SPECIFIC VOLUME AND DENSITY OF ATMOSPHERIC AIR AND SEA-WATER. 3,3 



Thus 8 a and 8 t depend each on one variable, & ST , 8^, S Tp r each on two, and only S on 

 all three variables. The main point is now to determine these terms so that the 

 terms depending upon more than one variable become as small as possible. This 

 is done if we give them the following values: 



s = a t, 0, a 35, 0, 



t = <*35, t, a 35, 0, 



.'T = \ a s, t,0 a 35, r,o) \ a i, 0,0 a 35, 0, 0) 



( C ) $*p = (<*, 0, p a 35, 0,p) ( a ,0, a 35, 0, 0) 



&TP = 0*35, T, ;. a 35, 0, p ) ( a 35, t, a 35, 0, o) 

 $srp = [(<*, t,p a 35,r,;.) ( a s,T,0 a 35,T,o)] [(<**, O.p a 36,<,,p) ~ ( ., 0, ~ %>,0,o)] 



It is easily verified that the substitution of (c) and (b) in (a) makes this 

 equation identical. Now, each of the quantities *35,o, P , 8 S , 8 r , 8 ST , 8^, 8 TP , 8 STP are easily 

 tabulated separately. The values of^,,, are found from Ekman's formula, putting 

 s = 35, t = o, and using the values 35f0 ,o = -97364 and <r m = <r 36i 0> = 28.13, calcu- 

 lated from Martin Knudsen's tables. The result for rooo values of the pressure is 

 given in table 8 h. The correction o t for salinity at temperature zero and the cor- 

 rection 8 T for temperature at salinity 35 /oo are both found from Martin Knudsen's 

 formulae or tables. The result is given in tables 9H and 10 H for 400 values of the 

 salinity and 320 values of the temperature, respectively. 



Being differences of the second order, the quantities depending upon two 

 variables 8 sr , 8 sp , 8 Tp are sufficiently small to be tabulated for ten times greater 

 intervals of the independent variables, viz, for 40 values of the salinity, 32 values of 

 the centigrade degrees, and 100 values of the pressure. 8 ST is found from Martin 

 Knudsen's formulas or tables. The expressions of 8^ and 8 Tp , which are rather 

 long in spite of the smallness of the numerical values, are formed from Ekman's 

 formula. The results are given in tables 11 h, 12 h, and 13 h. The quantity 8 3r 

 finally, depending upon three variables, is given by a very long expression 

 deduced from Ekman's formula. But being a difference of the third order, it is 

 sufficiently small to be tabulated for still greater intervals of the independent 

 variables. The result is given in table 14 h as a system of 17 small tables, each 

 corresponding to a certain salinity, while within each table temperature and pressure 

 figure as the independent variables, the intervals of pressure being 1000 decibars. 



The tabulation of the specific volume of sea-water has thus been accomplished 

 by seven small tables covering 10 pages. This system of small tables is equivalent 

 to the one table of 256,000 pages on account of the possible permutations in the 

 sum (a) and (b) of the values taken from the different small tables. 



The three last tables, involving the pressure as one of the independent variables, 

 are not calculated completely, those combinations of the variables being left out 

 which are not found in the sea. The general distribution of temperature and 

 salinity in the sea is readily seen from the charts worked out by Dr. G. Schott.* 

 The greatest variation of temperature is found on the surface of the sea, extending 

 from the evident lower limit, the freezing-point of sea-water, between 1 and 



* Wissenschaftliche Ergebnisse der deutschen Tiefsee-Expedition auf dem Dampfer " Valdivia," 1898-99. 

 T. I. V. Oceanographie und maritime Meteorologie von Dr. G. Schott. Jena, 1902. 



