SPECIFIC VOLUME AND DENSITY OF ATMOSPHERIC AIR AND SEA-WATER. 37 



The three terms corresponding to the case p = D= o, viz, e e t , e, T , are calculated 

 directly from Martin Knudsen's formulae or tables. Thus the only difficulty con- 

 cerns the terms p Mi o,z >m tz *std containing the depth as an independent variable. 

 To perform the transition from the variable p to the variable D, we must know 

 with a sufficient approximation the relation between pressure and depth in the sea. 

 For the case of normal sea-water of 35 %o and o C. this relation is easily deter- 

 mined by a method explained in the next chapter. The result is contained in table 

 7 h, which gives the dynamic depth of any given pressure for intervals of 10 d-bars. 

 By interpolation in this table we can determine the pressure in any depth expressed 

 by any integer number of dynamic meters. The result of these interpolations is 

 given in table 15 h, which contains the pressures in depths expressed by any 

 integer number of dynamic meters, registered for intervals of 10 dynamic meters. 

 We can now by table 8 determine the specific volume of the sea- water correspond- 

 ing to the pressures registered in table 15. These will be the specific volumes ol 

 normal sea-water for the depths figuring as arguments in table 15 H. Passing to 

 the reciprocal values by use of the inversion-table 23 h, we get table 16 h, giving 

 the normal density p 3 - Oi0 ,i> of sea-water in 1000 different dynamic depths. 



For the calculation of the small quantities e from the corresponding quantities 8, 

 we can make use of simple approximation rules. Differentiating the equation con- 

 necting the density p with the corresponding specific volume a, w,e get dp = dale?. 

 Applying this for the transition from the correction S of any value of the specific 

 volume to the corresponding correction e of the density, we get 



8 

 (a) B = -- t 



Using, as above, table 15 h to find the pressure corresponding to the given dynamic 

 depth, and this pressure to find 8-values from tables 12 h or 13 H, the corresponding 

 values of e are calculated by equation (a). In this way the main tables 20 h and 

 21 h are calculated. These would give exactly the required corrections s sD and T 

 if the pressure in the depth considered had exactly the normal value given by 

 table 15 H. But if the water above the level considered has other than the normal 

 salinity 35 / 00 or other than the normal temperature o C, the pressure will be 

 slightly different, and this will have a slight influence upon the density of the sea- 

 water in the level considered. The anomaly of pressure in question can easily be 

 estimated with sufficient approximation from the average salinity and the average 

 temperature of the water above the level considered, and thus the corresponding 

 correction of the density as the consequence of the compression found. These cor- 

 rections are given in the small tables placed at the foot of the main tables 20 h and 

 21 h, having the average instead of the local values of salinity and temperature as 

 argument. 



It is seen that as a 2 never difters very much from unity, corresponding values of 

 B^ and s tD , as well as of h rp and e rD , are very nearly like each other, but with opposite 

 signs. Passing to the calculation of the term of the third order, e srp , we can simply 

 put a 2 = 1, and identify the numbers expressing depths in dynamic meters with 

 those expressing pressures in decibars. Table 22 h, giving the values of e D , is 



