218 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



vapor that is condensed by cooling, as in expansion, be again evapo- 

 rated by warming or compression. But as soon as the small quantity 

 of water is evaporated, then by a further warming, the air enters again 

 into the dry stadium but with a different quantity of vapor than it 

 originally had, so that now it will pass through other conditions than 

 at first, when the air expanded under continued loss of water. In order 

 now to be able to determine perfectly the condition of the mass of air, 

 we need beside the variables that occur in the equations of mixture to 

 know also the volume v that the mass .If occupies and the pressure p. 

 The latter we measure by the pressure in kilograms per square metre, 

 wherein we now have to understand by kilogram the weight that a 

 kilogram of mass has at 45° Lat. The simple relation 



p = 13.6/i 



exists between the pressure p thus measured or the so called specific 

 pressure and the barometric pressure (i expressed in millimetres of 

 mercury; whereas expressed in atmospheres it has the value 



10333 



so that one can without difficulty pass from one mode of measurement 

 to the other. 



This much being prefaced, we can now establish the equations for 

 the gaseous condition [equations of elasticity] for the different stages. 

 Their general form is 



f(v, p, t,x)=0 



therefore they contain one variable more than we generally find in the 

 equations of elasticity. The quantities x' and x" do not appear in these 

 since in general they are so small that they exert no influence on p 

 and v. 



If now we would geometrically picture a condition of mixture we 

 must (besides p and v which will be represented in the ordinary method 

 by ordinates and abscissas in a rectangular system of coordinates with 

 the axes OP and V) make use further of a third coordinate ; as such 

 we advantageously choose the value of x, and lay this off parallel to 

 the axis OX in a direction perpendicular to the plane PV. In this 

 method of presentation, all conditions that correspond to any value of 

 x find their representation in one and the same plane, which only 

 slightly differs from the P V plane if we adopt the atmospheric pressure 

 as the unit of pressure, and adopt lines of equal length in the direction 

 of the axes of Y and X as expressing the units of volume (one cubic 

 metre) and of mass (one kilogram). 



If now we imagine successive planes lying above each other, on 

 which conditions are represented that differ progressively from gram to 

 gram (that is, by a thousandth of the adopted unit), then these will lie 



