density changes with time there would not be much change in the 

 coefficients, but this has not as yet been shown. However, 

 Pekerls (1937) and Wilkes ( 19i4-9 ) have investigated a similar 

 problem in the atmosphere, with the difference that they postu- 

 late a driving force rather than assume free waves. An exami- 

 nation of their work reveals the hope that a similar treatment 

 of the oceans will show that the Fourier coefficients will re- 

 main relatively conservative with time, since analogous terms 

 in the work of Pekerls depend only on the vertical density dis- 

 tribution and the location. 



Since the approximate conservativeness of the Fourier co- 

 efficients could not be demonstrated, it was decided to proceed 

 upon the assumption that a change in these values occurs. It 

 was further assumed that when this change occurred, it occurred 

 in such a manner that the change in che time components of the 

 semidiurnal and diurnal waves was a minimiun. This assumption 

 was predicated on the concept that, for any new set of initial 

 conditions, the ocean like all fluids will reach equilibrium 

 with these new conditions with the least possible change in the 

 motion. 



Many possibilities for minimizing changes other than the 

 above present themselves. For Instance, one could attack the 

 problem of minimizing the change in energy from one set of 

 conditions to another by minimizing the change in the square 

 of the amplitude. Another possibility would be to attempt to 

 minimize the change in the amplitudes and the phases themselves. 

 While these techniques obviously have merit, they were super- 

 Si 



