230 The late Lord Rayleigh on Resonant 



(B, A, fig. 1) representing the two members of (27), 

 regarding X^ and k 2 as abscissae and taking as ordinates 



2/ = & 1 sin2& 1 , y' = k 2 smb. 2k 2 . . . . (30) 



Fig. 1. 



If k, and k 9 be both small, 



y=2h\l-W), ;/ = 2V(l +p-/) ; 



(31) 



so that at the origin both curves touch the line of abscissae 

 and start with the same curvature. Subsequently y ' >y and 

 increases with great rapidity. On the other hand, y vanishes 

 whenever k x is a multiple of \tt, although the successive loops 



