PAPER BY PROF. BEZOLD. 217 



If we assume that by cooliug, as for example through adiabatic ex- 

 pansion, the air has passed from the dry stage to the rainy stage, then 

 will 



wherein the equality sign is the limiting case but in general the in- 

 equality is to be considered as the characteristic sign. The quantity 

 x\ IS always very small and can only assume a somewhat greater value 

 in exceptional cases, as for instance in the case of a remarkably strong 

 ascending current of air that hinders the fall of the rain or rather that 

 carries the drops upward with itself. How large this value may become 

 we have as yet no indications whatever. 

 (C). — The hail stage: for this case 



wherein x^ is the quantity of saturated vapor; x'^ the quantity of water 

 present in the fluid condition ; x"^ the quantity of ice that is present. 

 Here as above, under the corresponding assumptions, we have 



this stage can, in general, only occur when fluid water is mixed with the 

 air and this mixture is cooled to 0° Cent. 

 (D). — The snow stage; for this case 



J\I,=l-\-x,+x", 



where the notation is easily understood by what precedes and where 

 again so far as the mixture can be considered as coming from the pre- 

 vious stage, we must have 



In the most common case, where an ascending mass of air j) by cool- 

 ing gradually goes through all the different conditions, x' and x" are 

 generally exceedingly small, so that the hail stage is entirely passed 

 over, and in all formulae only one independent variable x appears. In 

 this case M steadily diminishes. 



Hertz in his investigation has not considered the change of M, but 

 has considered this quantity as constant. This was allowable in view 

 of his object, but here as already stated in the beginning, this limita- 

 tion must be avoided. The present more general consideration leads 

 first of all to the recognition of the fact that here we have to do with a 

 class of processes which so far as I know have not yet been considered 

 in the mechanical theory of heat; such namely, as are reversible in 

 their smallest parts but are not reversible as a whole. 



So long as the quantities x' and x" are not equal to zero but possess 

 a finite value even though exceedingly small, then can the quantity of 



