2o8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



We conclude from equation (2) that the pressure diminishes when 

 the incoming air is warmer, and the pressure increases when the in- 

 coming air is colder.' Applying this result to nature we infer that 

 the supplementary air is colder than the alimentary air. 



Denoting by d the change of the pressure per hour and in milli- 

 meters and expressing h in kilometers we shall have 



3600.760 ap w 

 3 = 10333 ' 1000 ' h ^ ~ T ^ 



and for an average value of p (0.1318) we have 



w 

 d = \0j (t - r') (3) 



Let us consider a stationary cyclone whose pressure at the center 

 varies; d represents the variation of the horizontal depression D n . 

 In order to introduce the relation given by equation (1) we notice 

 that this can be written 



dp w 



Jt = Tz {p ' ~ p) 



In passing from these infinitesimal values of altitude to the 

 finite differences, it is necessary to consider the whole height h of 

 the horizontal current, because in the latter we do not know the 

 variations of velocity with the height and when w expresses the 

 vertical velocity in the ascending current at the height h, that is 

 to say, at the level where the motion commences to be purely ascen- 

 sional, we can introduce the relation given by equation (1) of §26, 

 and expressing r in degrees of a great circle we shall have 



U cos O 

 d = 0.18 (t-t0 (4) 



' (i 



By the aid of equation (3) we can easily calculate the variation 

 of the pressure in the cyclones given in the tables of §26. 



Equation (2) applies only for the first few moments. If the 

 vertical current is continually being supplied by heterogeneous air, 

 the change of pressure must depend also on the humidity of the 

 air. According to § 5 moist air has during ascension a mean tem- 

 perature higher than dry air. If we consider r and r' as approxi- 

 mately mean temperatures, we arrive at the conclusion that the 

 supplementary air is colder and dryer than the alimentary air. If 



