Density of Water Masses in Ocean, Vertical and Horizontal Density Distribution 195 



an "isentropic" chart for the salinity distribution at the 25-5 c7<-surface in the North 

 Atlantic between 0° and 30° N. This surface intersects the sea surface at the dotted 

 line and south of this it lies mostly at a depth of between 75 and 125 m. The arrows 

 show the main direction of spreading of the highly saline {S) and low saline (F) water 

 according to Montgomery. The arrows pointing in the west-east-direction show the 

 Equatorial Countercurrent and correspond to actual flow. Only the east-west-arrows 

 in the low-salinity tongue between the Equatorial Current and the southern branch 

 of the north Equatorial Current and those directed from south to north off the West 

 African coast may have little relation to actual currents; the first low-salinity tongue 

 represents the salinity minimum between the intrusions of highly saline water to the 

 north and the south, the latter minima are due to upwelling water off the West 

 African coast. 



5. The Vertical Equilibrium in the Ocean and Stability 



The use of the potential temperature 6, or the potential density a^, as criteria for the 

 equilibrium conditions in the sea is only correct if the salinity is constant everywhere. 

 Under these conditions the equilibrium is stable, indifferent (neutral) or unstable 

 according to whether daejdz = 0. Correct equilibrium conditions can be derived in 

 the following way: a small mass of water displaced from a level r by a vertical distance 

 A^ towards the surface comes to a density p, while the surrounding water at this point 

 has a density p'. This displaced water quantum will then be subject to a vertical accelera- 

 tion proportional to p — p'. If the difference is positive then the displaced water mass 

 will be subject to a downward force tending to move it back to its previous position ; 

 the equilibirium is then said to be stable; if the difference is negative then it is subject 

 to an upward force tending to displace it further and further away from its new 

 position — the equilibrium is then unstable. If, after a displacement, it always has the 

 same density as the surrounding water then the equilibrium is indifferent (neutral). 

 The difference p — p' per unit length is thus a measure of the state of equilibrium. 

 Hesselberg (1918) therefore denoted the expression E = Spjdz as "stabihty", where 

 Spjdz is the individual change in density (in contrast to dp/dz which gives the geo- 

 metric change in p with height). For positive values of £ the stratification is stable and 

 is not altered by vertical displacement of individual small water quanta. For negative 

 values of E the stratification is unstable and the slightest disturbance is sufficient to 

 cause a new adjustment in stratification (Ekman, 1920). Between layers with positive 

 and negative stability there is always a surface with E — 0. A small mass of water on 

 displacement to the side where E is positive is always driven back to the surface, but 

 a displacement to the side where E is negative removes it more and more from that 

 sui face. 



Hesselberg and Sverdrup (1914, see also, Schulz, 1917) have given a simple 

 method for the calculation of the quantity E. If a small water quantum at a depth z 

 at point a (Fig. 91) is subject to a pressure p and has a salinity s and a temperature ^, 

 at a depth z + dz, the corresponding values are p -\- dp, s ~\- ds and {}• + d^. If the 

 water quantum is displaced near to point a, it will be subject to the pressure p and it 

 will retain a salinity s + ds, but its temperature will change due to adiabatic expansion 



