134 



THE MECHANICS OF THE EARTIl's ATMOSPHERE. 



The approximate course of the Hues tp=n and //>=<> is shown iu Fig. 4. 

 The completion of the boundary of the region of z is formed by the 

 line (p=— go, namely, 



x=2 k (p—2e~' l 'Gos f/'+«i 



y=2 k ip+2e~ <t> 8imp-{-bi 

 and by the line, <p=+co, namely, 



x=lc tp+ Vl—k 2 .t+<h 

 y=z1c cp- y/l—k 2 ><P+l>2 

 where ai, 6i, «2, 62 are constants whose values are easily obtainable 



and which are partly used in the 

 computation of a and b. The first 

 of these two lines can be defined as 

 a half circle that is described with 

 an infinitely large radius about the 

 origin of coordinates; the second is 

 astraight line that is perpendicular 

 to the jet at an infinitely gre.it dis- 

 tance from the origin; at this dis- 

 tance the jet forms an angle with the 

 positive axis of x whose cosine 

 equals k. 



If we assume that k equals 1 then 

 a becomes infinite and the point 

 Fig 4 («, b) removes to infinity ; the region 



of oa cau in this case be bounded 

 by the lines f=7t and f= — n instead of by the lines ^=7rand </=0; 

 thus we come to the case treated of by Helmholtz and illustrated by 

 Fig. 5. 



-X 



M 



y 



\ 



*-~*\— 



fc "\~ T 



( 



-*. ■> 



Fi-r. «. 



Fig. 5. 



If we make 7c equal zero then will b equal zero; iu this case the 

 boundary of the moving fluid is represented by Fig. 6. 



