PATHS OF MOVING PARTICLES SPRUNG 67 



A current of air in the neighborhood of the north pole can only 

 flow in a straight line no matter in what direction, when a force 

 to the amount of 2Vco in the opposite direction to this deflecting 

 force or directed from right to left renders this departure from the 

 path of inertia possible; in this case therefore the barometric or 

 elastic pressure in the current of air must increase from the left 

 towards the right. In the same manner in a straight channel, no 

 matter in what direction it trends, the moving liquid should stand a 

 little higher on the right than on the left, and in fact independently 

 of the nature of the liquid it results that we must have 9 



H — H 2vcu 



~^~ = T 



where H — H denotes the difference of height between the two 

 shores of the stream, and L the width of the stream assumed to 

 flow everywhere with uniform velocity. 



The special case of motion due to inertia in the region of the pole 

 has been treated so fully in the foregoing text because the construc- 

 tion of the paths in that region can be made on the basis of certain 



9 It will be proven presently that the above expression corresponds to 

 the following equation for any latitude cp: 



g (H — H ) = 2vcu sin <f>.L 



For example, if for <p = 50 , iut sin <P has the value 0.0001117; for a width 

 of river L = 100 meters and a velocity v = 10 meters there results H — H =» 

 0.0114 meter. Hence in every horizontal layer the pressure of the water 

 is by about 1.14 cm. of a column of water, greater toward the right than 

 toward the left. This amount certainly appears to be inconsiderable, but 

 geologists are accustomed to see very insignificant but constant causes 

 produce great results. Hence it has been attempted by the axial rotation 

 of the earth to account for such gradual displacement of river beds as is 

 seen in the frequently recurring and notable phenomenon that the right 

 side of a river is frequently closely bordered by a range of hills while on the 

 left side a tolerably broad strip of entirely flat land stretches along the 

 course of the river, as, for example, on the lower part of the courses of the 

 Elbe, Weser, Thames, Seine and Gironde and also on the Danube, Volga, 

 and other rivers of southern Russia where this is especially noticeable. 

 But recently this explanation, proposed by von Baer, has been freely con- 

 tradicted. 



The relation between the direction of the wind and its force and the dis- 

 tribution of atmospheric pressure which has found empirical expression in 

 Buys-Ballot's law can be easily derived from the above text. Further 

 details on this subject can be found in the works of Guldberg and Mohn 

 in the Zeitschrift der osterreichisches Gesellschaft fur Meteorologie, 1877, 

 Vol. XII, pp. 49, 177, 257 and 273; also Sprung. Ann. d. Hydr. u. maritime 

 Meteorol., VIII, Jahrg. 1SS0, p. 603, and Beiblatter, V, 1881, p. 237. 



