SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



With the same degree of approximation as before the right-h and 

 side of this equation can be put equal to -q; therefore the equation 

 takes the following form: 



n 



7) = b sin mx.e' 



m 



(18) 



which differs from equation (5') of the profile curve of the ground 

 only through the factor which is constant for each line of flow, which 

 factor causes the amplitude of the waves to steadily diminish up- 

 ward . 



TJcm Jim. Tfcm. Wffm. skm. xrf* 



FIG. 3 



If, now, the lines of flow are made through a definite point y' h 

 for the vertical and % = —^4, then for this point we determine the 

 appropriate value if from the transcendental equation: 



7)' - - b-e~ rn e~ n %- v) 

 m 



(19) 



and then substitute y h = y\— rf in equation 18. 



In this way we have computed the four lines of flow whose initial 

 and lowest points are at the altitude above sea level of 1000, 2000, 

 3000, and 4000 meters, and which are drawn as curves I, II, III, 

 IV, in fig. 3. The highest points of these curves are at the altitudes 

 2940, 3610, 4333, 5100 meters, respectively. 



