PAPEK BY PEOF. BEZOLD. 251 



This again is most simply done by tlie introduction of the idea of 

 the potential temperature. We can, namely, bring together all of the 

 considerations just expounded into the following theorems: 



(1) //' the potential temperature above and heloic is the same i. e.. con- 

 stant throughout the whole layer of air binder consideration, then the ver- 

 tical temperature gradient has the iceU-'knovfn value n = v. 



(2) If the potential temperature in the upper stratum is higher than in 

 the lower stratum (and tit is is in general the case), then is the temperature 

 gradient smaller, and smaller in proportion as for a given difference in 

 altitude, the difference of the potential temperatures is larger. 



If we indicate the potential temperature of the upper stratum by T^ 

 aad that of the lower stratum by Tj, then for T^y T^ we shall always 

 have n<.v and in fact the differences Tg— T; and r — n always increa e 

 simultaneously. 



A decided cooling in the lowest stratum alwa\s causes a diminution 

 of T, and with it also a (Timinution of n, whereby even a change in the 

 sign of n may occur within moderate altitudes. In the latter case, the 

 temperature below is lower than in somewhat higher layers, and in 

 that case we have the so called inversion of temperature. If the cool- 

 ing is not sufiQciently strong to bring about an actual inversion of the 

 temperature, still it causes a diminution of the gradient. Such decided 

 ■cooling always takes place in the lowest stratum at the time of increased 

 radiation, therefore especially in the region of the anti-cyclone, i. e., 

 under a clear sky, in winter, and in the night time. Tiierefore in tie 

 winter and in the night-time the vertical temper.iture gradient ?nnst be 

 smaller than during the summer and day-time, even if inversion in the 

 ^ distribution of temperature does not occur. This result agrees perfectly 

 ■with observations, as is especially proven by tlie many facts that 

 Hann and others have collected from the Alpine regions. 



On the other hand the investigation here carried out teaches that the 

 inversion of temperature and the diminution of vertical gradient con- 

 nected therewith are to be treated not as phenomena peculiar only 

 to the mountain regions, but that we are to expect them also above the 

 plains, and even above the ocean, at least insofar as the more violent 

 movements of the air do not interfere therewith. 



We are therefore obliged to agree with Woeikoff* when he from a 

 few data draws the conclusion that this inversion is also to be expected 

 in the region of the great winter anti-cyclone of eastern Siberia. 



On the other hand I can not agree with him when he deduces from 

 this the consequence that Messrs. Wild and Hann should have consid- 

 ered this circumstance in drawing their isotherms, and I consider the 

 .standpoint taken by them as perfectly justified. t 



* WoeikofF, Klimate der Erde, German edition, 1887, Bel . ii, p. 322; Meteorolo- 

 (fische Zeitschrift, 1884, Bd. I, p. 443. 



+ Hann, Atlas der Met., 1867, p. 5. Wild, Repert., 1888, Bd. xi, Nr. 14. 



