272 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



But in this case the lowering of the temperature must be forced down 

 to t a , if the quautity of precipitated water is to be equal to a, since 

 then the equation 



holds good for y' a , which represents the ordinate erected at T a . 



Here also the general course of the curve again shows that the fall 

 of temperature necessary in order that a definite quantity of precipita- 

 tion may be caused by adiabatic expansion is very much less than 

 when the same quantity is to be produced by mixture. 



A numerical example will best illustrate this principle: From the 

 above-given small tables we see that at 700 millimetres pressure satu- 

 rated air at0° C. mixed with saturated air at 20° can precipitate at the 

 most only 0.75 grams of water per kilogram of the mixture and that 

 the final temperature of the mixture will be 11°.0; that is to say, for a 

 cooling of the warmer component from 20° down to 11°. 



By direct cooling, on the other hand, the same quality of water 

 would be precipitated from 1 kilogram of the warmer component when 

 it is cooled from 20° down to 19°.2; whereas by adiabatic expansion a 

 cooling of from 20° down to 18°.4 would be necessary; that is to say, a 

 vertical ascent through a distance of about 31.0 metres. 



This example shows in a very striking manner how slight need be 

 the direct cooling by contact with cold objects, or by radiation, or even 

 by adiabatic expansion, in order to produce quantities of precipitation, 

 such as would by mixture be only obtainable in the extremest, scarcely 

 imaginable cases. 



"With this the consideration of the mixture of masses of moist air may 

 be brought to a close and only the single remark be made that the 

 difference t — t s is smaller as the quautity a of the precipitated liquid 

 decreases. The amount of this difference will therefore only exceed 

 the value of 1° or 2° in such extreme cases as are assumed in the pre- 

 vious tables and generally will remain far within this limit. 



Therefore in the majority of cases the mixing temperature may, with- 

 out important error, be put equal to that which we obtain by mixing 

 equal masses of dry air, whereby many computations experience a great 

 simplification. 



(6.) SUPER SATURATED AIR. 



In the foregoing solution of the problem of mixture it was assumed 

 for the sake of simplicity, that in the cases where the formation of 

 precipitation in this manner is really possible, super-saturation must first 

 occur, and then precipitation follows. 



This assumption was implied by Hann in his above-mentioned 

 memoir* at a time when we still knew nothing as to whether aqueous 

 vapor could actually exist in a supersaturated condition. 



* Zeitschrift Oest. Gesell. Met., 1874, vol. ix. [Smithson. Rep., 1877, p. 397.] 



