CHAPTER VIII. 



PRACTICAL SOLUTION OF THE HYDROSTATIC PROBLEM FOR THE SEA. 



75. Normal Equilibrium Relation and Small Deviations from this Relation. 



In order to illustrate the principle of unit-sheets, we have already calculated the 

 depth corresponding to a given pressure (section 36) and the pressure at a given 

 depth (section 39) of the sea having a constant salinity of 35 /oo and a constant tem- 

 perature of o C. This calculation gave us the fundamental tables 7 h and 15 h of 

 our Hydrographic Tables. In the ideal case of a sea with these constant values of 

 temperature and salinity we have thus fully solved the hydrostatic problem in both 

 its forms. 



The treatment of the problem generally is very much simplified by the circum- 

 stance that the variations in temperature and salinity only produce minute changes 

 in the equilibrium relation between depth and pressure. We can therefore con- 

 sider the equilibrium relation represented by tables 7 h or 15 h as the " normal " one. 

 The problem is then reduced to the determination of the small deviations from this 

 relation produced by the variations of temperature and salinity, or, as we may call 

 it, the "anomalies" of the equilibrium relation. 



To find the expressions for these anomalies, we have to start with the hydro- 

 static equation in either of its integral forms, section 40 (a) or (b). Instead of gravity 

 potential <f> we introduce the dynamic depth D, measured in dynamic meters and 

 counted positive downwards (section 10). Simultaneously we count the pressure 

 only as sea-pressure (section 27), expressed in decibars. Choosing the lower limit 

 of the integrals in the sea's surface, we then get as expression for the depth D cor- 

 responding to a given pressure p, 



(a) D= r a dj> 



and as expression for the pressure p at the given depth Z>, 



(b) p = j%dD 



Applying our notations from sections 27 and 29, and introducing 



( d ) P=Pk,o,i> + s 



we separate the specific volume and the density of the sea-water into their normal 

 values a^ A p , /> Mi o,/ and their anomalies S and e. Substituting this in the equations 

 (a) and (b), we get D and p separated in two terms, 



(0 Z> = A 6 ,o P + AZ 



(/) t=tu,*,D+*P 



123 



