PAPER BY PROF, OBERBECK. 179 



Let tbere be furthermore — 

 u, v, iv, the components of velocity ; 

 p, the pressure ; 

 //, the density; 

 A - , the coefficient of friction ; 

 6r, the acceleration of gravity ; 

 E, the radius of the earth ; 



r, the distance of any point from the center of the earth ; 

 e, the angular velocity of the earth. 

 Then we have — 



1 



dt t \r 1 1 Jx fx 



1 



dt dy > l M /' \ (i) 



dt & Pdz M 



dx jiy %& 



Since according to the law of Mariotte and Gay-Lussac 



we may put 



P=P° (1+aT) 





The zero point of temperature is arbitrary. It is most appropriate 

 to assume for it the average temperature of the atmosphere. 

 If c is the Newtonian value of the velocity of sound, then we have 



Mo 



After the introduction of these expressions into the above principal 

 equations, imagine the latter divided throughout by 1 -f a T. Except- 

 ing in that member in which the gravity occurs, one can omit from 



consideration the influence of the factor 1 , y - In the term just men- 

 tioned one can, as a first approximation, put (1 — aT) for the value of 

 this factor. Furthermore let 



k 



— — K 



