146 



A. TANAKADATE. 



Fk. 6 



pole, and tlie other through the antipode and its nearest pole. 

 Their form is independent of the depth or height of the source, 

 being determined solely by the co-ordinates of the pericenter. 

 When the pericenter is close to either of the poles, they are nearly 

 circles which gradually 

 flatten until they coincide 

 with the equator and 

 the meridian, when the 

 source comes to the plane 

 of the equator. 



Inside both of those 

 ellipses, the force X' is 

 positive and in the irre- 

 gular zone between them 

 negative. Fig. 6 is tlie 

 stereographie projection 

 of those curves for the 

 intervals of 15° in the 

 values of <po. 



The West Component Y' vanishes over the meridian circle 

 ^ = ^ and ^„ + ^ 

 this corresponds to the nodal ellipse in the case of the north 

 component ; tlie force is positive on the west half and negative 

 on the east half of the surface. 



The maximum and mininuun of the north component are on 

 this circle, the latitude to be found from the value of d in (7). 

 Those of the west component are either on the nodal ellipse or 

 on the meridian circle which is at quadrature with that through 

 the source, at the same distance from the pericenter as those of 

 the north component. 



