the Directive Power of Magnets, fyc. 235 



expressions become illusory, assuming the form f j they may, 

 however, be evaluated by the methods for the evaluation of 

 vanishing fractions. Y is clearly zero. X may be more readily 

 obtained directly from the expression for U; from that expres- 

 sion we find that for a single circular current the attraction on 

 such points is 



v . J « 2 3 a 4 15 a 6 ) 



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



attracted point from 0, the middle point of the axis of the bobbin, 



we have 



X fx-frb+c , a i 3 fl 4 15 a 6 v 



= _ b + ~c 3 -b 3 

 b + c — b 5 



[x+f -oc-f 



+ , 



which gives X for points situated on the axis for which x is not 

 less than (b + c+f). 



The expressions for forces which concern us now are those 



X Y 



given by the general formulae for — and — . And a moment's 



glance at these will show that they explain the apparent posi- 

 tion of the pole at the very extremity of the coil ; for in order 

 to ascertain the values of the forces in a plane at right angles to 

 the axis passing through the extremity of the coil, we must make 

 a = 90°, sina = l, cosa= 0; and if the other end of the coil be 

 very distant, /3 may be taken =0, sin/3 = 0, cos/3 = l. Substi- 

 tuting these values, it will be seen at once that X, the longitu- 

 dinal force, =0, while Y, the transversal force, has a value which 

 indicates a force directed to the extremity of the coil. 



In order to make a complete comparison, I have, for all the 

 eighteen stations treated in the former Tables, taken the values 

 of a, /3, and p graphically. For b I have adopted 045, and for 

 b + c 0*7. These numbers correspond to the internal and external 

 surfaces of the coil ; but they appear to me best to represent 

 (though doubtless with some inaccuracy) the quantities used in 

 the theoretical investigation. Then I have (with the kind as- 

 sistance of Edwin Dunkin, Esq., of the Royal Observatory) made 



