PAPER BY PROF. BEZOLD. 249 



temperature must, in the continuous interchange between cyclone and 

 anticyclone, retain an average value that lies between the maximum 

 value T" and the smaller value T corresponding to the base of the 

 cyclone; that is to say, to the point a on the diagram. This average 

 value is, however, certainly smaller than the maximum value T" corre- 

 sponding to the highest point of the path, and therefore to the condi- 

 tion c, and thus the theorem (b) is proven. Hence it follows that in 

 nature the diminution of temperature for a constant elevation, or we 

 will rather say, for 100 metres, that is to say ; the so-called vertical 

 temperature gradient, is, in general, smaller than results from the 

 theory of the dry stage. As is well known, this gradient is 0.993 for 

 the latter stage, that is to say, under the assumption of adiabatic 

 change one would expect in the dry stage a diminution of 1° centigrade 

 in temperature for an ascent of 100 metres. 



This value 0.993 I will call v. 



The above given theorems concerning the potential temperature 

 show at once that under the assumption of adiabatic exchange the real 

 value of the temperature gradient must be less than v. 



We reach this conclusion from the following considerations: 



Let t a and t d be the temperatures at the bases of the cyclone and 

 anticyclone respectively (that is to say, at the starting and resting 

 poiut, of the ascending and descending currents) then, under the 

 assumption of perfect adiabatic change, these will not greatly differ 

 from the potential temperatures T and T", as these correspond to the 

 ascending and descending branches in the dry stadium, that is to say, 

 to the conditions represented by the curved portions ab and cd in figure 

 30. In this process the departures from these temperatures are always 

 of such a nature that t a <iT' and t d >T". For, since the pressure p a at 

 the base of the cyclone is certainly smaller than the normal pressure, 

 but the pressure p b at the base of the anticyclone greater than it (at 

 least when a normal pressure is chosen appropriate to this case, 

 and therefore lying between p a and p b ), therefore the temperature t a 

 is increased by referring it back to this pressure, while t d by the cor- 

 responding process is diminished. Since the statement is thus proven 

 that t a <T' and t d >T", and since, moreover, T">T', therefore, by so 

 much the more must t d >t a . 



At the highest point of its path, such as corresponds to the point c 

 of the diagram, the particle of air has a potential temperature T" 

 that is to say, precisely the same as at the end. 



If now it be assumed that this point lies 100/t metres above the 

 earth's surface, then there results as temperature gradient for the 

 descending branch that is to say, as the increase of temperature for 

 each 100 metres of descent, the well-known value 



h 



