46 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



phere in the same direct way. But as such tables would be very bulky, we have 

 not calculated them, and we shall show later how to proceed without them. On 

 this occasion, therefore, we only remark that the pressure at sea-level is very 

 nearly 10 decibars. In the atmosphere we shall therefore have to count with 10 

 standard isobaric surfaces of the pressure from 10 to 1 decibars. These surfaces will 

 divide the atmosphere into 10 standard isobaric sheets, the highest of which, 

 however, has only a distinct lower limit, the standard surface of the pressure of 1 

 decibar, while the existence of the upper limit, the isobaric surface of pressure zero, 

 may be open to discussion. As a consequence of the decrease of the pressure, the 

 thickness of the standard sheets will increase upward. The thickness of each of 

 them will vary with the virtual temperature as shown in table 9 m of Meteorologic 

 Tables. The methods used for calculating this and other tables required for finding 

 the height of given pressures in the atmosphere will be given in Chapter VI. 



In the mercury column of a barometer we have the same number of standard 

 sheets as in the atmosphere. The specific volume of the mercury being 0.073554, 

 the thickness of the standard sheets is 0.073554 dynamic me ter, or 0.075008 meter 

 for the value of gravity at sea-level at 45 latitude. This is 75 millimeters, 

 practically. 



37. Condition of Equilibrium in Terms of Forces per Unit- Volume. To 



express the condition of equilibrium we can also use the forces per unit-volume, 

 section 33, (c). Equilibrium exists if the forces per unit-volume are equal and 

 oppositely directed. 

 (a) G=- P g 



Proceeding as in section 35, we derive from this 



and 



(c) dp = pdcf> 



Each of these equations may be formed from the corresponding equation of 

 section 35 simply by multiplying by the density p. The difference between the 

 equations is thus the slightest possible, but still important in its further consequences. 



38. Equilibrium Relation between the Fields of Potential, Pressure, and 

 Density. On interpreting geometrically the condition of equilibrium in this form, 

 characterized by the reference of the forces to the unit of volume, we find this 

 difference only, that the field of mass is described by the distribution of density 

 instead of, as previously, by the distribution of specific volume. We thus arrive at 

 the following two slightly changed forms of the principles formulated in section 35 : 



(I) Principle of Coincidence of Surfaces. Every isosteric surface being at 

 the same time an isopycnic surface, we immediately get from section 35 (I): 



In the state of equilibrium there is coincidence between the isobaric, the 

 isopycnic, and the equipotential surfaces. 



