Belas and Hartog — Path of a Small Permeable Body, Sfc. 37 



along the axis it is a position of unstable equilibrium, the sphere moving to 

 the nearer pole. 



We refer to this spot as the Eesting point or E. P. The two poles are, 

 of course, also E. P.'s, stable for all displacements. The most noteworthy 

 feature in this diagram is that while the curves are symmetrical about the 

 axis, the E. P. does not coincide with the C. F., and the diameter is curved. 



Fig. 2 shows the path of the same sphere in the field between two 

 South Poles. Here there is not such a lack of symmetry. The 0. F. and 

 E. P. are practically coincident, but there are in addition two other 



.•0... 

 '"■."/ 



*..••' ' ' • ' 



:r:':::.:::.v.v:--.vv s° 



•®. 



Fig. 2. 



" diametral " E. P.'s with a change in the sign of the curvature of the 

 trajectories on either side. Thus there are in this field five E. P.'s, viz. the 

 two poles stable for all displacements, the C. F. unstable for all displace- 

 ments, and the two new ones which are stable for displacements along the 

 diameter only, but unstable for all others, the particle moving along a curve 

 to one or other pole. The actual position of the diametral Eesting Points 

 of an inductor depends on the theory of greatest diameters. 



Fig. 3 shows the trajectories of the same sphere in the extra-polar 

 regions of the fields shown in fig. 1, and fig. 4 a similar region corresponding 

 to fig. 2. 



The lines are practically radial near the poles, and, beyond indicating 

 some changes of curvature in the outer regions, show little of interest. "We 



