Mr. J. Stuart on Galvanomagnetic Attraction. 221 



x bTc-b 3 



/* 6p 2 



{ — (cos (3 — cos a) + (cos 3 {3 — cos 3 a) } 



+ - ^q 4 55 { - ^(cos /3 - cos a) + 33(cos 3 /3 - cos 3 a ) 



-39(cos 5 /3— cos 5 a) + 15(cos 7 /3— cos 7 a)} 

 H — ^ Q c ~ { — 75(cos /3 — cos a) + 575(cos 3 /3— cos 3 a) 



- 1590(cos 5 /3 - cos 5 a) + 2070(cos 7 /3 - cos 7 a) 



- 1295(cos 9 13 - cos 9 a) + 315(cos n |8 - cos 11 a)} 



- = X a { + (sm 3 /3- sill 3 a)} 



+ ^±LZ^_{ _ 12(sui 5 /3- sin^ «) + 15(sin 7 /3 - sin 7 a) } 



+ 5 + c ^~ - { + 120(sin 7 j3 - sin 7 a) - 420(sin 9 - sin 9 a) 



+ +315(sin u /3-sin u a)} 



These expressions for X and T will be converging for all points 

 situated at a greater distance than b -\- c from any point of the axis 

 A B, inasmuch as they are composed by adding together correspond- 

 ing terms of series which are then all convergent. Among other 

 points, these expressions hold for such as are situated on the axis 

 external to the bobbin, and not nearer A or B than by the distance 

 (b-\-c). For such points, however, the expressions become illusory, 



assuming the form -. They may, however, be evaluated by the 



methods for the evaluation of vanishing fractions. T is clearly zero. 

 X may be more readily obtained directly from the expression for U. 

 From that expression we find that for a single circular current the 

 attraction on such points is 



{ r 3 2 r 5 8 r 1 J 



Hence, in the case of a bobbin, if x be the distance of the attracted 

 point from O, the middle point of the axis of the bobbin, we have 



T+c-V 



+8 40g-/')' ( * +/ -*- /) 



b+c-W 



112(^-/7 



+• , " 



{«+f-"-n 



