Interference Phenomena. 531 



group of waves the waves move through the group, and the 

 configuration of the group changes. We can speak of definite 

 rate of propagation (U) of the group, because at definite inter- 

 vals r the group takes up the same shape displaced through 

 a distance Ut. A good idea of some of the phenomena of 

 group velocities may be obtained by considering a medium 

 in which the wave-velocity varies as a linear function of the 

 wave-length, for in that case the group velocity is independent 

 of the period ; but the discussion of this subject must be 

 reserved for a separate communication. 



17. It will be useful at this stage to inquire in what cases 

 w r e can legitimately apply the word " interference " to an 

 optical phenomenon. The essence of interference is the inde- 

 pendence of superposed vibrations ; in other words, the most 

 important point of an interference phenomenon is that there 

 is no interference as regards amplitude. There may, however, 

 be interference as regards energy. 



If a wave-front is propagated, we may say that this implies 

 interference, for if the different points of the wave-front acted 

 as separately vibrating points, and we summed up for energy 

 instead of for amplitude, a very different result from that 

 actually obtained would be arrived at. Diffraction may in 

 this way be said to be the absence of interference. But in 

 speaking of interference phenomena we may reasonably leave 

 out of account that which is involved in the propagation of a 

 wave-front. 



Consider a succession of separate but exactly similar im- 

 pulses, such as is shown in 



fig. 6. If the different dis- Fig. 6. 



turbances do not overlap, 

 there can be no interfer- 

 ence between them. But 

 if each impulse is analysed 

 by Fourier's theorem, the 



different wave-lengths will be represented with different in- 

 tensities. If the sum of the disturbances is analysed, the 

 relative intensity of the different terms of the series will be 

 modified, and considerably so if the impulses are numerous 

 and succeed each other at regular intervals. The leading 

 term in the expansion will be that having a wave-length equal 

 to the distance between the impulses. From the point of view 

 of Fourier's series, we may say that the different disturbances 

 have " interfered/' but the series being only a mathematical 

 representation of the curve shown in the figure, I think the 

 term interference would be misleading. We shall reserve the 

 word interference exclusively for the case that the total energy 



