STEADY MOTIONS OF EARTH S ATMOSPHERE ERMAN 



33 



analysis precisely the opposite holds good in the earth's atmos- 

 phere. The temperature which Laplace assumed to be uniform 

 throughout the fluid is in the earth's atmosphere extremely unequal 

 and, indeed, not only so in respect to the periodical portion of its 

 expression depending on the time, but also as to the other perma- 

 nent portion, which we ordinarily call the mean temperature of the 

 place. These mean temperatures, which are invariable as to time, 

 are, as is well known, a function of the coordinates of the location 

 to which they belong and, not only the analytical form of this 

 function, but also the constants that enter it are already known 

 .vith considerable approximation. 3 In accordance with these re- 

 alts of experience, it is certainly worth while to investigate the 

 .ollowing problem : 

 What is the nature of the movement and how great is the pressure 

 reduced barometric reading at any point of an atmosphere for which 

 uoth the resultant of gravity and centrifugal force and, also, the tem- 

 perature are expressed as functions of the coordinates of locality and 

 are independent of the timet 



The remarks that follow seem to me to prove that this problem 

 can be solved. 



If at any point of a liquid, or an elastic fluid or gas, at the time 

 / and with reference to three rectangular axes, we have the coordi- 

 tes x, y, z\ the explicit forces X, Y, Z; the velocities of motion u, 

 w, and if at this same point x, y, z, we have the density p, the 

 assure p and the temperature x, then by combining the conditions 

 equilibrium of this fluid with the general theorem for the move- 

 nt of any system, remembering 4 that 



(1) 



->ee for example Erman's Memoirs in the Archiv Wiss. Kunde, Russland. 

 he translator has taken the liberty of substituting d for partial differ- 

 and d for total differential instead of Erman's notation. — C. A. 



