NIPPIER PROPERTIES OF A FIELD OF FORCE. 62 I 



with it an angle a , the component of F along this line 

 becomes 



P' _ ^^ (''' sin a -f- T) 



{r' ^+ 3 r'T'sina-l- T"^) f 

 The value of I^' =: o when 



T ^= — r' sin a , 



(3) 



the locus of which is a circle having the line r' as a diameter. 

 This circle is marked a a in Fig. i. F' also has a maximum 

 and a minimum value when 



'T-. , . , r cos a 



J =^ — r sm o. ± 



(4) 



V2 



The final term in this equation represents two circles tangent 

 to each other at the point O, having ""L as horizontal diameters, 



measured outwardly along the tangent line. They are marked c c 



m Fig. I. The value 7'in (4) represents two circles having radii 



— ''' "^f^- which intersect each other in m and O, and which 



r' 

 cut the tangent line in ± ~F^ respectively. They are marked 



d d in Fig. i. These latter points represent the locus of maxi- 

 mum and minimum F' along the tangent line. Lines from these 

 points through ?n pass through the centres of the two circles of 

 maximum, and make with the line r' angles whose tangent is 



-^, w^iatever may be the length of r'. 



The values of F' are graphically shown in Fig. 3 for a few 

 values of a- The areas of all these curves from T =. io 7 



= X , or 



A = / F'd T 



IS the same and is —, , or the potential at (J. 



If the values F' be laid off at right angles to the plane of Fig. 

 I, each curve being plotted on the line determined by the angle 

 a, the points determining the maximum and minimum F' will 



