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Transactions of the Society. 



aggregate effect will be the simple total of the individual effects The 

 whole disturbance produced by any one wave-front under these 

 conditions falls as a single blow at a single indivisible point of time. 

 There can be no interference by one wave-front with the work of its 

 predecessor, but every one in turn produces its whole effect without 

 impediment from wave-fronts that have gone before, and without 

 diminution from those that follow. Here the intensity of the resulting 

 light is at its maximum. 



But the point |; 2 is in a different case. Here the impulse received 

 from the extended wave-front does not fall as a single blow, for the 



simple reason that the distance 

 Fir,. 87. of the receiving point from one 



point upon the wave-front differs 

 from its distance from another 

 point. Hence those parts of 

 the whole impulse which are re- 

 ceived from nearer points upon 

 the wave-front will arrive earlier 

 than those other parts that have 

 had farther to travel, and. the 

 whole effect of the wave-front 

 will arrive in a stream of partial 

 effects ; — a pressure, so to speak , 

 lasting for a finite time, instead 

 of a sharp or single blow. Now 

 this extended duration of the 

 working of any one wave-front 

 on the point p., gives occasion 

 for the successive wave-fronts to 

 overlap in their action. Before 

 one has finished, another must 

 have begun, for there are no 

 gaps in their ranks, and so arises 

 (he possibility of interference. 

 And this is not a possibility only, 

 it is a thing that must occur ; for 

 two wave-fronts cannot (save exceptionally) concur in time and space 

 without more or less counter-working one another. The counter- 

 action may be very slight when they are nearly in the same phase, 

 and there is one, the exceptional case just referred to, in which they 

 simply reinforce one another without any counter-working. That 

 occurs when the successor is one exact wave-length or any integral 

 number of wave-lengths behind the predecessor. In that case the 

 two wave-fronts will coincide in phase, and such wave-fronts must of 

 necessity follow one another at intervals which are integral multiples 

 of the period of oscillation. But all the intervening wave-fronts must 

 coalesce only imperfectly with their leader, and therefore must counter- 



