MOVEMENTS OP ATMOSPHERE — -GULDBERG AND MOHN I 23 



physical state of the air of the upper strata. Moreover the velocity 

 of the wind and its direction are both eminently under the influence 

 of the surface of the earth, while their values at a certain height would 

 probably present the regularity that must obtain in order to be 

 able to predict the progress of meteorological phenomena. 



In studying horizontal currents under simple hypotheses, we have 

 introduced the friction due to the surface of the earth, and we have 

 applied our theory to the winds crossing over the equator, and to 

 whirlwinds. 3 



The numerical calculations accord with the phenomena of nature 

 \vithin such limits as correspond to the established hypotheses. 

 It follows that the exact observation of the velocity of the wind 

 will be of great importance to meteorology. We hope that these 

 results drawn from the mechanics of the atmosphere will show the 

 necessity of more extended meteorological observations especially 

 in the tropical regions and in the higher strata of the atmosphere, 

 and that true progress in meteorology is founded on the develop- 

 ment of the mechanics of the atmosphere. 



Chapter I 



THE ATMOSPHERE 



§1. Pressure, virtual temperature 



In studying the equilibrium and the movements of the atmos- 

 phere, it suffices to consider the air as a mixture of dry air and of 

 aqueous vapor. The other gases forming the elements of the atmos- 

 phere, of which carbonic acid gas is the most important, are found 

 only in such small quantities that their action may be neglected. 

 The quantity of aqueous vapor in the atmosphere is so small that 

 we can accept the law of Mariotte and Gay-Lussac for moist air 

 within the range of temperatures that occur on the earth. It is 

 necessary, however, to consider the cases in which the vapor con- 

 denses and passes into the liquid state or the solid state. 

 We use the notation 



p the pressure in kilograms on a square meter. 

 p the density or mass of a cubic meter. 4 

 t the temperature in degrees centigrade. 



3 M. C. M. Guldberg had already, in 1872, developed a part of this theory 

 in the Norwegian Polytechnic Journal (Polyteknisk Tideskrift), p. 73, 1872. 

 — Editor. 



4 In the absolute system here used this mass is the weight divided by 

 gravity. — Editor. 



