The Ocean at Rest {Statics of the Ocean) 



339 



Fig. 137. Quasi-static equilibrium in the ocean, A and B: two oceanographic stations. 

 At station A the pressures Pi, p^, P3, etc., under the assumption of static equilibrium are 

 found at the dynamic depths Di. D^, D3, etc., on the contrary at station B at the dynamic 

 depths D4', D2', D3' etc. From this the inclination of the isobaric surfaces relative to that 

 of the equi-potential surfaces can be deduced for the oceanic space between A and B. 



Taking the hydrostatic equation (XI. 1) gives after some rearrangements 



e . , .dp 



and from this 



{ph\ — (Ph)i = 





For a dynamic section the integral can be directly evaluated giving 



{piX — (ph)i = h(p2 — Pi), (XI.4) 



where ij, indicates the mean inchnation of the isopycnals. Introducing a mean value 

 of the density p in the thin layer under consideration the inclination of the upper iso- 

 baric surface relative to that of the lower ones is obtained 



'i>i 



Ipo = 



. P2 



Pi 



approx. — ia(Si — So) 



(XI.5) 



if the densities are replaced by corresponding anomaUes of specific volume. This 

 equation permits the relative inclination of the isobaric surfaces to be readily deter- 

 mined from the distribution of the specific volume anomaly in a dynamic section. It 

 also allows a determination of how closely isobaric and isosteric profiles fit together 

 in dynamic profiles that have been obtained and plotted from oceanographic data. 



3. Disturbances and Re-establishment of Static Equilibrium 



According to the principle of Archimedes, a stationary water mass will remain 

 floating and at rest within a more extended water mass if its weight is equal to the 

 weight of the displaced water. If it is heavier than the surrounding water it will sink 



