STEADY MOTIONS OF EARTH'S ATMOSPHERE ERMAN 41 



which agrees with the form of the converging series by putting 

 a = (a + br) 



£ = £ = 6= *. . =0 



X = + c 



In agreement with these assumptions determine the functions of 

 r that I will in general indicate by 



fi.n) 



and the constants 



A in) B (n) tc 



(to) (to) 



that enter into the following general expression for (f, 



? = fo° + h° 00 + ft 0V sin * + B x cos *) (! - /* 2 )* 



f U° W -*)+/»'(!- P 2 )*- /* ■ W sin ;, + S 2 ' cos /I) (1 - // 2 ) 

 + / 2 2 (A 2 2 sin 2 ^ -f B 2 cos 2 i) 



+ /4- 3 2 |,) + / 8 '(i-^) ! (/^)x 



X (^4 3 ' sin ^ + B 3 ' cos >i ) + . . 



From equation (C) it is evident tnat in this special case the terms 

 in <p that are multiplied by functions of X must disappear and that 

 therefore also the direction and velocity of the steady wind must 

 be as independent of the longitude of the place as is the assumed 

 distribution of temperature. 



If we have thus carried out the determination of <p, then, from 

 equation (A) there follows 



log£ = 



JM 



/ /a^V , /a^yi-V /a^y i 



d 



\ \dr/ \dnj- r \dX) (1 - n 2 )r 2 



2F 

 + Constant. 



and since the quantities under the integration sign can also be devel- 

 oped in series of the kind above considered, then, for all points of the 

 atmosphere, we shall know 



