402 



Transactions of the Socirti/. 



progression : for the fact that polarised light behaves differently in 

 different azimuths can only be explained by the assumption of 

 transverse disturbances. These three experimental facts, in con- 

 junction with some others, lead to the equation expressing light 

 undulations, which for our present purposes may be put into the 

 simple form 



(I) 



£ = A sin 2?r (V.t - x) 

 \ 



where f is the disturbance at the time t in a given point at the 

 distance x from a fixed point. V is the velocity, and X the wave- 

 length of the light, whilst A, the " amplitude," introduces the 

 brightness of the light which is proportional to the square of A. 

 The equation shows that at any one point the disturbance at 



regular intervals of time f =— ) attains a maximum value equal 



to A ; that, having attained this value, it gradually diminishes and 

 passes through zero ; that it next assumes negative valves down 

 to — A ; and thence returns gradually to the maximum value -f-A. 



<r 



A 



Fig. 74. 



It also shows that for different values of x, i.e. for different 

 points in the line of propagation, the disturbance is different at the 

 same instant, and passes through the complete cycle of values for 

 each increase of x by \, hence the " ether-particles " at any given 

 instant lie in a wave-line like fig. 1, and the wave propagation is 

 equivalent to this curve travelling along at the velocity V. 



When two or more such wave-motions meet, each one causes 

 disturbances in the ether, or " displaces the ether- particles " as if 

 the latter were at rest, and the resultant disturbance is that which 

 follows if each wave is assumed to have moved the particles the 

 proper amount resulting from its own equation, independently of 

 the other waves. It will be seen that this must often lead to very 

 complicated disturbances ; but the result, as far as human eyes can 

 realise it, may be brought under one or other of two heads, i.e. 

 either there is some permanent relation between the two or more 

 undulations that meet, and then we have the possibility of inter- 

 ference phenomena, or the several undulations are independent of 



