CHAPTER III. 



SPECIFIC VOLUME AND DENSITY OF ATMOSPHERIC AIR AND 



SEA-WATER. 



19. Distribution of Mass. Every motion consists in the displacement of masses. 

 Only in certain definite distributions of mass will the causes of motion cease to 

 act. As introductory to the investigation of the conditions of equilibrium and 

 motion of the atmosphere and the hydrosphere, we will therefore have to consider 

 the distribution of mass in general, and the methods of finding and representing it- 



For the numerical representation of the distribution of mass in a continuous 

 medium, such as air or water, we have, as mentioned already (sec. 3), two methods: 

 We can specify the volume occupied by the different unit-masses, or we can specify 

 the masses present in the different units of volume. In the first case we register 

 the specific volume, in the second the density of the medium. The number rep- 

 resenting one of these quantities is the reciprocal of that representing the other. 

 These quantities are completely equivalent in representing the distribution of mass. 

 But which to choose is a question of importance, as it leads to one or the other of 

 two different methods already referred to (section 3) of formulating the conditions 

 of equilibrium and motion of the medium. Theoretically neither of these methods 

 has any advantage over the other, but they supplement each other in a convenient 

 manner. We shall therefore develop both side by side. 



Specific volume or density of atmospheric air or of sea-water are as a rule not 

 observed directly. Generally they will have to be calculated from other quantities, 

 more easily observed with sufficient precision. These quantities are pressure, 

 temperature, and humidity in the case of the atmosphere; depth, temperature, and 

 salinity in the case of the sea. 



20. Equation of State of the Atmospheric Air. To calculate the specific vol- 

 ume of dry atmospheric air, we use the equation of Boyle-Gay-Lussac. As the 

 letter / will be reserved for the most fundamental of all independent variables, time, 

 and the letter v for the most important vector quantity related to the motion of the 

 atmosphere or the sea, velocity, we shall represent the temperature according to 

 the common centigrade scale by t, and the corresponding temperature referred to 

 the absolute zero by &, thus 



{<>) & = t + 273 



while we shall denote the specific volume by a. The equation connecting pressure, 

 specific volume, and temperature of a perfect gas is then 



{b) pa = R 



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