394 RECORD OF SCIENCE FOR 1887 AND 1888. 



Approximately, Ex =29.272 and K5 =47.0G1 iu the metric system of 

 units. 



Comparing this with the corresponding equation for dry air, we see 

 that (1) contains the additional variable x, and that the thermal condi- 

 tion of the gas is not defined until we know^, v, and x. Geometrically 

 the condition of the gas would be represented by the location of a point 

 in space whose co-ordinates are these three variables. 



Let^ov, iu Figs. 2 and 3, be called the "plane of co-ordinates," as 

 that term is used by Bezold, and let x be measured perpendicular 

 thereto; we have thus the necessary system of three rectangular co or- 

 dinates. The value of x in ordinary meteorological problems is gener- 

 ally very small in comparison with_2> and v. For any given constant 

 value oi X the indicator iioint, showing the thern)al condition of the air, 

 would move iu a i)lane parallel and very near to the plauejpov. If x 

 is zero the equation and the curve becomes the same as for dry air. 



Isotherms. — If we assume that the temperature T is maintained con- 

 stant, then the indicator moves along an isotherm, as above described. 

 For a given value of x equation (1) shows that the isotherm is an equi- 

 lateral hyperbola precisely like that iu dry air, but situated in a plane 

 parallel to the plane of co-ordinates. The isotherms for the same tem- 

 perature T and for different values of iP, when i)rojected upon the plane 

 pov, agree sensibly. In fact the ordinates ^1 aud ^^2 of the two isotherms 

 coriesponding to a given abscissa, v, and to the given quantities of 

 aqueous vapor Xi and Xz are connected by the relation 



Since the second member of this equation is rery nearly zero, since 

 the values of x are generally less than 0.03, therefore the ordinates |Ji 

 and ^2 are sensibly equal. One may then be content to consider in the 

 geometrical interpretation of the facts, not the isotherms themselves, 

 but their approximately common projection upon the plane of co-ordi- 

 nates ; this amounts to saying that we may consider x as constant. 



Tlie line of saturation. — The changes iu the condition of the air are not 

 reversible, and the equation (1) holds good only for certain values of v. 

 In fact the fundamental condition of the dry stage is that the vapor 

 pressure j?5 shall be rather less than the maximum pressure of the sat- 

 urated vapor for the temperature T. Designating this maximum press- 

 ure by e it is necessarj^ that we should have 



or rather by replacing 2>5 by its value as a function of v that we should 

 have 



xR,T^ 



