12 PHYSICAL PROPERTIES OF SEA WATER 



examined by Ekman, who established a compUcated empirical formula 

 for the mean compressibility between pressures and p decibars. From 

 this formula, correction terms have been computed which, added to the 

 value of (Tt, give the corresponding value o-s,^,p for any value of pressure. 

 Computation of Density and Specific Volume in Situ. Tables 

 from which the density in situ, (Ts,d.p, could be obtained directly from the 

 temperature, salinity, and pressure with sufficiently close intervals in the 

 three variables would fill many large volumes, but by means of various 

 artifices convenient tables have been prepared. Following the procedure 

 of Bjerknes and Sandstrom (1910), one can write 



O's.^.p — O'Sb, 0,0 



+ es + €^ + es,d + €p + 6.5, p + e^,p + es,^,p. (II, 3) 



The first four terms of this equation are equal to at, which can readily be 

 determined by the methods outlined above, and the remaining terms 

 represent the effects of the compressibility. 



Instead of the density in situ, its reciprocal value, the specific volume 

 in situ, as,-&,p, is generally used in dynamic oceanography. In order to 

 avoid operating with large numbers, the specific volume is commonly 

 expressed as an anomaly, 5, defined in the following waj^: 



5 = Ois,^,p — 0:35, 0,p, (II, 4) 



where 0:35, o.p is the specific volume of water of salinity, 35°/oo and 0°C, at 

 the pressure p in decibars. The anomaly depends on the temperature, 

 salinity, and pressure, and hence can be expressed as 



5 = 5s + 5^ + ds,i} + 5s, p + 5^,p + ds,d,p- (H? 5) 



It should be observed that the anomaly, by definition, does not contain a 

 term 5p, which would represent the effect of pressure at temperature 0° 

 and salinity 35.00 °/oo. The reason for this is explained on p. 100. Of 

 the above terms, the last one, 5s,d,p, is so small that it can alwaj^s be 

 neglected. Thus, five terms are needed for obtaining 5, and these were 

 tabulated by Bjerknes and Sandstrom (1910). If o-^ has already been 

 computed, the terms that are independent of pressure can be combined as 



A«., = 0.02736 - ^ ^^iQ-V/ ^"' ^^ 



and the specific volume anomaly can be computed b}' means of three 

 small tables. 



Thermal Properties of Sea Water 



Thermal Expansion. The coefficient of thermal expansion, e, of 

 sea water as defined by 6=1/0; {da/dd^) increases with increasing temper- 

 ature and pressure and is somewhat greater than the corresponding 



