220 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



where R K and R s are the constants of the equations of elasticity* for air 

 and vapor, namely, R*= 29.272 and R s — 47.061. If now x remains con- 

 stant, then for a constant T this equation becomes that for an equila- 

 teral hyperbola. The isotherm for moist but not saturated air is there, 

 fore, as for dry air, an equilateral hyperbola or a portion of one; but 

 for certain values of v this equation loses its meaning. 



The fundamental condition of the dry stage consists simply in this: 

 that the pressure p& shall be smaller than the pressure e corresponding 

 to that of saturated vapor at the same temperature, or expressed alge- 

 braically 



v 



where e is a quantity depending upon Tand rapidly increasing with T. 

 The equation (1) holds good, however, only when 



V > X J**1 (2) 



e 



and, therefore, the effective portion of the hyperbola begins with the 



point whose abscissa is 



XR& T /ox 



^ = -T"- (3) 



Since e increases more rapidly than T, therefore this initial abscissa 

 diminishes with increasing temperature. The initial points of all 

 isotherms belonging to one and the same quantity of vapor x lie there- 

 fore on a curve whose course is to be seen approximately on the figures 

 to be given hereafter, in which such curves are designated by 8 S with 

 corresponding indices. 



Hence the area within which are represented the conditions of 

 the dry stadium for constant quantities of vapor x is bounded by this 

 curve on the side toward the co-ordinate axes. If this curve is so in- 

 tersected by another curve, representing any change of condition that 

 one passes from the side that is concave away from the axis over to 

 its convex side then one leaves the dry stage and arrives in that of 

 condensation, that is to say, in the rain or snow stage. I will therefore 

 designate this curve as the curve of saturation or of dew-point. Points 

 on this saturation curve are, in accord with the considerations just de- 

 veloped, determined by the hyperbolic isotherm and the initial abscissa. 

 We can, however, equally well utilize also the corresponding ordiuates 

 and the initial abscissa. In the dry stage the following equation holds 

 good for the ordinate : 



P=P\ +ps<%>\ + e 



consequently for the initial ordinate of the isotherm T, which will be 



* Throughout this work, the ' ' equation of elasticity " is used as a translation of the 

 German Zustandsgleichung, as being preferable and more general than the ordinary 

 expression '• Equation for a gas" or " equation of condition." — C. J. 



