HiLiGENDOKF.— Om Infiueuce of the Earth' a Rotation. 207 



A stream flowing straight has a symmetrical cross-section, 

 the swiftest current in the centre. Admit a curve and centri- 

 fugal force comes into play ; and since this force varies as the 

 square of the velocity, it throws the swifter strands of the stream 

 towards the outer bank ; corrasion results there, a deposit is 

 formed on the inner bank, and the eccentricity, so far from 

 correcting itself, goes on increasing until quite other forces come 

 into play. 



Now, Ferrel proves that the deflective force of the earth's- 

 rotation (be its apparent efiect large or small) varies as the velo- 

 city of the stream ; and this is the main point of the argument. 

 If it varies as the velocities, it must exert a selective action 

 on the various strands of water moving at different velocities. 

 It moves over to the left bank* the strands of water moving 

 most quickly. Now, in water moving round a curve, with the 

 outside to the left, the centrifugal force moves the water to the 

 left as the square of the velocities, and the rotational force 

 moves the water to the left as the velocities, and these two forces 

 act in concert, and their effects are summed. If the curvature 

 has its outside to the right, the centrifugal force tends to['move 

 the thread of greatest velocity to the right, but the rotational 

 force tends to move it to the left, and the two forces are opposed. 

 Gilbert expresses this by means of the follo'wing equation : — •'" 



V = Velocity of stream ; 

 r = Radius of curvature of stream-course ; 

 n = Angular velocity of earth's rotation ; 

 / = Latitude of locality : 



Total displacement of velocity to left v + r sin I 

 Total displacement of velocity to right v — r sin I 



Giving the values derived from the study of the Mississippi, 



n = 0-000072924 rad. per second, 

 V = 8-4 ft. per second, 

 r = 8,000 ft., 

 I = 37°, 

 we have, were it in Southern Hemisphere, '. 



^ = 1087 

 R 



— that is, the selective movement of velocities to left bank is 

 nearly 9 per cent, greater than to right bank. 



Let me refer now to the law that the transporting-power of 

 a stream varies as the sixth power of its velocity. It is a matter 



* All streams are supposed to be in the Southern Hemisi)here. 



