PART II. POLAR MAGNETIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP. VI. 679 



where A, / and M (the magnetic moment of the globe) are constants. 

 From these equations we obtain in the first place 



t/x d-x . dy d-y ft ilr 



dt ~dP ^"dt ~dP ~ ~r* dt ' 



whence 



in, "; 



In the second place we obtain from (I) 



dr 

 ~dt' 



whence 



dx dy _ iM 



>r in polar co-ordinates, 



ind 



dt 

 By dividing (II) by (III), we obtain 



Js 



dtp iAf + 



Now, however, 



_ 



T) r/. " 



nd thus 





nd hence 



ar dr 



2 /ir 3 (ar -f Ji 



drp = 



Now it is evident that the particle must move in such a manner that the square root in the last 



xpression is always real. The radicand must thus be either positive or zero, and hence it follows 



lat those values of r which cause the vanishing of the radicand, define limiting circles, which the 

 article in its motion can never cross. 



It will be seen, moreover, from the expression for [3-] , that -j- is always and only then (apart 

 r om the value r = 0), when 



(IV) Cr 4 - 



