to the wave fronts. As the reflected waves cross the incident 

 waves, a pattern is set up consisting of equal parallelograms 

 advancing in the direction of one set of diagonals. 



At the corners of each parallelogram, the two trains of waves 

 are superposed giving maximum condensation, and likewise the cen- 

 ter of each parallelogram is a point of maximum rarefaction. Hence, 

 in each diagonal, there is a series of maxima and minima conden- 

 sations advancing with a velocity a/cosa. There are parallel lines 

 of zero condensation between each adjacent pair of lines in maxima 

 and minima. 



Rayleigh says, "It is especially remarkable that, if the 

 wave pattern were visible (like the corresponding water wave- 

 pattern to which the whole of the preceding argiiment is appli- 

 cable), it would appear to move forward without change of type 

 in a direction different from that of either component train, 

 and with a velocity different from that with which both component 

 trains move." This phenomenon has been observed in the N.Y.U. 

 ripple tank and a photograph showing one of the stages is pre- 

 sented here (fig. 12). If the conditions were the same as shown 

 in figiire 11, the wave pattern would appear to move in the direction 

 of the arrow, that is, in the positive x direction. 



Since the angle between the incident and reflected rays is 

 2a, the angle between either ray and the normal to the reflecting 

 plane is a. Then, the condensations may be written as 



cos ~ (at - X cosa - y sina) (9.1) 



A 



where A is the wave length, and 



28 



