680 Prof. J. J. Tlioinsoii on the Magnetic l^roperties of 



>1 fcoaPp d r f d\v—^ 



ipior 



. o>i ea)a/y a C / d\V 



r 



tpior 



=-<-'>^r™f'^,-r-:ii{..-.,)^-.(;:',r'^';^' 



+ (.. + .,>-:fA) 



'^=(-)-^xT.S:n 4a (--)-^(ir"'^'' ^' 





r 



wr 



_(,+ ,y),-i(_^)' 



These expressions give the intensity of the magnetic force 

 at any distance from the rotating system : the terms in these 

 expressions most important for the study of the physical pro- 

 perties of the system are those proportional to 1/r, as at 

 a distance from the system large compared with the wave- 

 length of the vibration the other terms become insignificant. 

 Confining ourselves to these terms we find after a little 

 reduction that the magnetic force at a point P is equivalent 

 to (1) a component M in the plane PO^ at right-angles to 

 OP given by the equation 



^ ^ 1.2.3...(;?-1)V2V; 



COS^ j( (Ot— ^ j — <^ — --- 



sin^'-l 6 



and to a component L at right-angles to this plane given by 

 the equation 



2e(Dp /apw\P 



sinP-^d coaO . \f o>r\ , tt i 

 smp[[o,t-yj-4>- 5- j, 



where, as before, 6 is the angle between OP and 0^^ and ^ the 

 angle the plane PO^ makes wi=:h the plane of xz. 



The components of the electric force are VL in the meiidian 

 plane and \'3I at right-angles to it. 



