n8 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



To obtain the upper pressure gradient, we consider the upper 

 isobars over B and A'. The difference of tern] erature between B 

 and .V is assumed y/x . dp cos W = dt. 



Therefore the upper pressure difference is 



(/>» + dp*) e~'/k (T m + dt) - p e-*/kT m =e-*/kT„ 



p z . y cos c 



j P a zdt 



dp* + 



kTJ 



= P<T z lkT, 



1 + 



xkTJ 



The distance between these isobars is \dp, ) cos <f> and the upper 

 gradient is consequently 



, 1 



y cos <j> 

 1 



e-°/kT, 



1 + 



/ i „cr cos </> 

 xkTJ 



y cos ^ 



e-'/kT, 



j , gflpg^o ycos <p 



T. 



and the ratio 



1 dp, 1 a/? . 



is sec 



o 2 6r ,o dr 



1 + 





y cos 1 T z 



% J r ' 



whi< 



gpz cosec <£. 



y si" v 



taking TJT to be unity, namely, 

 cosec ^ 



or 



sin 



cot ^ — cot (// sin (</> — </•>) 

 In the special cases. = o or 180 , the ratios are 



T ' x 



or 



1 ± - ), for z = 1000 meters. 



2.8a; 



If x = 2y, which would represent a possible case, the increase or 

 decrease would be about 18 ] er cent. 



For 4> = i~ tl e rotation would in the same circumstances be 

 lit io°. 



During tl e year 1905 aseries of observations in theupper airwas 

 made at Berlin and Lindenberg, near the time of the general 8a.m. 



