* 



80 INTERFERENCE OF LTGIIT. 



phases. Let the waving lines AB and A'B', or AB and 

 A /X B /X , represent the two undulations, the distance of any 

 particle from its state of rest being represented by the ordi- 

 nate, or perpendicular, at the corresponding point of the 

 horizontal or mean line. Then, if the undulation A'B' be 

 superposed upon AB, the corresponding points of each being 

 in the same phase, it is evident that the distances by which 

 the particle at any point is removed from its state of rest by 

 each, mn and m'n', will be added together, and the space of 

 vibration doubled. "Whereas, if the undulations A X/ B /X and 

 AB, whose corresponding points are in opposite phases, be 

 superposed, the distances from the position of rest, mn and 

 ni"n", lie on opposite sides of the mean line, and when added 

 together destroy one another. Thus the space of vibration is 

 doubled, when the waves arrive at the same point in the 

 same phase : it is annihilated, when they arrive in opposite 

 phases. Now the intensity of the light is as the square of the 

 amplitude of vibration ; the intensity, therefore, is quadrupled 

 in the former case, and reduced to nothing in the latter. 



(100) Before we proceed to examine more particularly this 

 indication of theory, we may observe that it is altogether 

 analogous to what is known to take place in other cases of 

 vibratory motion. If two waves of water arrive at the same 

 point at the same instant, in such a manner that the crest of 

 one wave coincides with that of the other, their effects will 

 be added together, and the water at that point will be raised 

 into a wave, whose height is the sum of the heights of the 

 conspiring waves. If, on the other hand, the crest of one 

 wave coincides with the sinus, or depression of the other, the 

 height of the resultant wave will be the difference of the 

 components ; and, when these are equal, the resultant wave 

 will entirely disappear. 



The peculiarity of the tides in the port of Batsha fur- 



