The Geophysical Structure of the Sea 



307 



sense (anticlockwise) on the isostere with the higher value for the specific volume, the 

 higher pressure comes before or after the lower. The solenoids have the same proper- 

 ties as the isobaric-isosteric tubes ; they must be either fully enclosed or must terminate 

 against a boundary surface. In the case of hydrostatic equilibrium the two sets of 

 surfaces will not intersect and there will thus be no solenoids. On the other hand, as 

 the incUnation of the two sets of surfaces relative to each other increases, the number 

 of solenoids will also increase, so that their number can be taken as a measure of the 

 deviation of this state from hydrostatic equihbrium. Since the isobars in practice 

 appear in the dynamic section as horizontal lines, the number of solenoids in a section 

 enclosed by a closed curve is determined primarily by the degree of concentration of 

 the isosteres and their slope. The number A'^ of solenoids within a closed curve s is 

 given by the equation 



(IX.ll) 



A^ = 



a dp. 



where the integral is taken along the curve 5 in a positive sense of rotation. This is 

 easily understood if the oblique-angled co-ordinate system of the p- and a-lines is 

 transformed into rectangular co-ordinates, with the /?-values as abscissa and the a- 

 values as ordinate. 



Of particular interest is the case of a curve s formed by two vertical lines and two 

 isobars. The first two correspond to lump-lines at two oceanographic stations a 

 and b, the latter two represent the intersection of the two dynamic topographies of 

 certain pressure surfaces. The pressure at the upper isobaric line at sea-level will be 

 /?o, the pressure at the lower one p^, and will occur at station a at the dynamic depth 

 Da, and at station b at the dynamic depth D^ (see Fig. 132). Since along the two iso- 



FiG. 132. To the computation of the number of solenoids enclosed by the curve aa' bb'. 



baric lines dp = these two parts of the curve s will not contribute to the integral 

 in (IX. 1 1), so that 



— (h a dp 



a dp 



+ 



However, from the definition of equation (IX. 9) 



Da 



a dp 



and Dt 



a dp 



a dp 



