244 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



I. THE POTENTIAL TEMPERATURE. 



According to what has jiist been said tbe potential temperature is 

 that absolute temperature that a bod\' assumes when without gain 

 or loss of heat it is adiabatically or pseudo adiabatically reduced to 

 the normal pressure. I intentionally give this definition the form 

 here chosen since we are here concerned with the api)lication of the 

 idea to meteorological processes, and since in our case the processes 

 without increase or loss of heat do not need to be strictly adiabatic 

 in the ordinary sense of the word. As I have shown in the pre- 

 vious memoir we have only to do with adiabatic processes when the 

 water formed by condensation does not fall to tbe earth but is carried 

 along with the air, a condition that is only fultilled in exceptional cases. 

 As soon as water is lost, and this is generally the rule, even though 

 no heat be gained or lost, we have to do with a process that is only 

 pseudo adiabatic. When therefore in the following, mention is made 

 of adiabatic changes, the pseudo-adiabatic will always be included 

 therein in so far as this class is not excluded by the special term 

 " strictly adiabatic." 



This much being premised we may now first investigate whether and 

 how the potential temperature can be represented in a diagram. The 

 answer to this question is extremely simple. From the equation of 

 condition for the dry stage 



vj) = R* T 

 there results 



P 

 or if we substitute forp the normal pressure ^o 



R* 



Po 



Therefore under constant i^ressure the absolute temperature is simply 

 proportional to the volume, that is to say to the abscissa. But this 

 absolute temperature under the pressure 2?o is the "potential tempera- 

 ture" for all other conditions that find their representation on the 

 adiabatic passing througii the point whose coordinates are v and p^. 

 We therefore obtain the following rule: 



If a condition is given that is represented in the diagram, Fig. 3(5, by 

 the point «, then tee find the corresponding potential temperature by draw- 

 ing an adiabatic line through a and seeking its point of intersection N' 

 tinth a straight line I\ N drawn parallel to the axis of abscissas and dis- 

 lantihcrefrom by p„. Ihe distance of this point of intersection 1^' from 

 the axis of ordinates, namely, the abscissa of X' {or y Po) is now a meas- 

 ure of the potential temperature. 



We find the numerical values of r and T belonging to p,^ (and which 

 I will now designate by v' and T corresi)ondiug to the point A'', while I 



