l8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



magnetic energy than this, which, however, is not so symmetrical — 

 this is a triangular-prism arrangement Consisting of two parallel 

 groups of three. 



But quite apart from the lack of three-dimensional symmetry of 

 some of these configurations (the effect of which will be seen 

 shortly), they can none of them have so low a magnetic energy (in 

 proportion to the number of magnetons) as the cubical arrangement 

 of eight. This, with its three fourfold axes of symmetry, is mag- 

 netically ideal ; and although it is not quite stable for spherical elec- 

 trons, there is no doubt that it would be exceedingly stable for 

 magnetons, because no other arrangement of eight can be nearly so 

 symmetrical. 



To illustrate the unique properties to be expected in this group of 

 eight, I have made a model (plate i) in which eight coils of insulated 

 wire are set in gimbals at the corners of a cube, the side of which is 

 two and a half times the radius of the coils. This cannot completely 

 illustrate the behavior of the group, because the cubical arrangement 

 is made compulsory, the distances are fixed, and the electric forces 

 are absent; but, when excited by an electric current, it shows what 

 configurations the eight can assume under such conditions. Most of 

 these are shown on plate 2, where it may be seen that the most sym- 

 metrical and stable configurations resolve themselves into a cycle of 

 six (figs. 1-6) which are very closely related to one another and 

 easily interconvertible: 1, 3, and 5 are identical except for their 

 relative attitudes in space, and the same is true of 2, 4, and 6. The 

 group is thus very stable, and yet very mobile, for its magnetons can 

 easily veer in all directions without destroying its identity. This 

 mobility, which is not possible without three-dimensional symmetry, 

 is a source of additional stability, for the group can adjust itself to 

 casual external fields, such as it would continually meet with owing 

 to the motion of the molecules, without needing to turn as a whole. 

 The directions of the currents and of the flux in configuration 1 are 

 shown in the following diagrammatic section of the upper four 



\ S 



coils : l\ 1 ■ ■ $ ! " ( ) . For the lower coils they are exactly 



N|S 



reversed. The less symmetrical configuration numbered 7 is most 

 easily described by saying that the four coils nearest to the camera 

 have their " N " poles to the left, and the others have them to the 



