Admittance and Impedance Loci. 301 



value either of the current or of the electromotive force : thus 

 we may assume a certain current to be constant (as the pri- 

 mary current of a transformer), and construct an electromotive- 

 force diagram with loci showing the changes in the various 

 electromotive forces as some part of the circuit is changed ; 

 or we may assume the impressed electromotive force constant, 

 and ascertain current loci for the same variation. Let us 

 limit ourselves to the transformer. In the first case above it 

 will be found that the constant assumed primary current I x is 

 a factor in the value of every line representing the compo- 

 nents of the primary electromotive force E x . By factoring 

 out Ij we have an impedance diagram similar to the electro- 

 motive-force diagram, and without any assumption as to the 

 value of the current or electromotive force. Similarly each 

 line in a current diagram, constructed for a constant impressed 

 electromotive force E 1? represents a current which is a mul- 

 tiple of an admittance (the reciprocal of an impedance) and 

 the factor Ej. By factoring out E x an admittance diagram 

 is consequently obtained, similar to the current diagram but 

 with no assumption as to the current or electromotive force. 

 Admittance and impedance diagrams accordingly correspond 

 to current and electromotive-force diagrams respectively, 

 differing from them only by a factor. 



Impedance and admittance loci, or electromotive force and 

 current loci, for the primary of a transformer will in general 

 be arcs of circles for changes in any one of the constants of 

 the primary or the secondary circuit. 



Some interesting relations arise from the reciprocal nature 

 of admittance and impedance. Let us note the following 

 relations between reciprocal vectors : — 



If any vector has an arc of a circle for its locus, a vector 

 proportional to its reciprocal will have an arc of a circle for 

 a locus. In fig. 1 let p x be any vector from the origin 0, 

 having its locus as shown upon the arc of a circle. The 

 vector p 2 , drawn in the direction of p L and proportional to its 

 reciprocal, will have its locus upon an arc of a .circle, which 

 may be shown as follows. Let p Y and />/ represent the vector 

 in any two positions, OA and QA'. The intercepts Oa and 

 Oa f will represent the reciprocal vectors p 2 and p 2 ' ; for in the 

 similar triangles OA'a and 0A</, 



Pi = Pi '• • pz ' p-2- 

 Hence 



pi p2 =piP'2— a constant. 

 The value of this constant product of p i and p 2 is OG". 



