266 Prof.W. Peddie on the 



greatly diminished by distance, these changes will not readily 

 occur, will occur only under special circumstances, and the 

 effect of an external field on the emission of radiation will 

 be slight. The axes of rotation or! the shells will always, 

 apart from slight vibrations due to disturbances caused by 

 electrons or other atoms, be co-linear. The trouble arising 

 from want of parallelism of the elementary magnets, which 

 appeared for example in Bitz's model, does not arise in this 

 system, which thus gives a ready explanation of that con- 

 stancy of the magneton to which Weiss's work has given a 

 fairly broad basis of experimental support. 



No more than one stable condition is possible unless the 

 number of shells exceeds three. In the case of four, if we 

 write r /J d /r n z^2 n A fl , m*.u y y v .-=w v ., and a^ for 3/871- cos 6 times 

 the equatorial field acting on the /xth shell, we have 



0.^1+^2 +%d 4#4 — «i=0, 



gAx. #! + (). # 2 +#3> +«4 — «2 — 0> 



8 A x . X 1 + 3 A 2 . X 2 + , #3, +^4 —^3 = 0, 



4 Ai . %i + 4 A 2 . x 2 + 4 A 3 . o? 3 , -f0.^ 4 -a 4 = 0, 



If we reverse a^ we must reverse ot^ Hence no case with 

 one x reverse and the others direct is possible. 



Now consider the moments of all the shells to be equal 

 and write ^—p^u ^s^Q^iy x^ — rx^ The conditions are 



+p 



+ q 



+ r 



-«i'=0, 



pi+0 



+ </ 



+ r 



— 1' = 0, 



-< 



>*+» 



+ r 



-«•' = <>, 



3 , (r 



" \P 



f< 



) + 



— a 4 '=:0, 





i>p> 



q>r. 





and 



With the second and third terms, and therefore a 2 and u 3 r , 

 negative, the first equation cannot be satisfied; with the 

 second and fourth terms, and therefore a 2 ' and e^', negative, 

 the second equation cannot be satisfied. Similarly, if the 

 third and fourth terms are negative, the third equation 

 cannot be satisfied ; and the first condition prevents the 

 second, third, and fourth terms from being negative simul- 

 taneously. So only one stable arrangement (all terms in- 

 volving p, q, r positive) is possible with four, as with three, 

 shells provided that the magnetic moments of the four are 



