The pressure gradient in the x direction is 



£ * - k M &) <=os Ctoc+(«0 • (32) 



WTT* 



C-cos-^ (33 } 



Thus j the hodograph with respect to time is in the form of an ellipse, and 

 also the particle motion is elliptical in the xy plane. The horizontal 

 particle path is shown in figure 7. 'The horizontal and vertical motions 

 are represented schematically in figure 7. The figure consists of three 

 parts. The uppermost represents the ellipses of motion near the surface 

 and near the bottom., which are 180° out of phase. The middle portion of 

 the figure shows an east-west vertical section with one wavelength repre- 

 sented. At the points marked with plus and minus signs the flow is out of 

 and into the paper respectively. Three pressure surfaces, Pj_, P?j and P3, 

 indicate the perturbation pressure gradients. It will be noted that P2 xs 

 shown somewhat nearer the bottom than the corresponding depth h/2, and that 

 for this pressure there is no horizontal pressure gradient and thus no hori- 

 zontal motion^ all the motion is vertical at this point. This follows since 

 the second term in equation (12) is not zero at h/2, so that the minimum per- 

 turbation pressure P = is found at some z = h/2 plus a small amount. The 

 third part of the figure shows the displacement of the 66° F. isotherm is 

 relation to the wave propagation. In actuality, the wavelength is essen- 

 tially that of the earth's circumference, so that only a portion of one cell 

 is found in the Atlantic Ocean. However, the complete cycle passes each 

 point in the ocean during a lunar day as the wave propagates westward. 



Figure 3 maybe reexamined In the light of the above findings. It is 

 suggested that since the inertial period is 21.7 hours plus an unknown amount 

 depending on the ratio of the depth to the wave length (from equation 30 ), 

 the spectral bands center-id at 20 and 2\x hours show the greatest power. 

 There is a sharper peak in the band from 21.8 to 26.7 hours possibly be- 

 cause the diurnal tide acts in resonance with the inertial force. Corres- 

 pondingly, It is possible that no semidiurnal period shows on the power 

 spectrum because the inertial filter is "transparent" to waves of 12-hour 

 period^ i.e., the natural period (21.7 hrs.) of the inertial oscillations 

 is unresponsive to the 12-hour tidal constituent. 



In the case of stratified water, where a component due to gravity 



modifies %f ^~ by analysis similar to that given above, it can be shown 



that (5 for the free wave is given by the following approximate relation: 



