Mr Priestley, On the Oscillations of Superposed Fluids. 309 



Comparing this with the standing wave given by (10) [section II] 

 we see that the forms of the propagated and standing waves 

 are the same if we neglect the second power of the ratio of the 

 amplitude to the wave length but are different if we proceed to 

 a higher approximation. 



Period. 



We have seen that the period equations are not altered by 

 terms of order k^. When we proceed to the next approximation 

 the period of the standing wave is given by (9) [section II] while 

 that of the propagated wave is found from 



p2 = gk{l- s)/(l + s) [1 + k'^' (1 + sO/(l + s)'] 

 [(5) section I]. 



We see that the period 2'7r/p given by the first order equation 

 is too long for the propagated waves and too short for the standing 

 ones. We proceed to tabulate the periods for waves of length 

 10 ft. and 100 ft. We take 



k^ = "5 and g = 3216 f.s.s. 



