The Sea-water and its Physical and Chemical Properties 41 



Only that part of the element remaining in solution disintegrates to give radium and its 

 disintegration products in the sea (see also Hess, 1918). 



4. The Density of Sea-water and its Dependence on Temperature, Salinity and Pressure 



The density p of a material is the mass of a unit volume [g cm"^]. Frequently the 

 specific weight is given instead of the density; this is defined as the quotient of two 

 densities p/p„., where p is the density of the substance in question and p,,, is the density 

 of distilled water at a fixed temperature. The specific weight is thus a dimensionless 

 quantity. In the CGS system the density and the specific gravity are numerically 

 equal if distilled water at 4°C is taken as the comparison liquid. 



Due to its salt content sea-water is heavier (more dense) than pure water. The den- 

 sity is always fairly close to 1 and varies depending on the salinity S, the temperature 

 / and the pressure p between narrow limits ; for example, at the surface of the open 

 ocean between 1-02750 and 1-02100. For oceanographic purposes it is necessary to 

 know the density correctly to at least 5 decimal places. For simplicity instead of using 

 p it is customary to use a density value o derived from the equation a = (p— 1) x 10^; 

 for instance instead of p = 1-02754, a = 27-54 is used. Very often the reciprocal of 

 the density 1/p = v, the specific volume [cm^ g-^] is used. This also is required cor- 

 rect to the fifth decimal place and for simplicity and convenience only the last three 

 figures are given according to the equation a = (i; — 0-97) x 10^. For example when 

 V = 0-97320, a = 320. 



The dependence of the density and the specific volume on the temperature, the 

 salinity and the pressure were first investigated at the beginning of this century (1899) 

 by an international commission headed by K>ajDSEN (1902, 1903). The relationship 

 of the density at 0°C and atmospheric pressure at sea-level to the chlorinity is given 

 by 



ao = -0-069 + 1-4708 CI - 0-001570 Cl^ + 00000398 C\\ 



This equation is valid for chlorinities between 1-47362 and 22-2306. 



The dependence of the density of sea-water on the temperature requires a knowledge 

 of the thermal expansion of sea-water. The thermal expansion coeflficient determined 

 in the laboratory shows that the density has a pronounced dependence on the tem- 

 perature; at atmospheric pressure (sea surface) is given by o-^ — CTq — Z). Z) is a 

 very complicated function of a^ and of the temperature / and has been given to the 

 fifth place in Knudsen's hydrographic tables (1901). Schumacher (1922) has also given 

 graphical tables, and further tables for the determination of the density of sea-water 

 under normal pressure have been given by Matthews (1932) and Thorade and Kalle 

 (1940). These tables show that an increase of 0-01%o in the salinity gives an approxi- 

 mate increase in the density (ct^) of 8 units in the third decimal place. The increase is 

 about the same for all temperatures and salinities. For low and high temperatures 

 the density change is very different and depends also somewhat on the salinity. 

 Figure 21 (Helland-Hansen, 1911-12) shows the eff"ect of variations in temperature 

 on the densities of distilled water and of sea-water with sahnity 35%o. From the re- 

 lationship between temperature and density the temperature of maximum density 

 can be determined for different salinities. This is also given with somewhat less ac- 

 curacy by the equation 



/max = 3-95 - 0-266ao. 



