134 



THE MECHANICS OF THE EARTH's AT:yiOSPHERE. 



The approximate course of the lines ^■=/T and //'=() is showu iu Fig. 4 



The completiou of the boundary of the regiou of z is formed by tht 



Hue q)=— X, namelj', 



—A, « 



,r=2 A- cp—le cos '/•+fli 



y=-2l- ,i--\.2e"''sini/-+bi 

 and by the line, ^=+00, namely, 



II =1- (p- ■v/i"r^2.9+/>2 



where «j, &i, Hi. b> are constants whose values are easily obtainable 



and which are i)art]y used in the 

 computation of a and h. The first 

 of these two lines can be defined as 

 a half circle that is described withl 

 an infinitely large radius about thei 

 origin of coordinates; the second is 

 a straight line that is perpendicular! 

 to the jet at an infinitely gre^it dis- 

 tance from the ori-in; at this dis- 

 tance the jet forms an angle with the 

 positive axis of .r whose cosine 

 equals A'. 



If we assume that A; equals 1 them 

 a becomes infinite and the point t! 

 [a, h) removes to infinity ; the region 1 

 of cj can in this case be bounded I 



by the lines //• = ;r and tj-= — 7T instead of by the lines c'' = 7rand ^=0;; 



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



Fig. 5. 



^ 



^ 



I 



ac 



( 



V~^ 



Fis. 5. 



,JC. 



Yi<'. 6. 



If we make A- equal zero then will h equal zero; in this case the 

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



