The Ocean at Rest (Statics of the Ocean) 341 



relative to them show that the system is not in static equilibrium (disturbed equih- 

 brium). The water at A is lighter than that at B in the same isobaric level, so that to 

 estabhsh hydrostatic equihbrium the water mass at A must rise and that at B must 

 sink. The forces indicated by the mass distribution (solenoids) show a rotational 

 movement (circulation) which tends to adjust the mass distribution closer to that of 

 static equiHbrium, In the final state the isobars must run parallel to the isosteres; 

 a barotropic mass field is then estabhshed out from a baroclinic one. The direction 

 of the circulation set up is given by the rule that it always proceeds along the shortest 

 path from the mobihty vector B(da8n) to the pressure gradient G(8pldn) (Fig. 138). 

 The strength of the forces and the intensity of the resultant circulation have been dis- 

 cussed in II/5; see Fig. 136c. A more convenient method of characterizing the nature 

 of the equilibrium is by comparison of the piezotropy coefficient of the density yp with 

 the barotropy coefficient Fp (see p. 308). The first determines the behaviour of an 

 individual small element on changes in pressure (depth), while the second characterizes 

 the state of a water mass in vertical direction. If Fp = yp then the mass field is not 

 aff'ected by an interchange of any two small elements. In autobarotropism the equili- 

 brium condition is thus indifferent (neutral), for Fp > yp it will be stable and for Fp < yp 

 it will be unstable. Since in the first case the density diff'erences set up by vertical 

 displacements will tend to return the displaced elements to their initial positions, while 

 in the second, on the other hand, they will tend to displace them further and further 

 from it. Rhythmic (periodic) circulatory movements may be set up in this way, but in 

 the sea, according to their nature, they can hardly persist for very long since the 

 energy of these movements will soon be dissipated by turbulence (Inertia oscillations, 

 see Chap. XIII, 6. 



