INVESTIGATION BY POTENTIALS. 



33 



result is subject to the same remark as those of Articles 

 15 and 17. 



19. Remarks on the computation of these quantities 

 by the method of Potentials. 



The method of Potentials depends on the algebraical 

 fact, representing a mechanical law like that of Virtual 

 Velocity, that when a point x'y'z attracts a point xyz 

 with a force R which is a function of the distance r be- 

 tween the points, the force in the direction x, or 



R . - , can be expressed as - R . -j- : and therefore, 

 v ax 



f T\ Ct/ O -. * d O \AJt \A/*^J -1 



if R = , it can be expressed as -7- . or : and 



dS dr dS 



T ~J~ or T~ 



dr dx dx 

 so in the directions of the other co- 

 ordinates. (Repulsion must be con- 

 sidered as negative attraction.) Here 

 S is the Potential. 



In the case of a needle B, let x 

 be measured upwards on the paper 

 and y to the right hand : if its semi- 

 length is b inclined at an angle to 

 the axis of x, and its center has for 

 co-ordinates c in x and e in y, x will 

 = c -f b cos 6, y = e + b sin 6. These 

 apply to the pole which is on the 

 right hand of the diagram Fig. 15 : 

 for the opposite pole, b is negative. 

 The form of the general theorem can 

 then be conveniently altered, thus : 



3 



