SECT. 1] PHYSICAL PROPERTIES OF SEA-WATER 9 



by the formula by an average of + 0.02 units of ctq- No changes in the formula 

 for CTo were made on the basis of these measurements. 



Carritt and Carpenter (1958) discussed both series of measurements used to 

 derive the relationships among chlorinity, salinity and density. They conclude 

 from the observations that salinity may vary by ± 0.01 7 %o and ctq by at least 

 ± 0.04 for a given chlorinity. They suggest that these variations in the measure- 

 ments cannot be attributed entirely to experimental error and are probably 

 due to regional variations in the ratios of dissolved ionic constituents in sea- 

 water. Consequently, they interpret these variations as rejaresenting a limit of 

 accuracy to which we may define S or ctq in terms of chlorinity. 



The second set of measurements by Forsch et al. (1902) was used to establish 

 the thermal expansion of sea-water at atmospheric pressure. These determina- 

 tions were reduced to an empirical formula for the specific gravity anomaly at, 

 expressed in terms of temperature and ctq in the form 



at = A + Bao + Cao^ (22) 



where A, B and C are functions of temperature. For pure water, the formula 

 becomes 



Et = A^BEq + CEq'^, (23) 



where Et, Eq denote the specific gravity anomaly of pure water. By subtracting 

 (23) from (22), the formula can be put in the form used by Knudsen (1901) ; i.e. 



at = Et + {ao-Eo)[l-At + Bt{ao^EQ)l (24) 



where i;«= -(;^-3.98)2(^ + 283)/503.570(7^ + 67.26), Eq= -0.1324, B=\-At = 

 1_ 4.7867 X 10-3,^ + 9.8185 X 10-57^2 _ 1.0843 X lO-^j^^ C'= ^<= 1.8030 x 10-5,^ - 

 8.164 X 10-'^j^2_|_ 1.667 X 10-8^3^ and d' is the temperature in degrees Celsius. 

 Formula (22) is more convenient in some applications. The coefficient A is 

 given by 



A = (4.53168j^-0.545939j?2_ 1.98248 X 10-3^3_ 1.438 X 10-7,^4)/(^+ 67.26) 



For pure water (cro = i7o= —0.1324), formula (24) reduces to Et. This formula 

 for the specific gravity anomaly of pure water was developed by Thiesen (1897). 

 Tilton and Taylor (1937) constructed a more accurate formula of the same 

 form using observations of density made by Chappius (1907). The revised 

 formula differs from Et by less than 0.005 (Dorsey, 1940, table 100). The 

 revision has not been incorporated into the sea-water formula. 



Formulas (21) and (24) do not reduce to the pure water formula for either 

 S = Q or Cl = because of the constant terms in the relationships between S 

 and CI, and between o-q and CI. 



The most recent determinations of density of sea-water are those of Bein 

 et al. (1935). The densities agreed within ±0.02 units of at with values com- 

 puted from Knudsen's (1901) tables. 



Ekman (1908) carried out the third set of measurements to determine the 

 effect of pressure on specific volume. He used a single sample of sea- water 



