PAPER BY PKOF. OBEKBECK. 179 



Let tbere be furtbenuore — 



«, r, ic, the compouents of velocity; 



p, the pressure; 



//, the density; 



A-, the coefficient of friction ; 

 G, the acceleration of gravity ; 

 R, the radius of the earth ; 



>•, the distance of any point from the center of the earth ; 



f, the angular velocity of the earth. 

 Then we ha%'e — 



1 



(It ?X /-I ^x ' /x 



I 



dt ^ij i^dy fi )..,... (1) 



dt :)z M ?^ M 



Jx ?y ^z 

 Since according to the law of Mariotte and Gay-Lussac 



we may put 







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 + o'T. Except- 

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



consideration the influence of the factor jrr^'- ^^ the term just men- 

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

 this factor. Furthermore let 



Jc 



— = K 



M 



