REFLECTION OF DIVERGING WAVES 385 



However, we are also interested in the case where the amplitudes are 

 not negligible. We shall confine our attention to those cases where, as in 

 plane or spherical waves at a distance from the source, the velocity is nor- 

 mal to the direction of propagation and the variations in the plane of the 

 wave front are negligible. (5a) then becomes much more complicated. 



V X 9 is, however, still a function of — , say 2Fi I — I . Then, for small varia- 



dt \dt/ 



*i — 



tions of — in the neighborhood of a particular value, we may write 

 dt 



where Fi i — ) is a function of the particular value of — . This relation is 

 to take the place of (5a). Similarly, if 



then, in place of (8a), we are to use, for small variations, 



When we come to the transition from (5a) to (6a), however, the situation 

 is somewhat different. To see how this comes about, we go back to the 

 behavior of the single gyrostat of Fig. 1. It was assumed above that the B 

 axis coincided with the y axis However, when the displacement of the 

 rotor about A is finite, this is no longer exactly true. The situation is then 

 as shown in Fig. 3. A rotation (p of the lattice about y displaces A in the .r z 

 plane by if. The accompanying rotation of the rotor about A causes B to 

 make an angle 6 with y, which is independent of <p. Then 



d^ a 



(ji2 = -r cos d. 



dt 



From (la) 



C - A f d<p . ,^ 



coi = ojs / -r cos 6 dt. 



A J dt 



Also 



d = I oji dt, 



C - A 



cos U -J- cos ddtdt, (11a) 



