21 



that the surface of the earth was veering to the left in the Northern 

 Hemisphere. It is more natm-al to regard the inverse perspective — 

 that is, the earth and resting bodies as stationary — then the paths 

 of inertia are apparently being continuously deflected to the right. 

 Earth rotation exerts no effect on a water mass free from circulation 

 relatively to the earth, but on the other hand no true conception of 

 free-moving currents can be had unless this great influence is con- 

 sidered. In this connection it should be realized, from the foregoing 

 remarks on motion on a rotating sphere, that currents can not be 

 traced solely to a provocative force at their source, but they are 

 only to be observed as a resultant of a force, the effect of which is 

 constantly being deformed by the earth ''sliding" beneath it. If 

 a water particle moves solely due to inertia, without being acted 

 upon by any force, it will follow a course ''cum sole" (clockwise with 

 the sun). As the latitude increases the tendency which drives a 

 water particle to the right of its course becomes more and more 

 intensified, and the faster it moves, the greater becomes the quasi 

 force tending to deflect it. 



In order to study this quasi force in detail, it is convenient, similar 

 to the procedure employed in the investigation of varying mass and 

 pressure (see fig. 4, p. 12) to regard the circulation of the curve in a 

 plane between any two verticals. We may take, for example, stations 

 A and B (fig. 6, p. 22), with their verticals AC and BD forming the 

 plane ABD C. The development of an equation for expressing the rota- 

 tion effect demands too great a digression into mathematics and is not 

 warranted here, but it has been evolved by V. Bjerknes as equal to 



ds 



where co represents the angular velocity of the earth, viz, 0.0000729; 



and is the projection of the closed curve of the circulation, as illus- 



ds 

 trated here by the rectangle ABDC, on the equatorial plane; and -,: 



represents the rate of change of the projection on the plane of the 

 equator. 



In Figure 6, page 22, if the curve of circulation ABDC, which is 

 being investigated, is projcted upon the equatorial plane, it is evident 

 that a change of the proportional area is eft'ected only by components 

 normal to the plane and not by those tangential to it. Also the 

 vertical movements can be considered negligible, since they are in- 

 significant as compared with horizontal magnitudes. Helland- 

 Hansen and Sandstrom have, by this means, found the value for 

 Bjerknes' equation in terms of the projection on the plane of the sea 

 surface 



ds da . 



dt = dJ'''''^ 



