150 A. TANAKADATE. 



which way the source lies by observing the vertical force and 

 its vertical variation at the place : but when the effect is super- 

 posed with a larger field of force as usually the case is, what is 

 now described in algebraic sense will happen in arithmetical 

 sense, and it will be impossible to decide, from the variations of 

 vertical component alone, which way the seat of that field lies, 

 unless we have some means of separating the two effects. 



The succession of various states of the distribution of vertical 

 variation on the sphere, as the source recedes from it, is reversed 

 essentially in similar way to that which was observed when it 

 approached the surface from below, only reduced in magnitude. 



When the height of the source is small, the circle of no 

 variation and that of maximum variation will be found close to 

 the subcenter, the other circle of no variation being found in 

 the neighbourhood of 70° 2 from the subcenter dividing the sur- 

 face into three regions as before. The circle of minimum varia- 

 tion is now wanted, being confounded with the ill-defined maximum 

 at the antipode. 



As the source recedes further from the sphere all those 

 places of demarkatiou will be shifted toward the antipode, the 

 maxima and miiiima becoming less and less distinct, the varia- 

 tion itself subsiding in assymptotic decay. The limiting positions 

 of the circles of no variation are 54° 5 and 135° i from the sub- 

 center and that of the greatest variation 90° from the same point. 



The Variation of the Horizontal Component 



ÖH 



' _ Q rsiQÖ(R — rcos^) 



03 p"" 



vanishes always at ^ = i.e. pericenter 



and. d = 71 i.e. antipode. 



When the source is above, it vanishes also at 



