3Jt) SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



parison with the work of expansion done by the ascending air, as 

 will be seen by the formula to be developed hereafter. It is evident 

 that such processes are in general only possible when actual changes, 

 that is, motions of the atmosphere sufficient to overcome the exist- 

 ing gradients, are produced by the buoyancy of other portions of 

 the atmosphere. 



If, however, we ignore such special cases and consider only the 

 normal interchange of air between cyclones and anticylones under 

 the assumption that a steady state of motion has been established 

 and omitting the vortex motions due to the rotation of the earth, 

 then we may imagine a number of stream lines united to form a 

 closed ring and we have a process analogous to that in the closed 

 system of a hot-water heating system. 



If now we study the process within such a ring, assuming for the 

 sake of simplicity that it has only a slight vertical range so that 

 equal differences of altitude correspond to equal differences of pres- 

 sure then we may consider it as represented by the scheme outlined 

 in fig. 54. 



In this figure let A B represent the ascending and CD the descend- 

 ing branch, and so choose the connecting pieces B C 

 and A D that the masses contained in them are in 

 equilibrium with each other (that is to say that equal 

 masses are contained in those portions on the right 

 and left hand of the central line) (which of course re- 

 quires that C shall stand a little higher than B, and D 

 somewhat lower than A) then the excess of pressure at 

 D is equal to the difference of the weights of the fluid 

 fig. 54 columns A B and C D. If now we further assume 



that the horizontal lines or divisions indicated in this 

 figure correspond to equal differences of pressure, then equal masses 

 of fluid are contained between two successive sections (if the areas 

 of the sections of the tubes are uniform), and the weights of the two 

 vertical columns are proportional to the total number of the sec- 

 tions. 



But the excess of pressure corresponding to the difference of the 

 weights of these columns is the same at each cross-section of this 

 closed system. 



Now, when vertical motion is set up and a steady condition of 

 motion is established, the ascent of any mass in A B is always at the 

 expense of the sinking of equal mass in D C, since the masses that 

 flow through a unit section in a unit time must be the same for every 

 section. In consideration of the different densities in the ascending 



