal maximum the two 

 periods agree ; at other places they differ. 



13. We may now consider the case of two disturbances of 

 the same type following each other after an interval 2r. If 

 both consist of a single impulsive velocity, our previous result 

 can at once be applied. Such an impulse will at the focus of 

 a telescope produce as many oscillations as there are lines on 

 the grating, the complete time t' of each oscillation depending 

 on the position of the focussing lens. The disturbance will 

 therefore last through a time 2NV, and as long as t<NV 

 interference will take place — that is, the two trains of waves 

 will partially cover each other, and according to the relative 

 value of t' and t the energy during the period of overlapping 

 may be greater or smaller than the energy of the original 

 vibrations. But as soon as t^Nt', the waves are clear of 

 each other and no interference can take place. 



Let us now treat the same problem, taking the white light 

 to be " regular/' that is, to give an ultimately discontinuous 

 spectrum of homogeneous vibrations. 



We take the maximum velocity of the incident light to be 

 the same for all wave-lengths, in order to make it more closely 

 correspond to the single impulsive velocity, which, when 

 resolved by Fourier's theorem, draws no distinction between 

 different wave-lengths. The original disturbance, consisting 

 of two trains of waves following each other at a time 2t, is 

 now expressed by 



/(at) = cos/>£ + cosp(£— 2t), 



from which the disturbance at the focus of the telescope is 

 obtained as in (3) and found to be 



2 g sin kI [cos j)t + cos p (t — 2t) ] . 



