214 POLYPHASE CURRENTS. [Exp. 



reach the original potential ; the algebraic sum of the potential differ- 

 ences at any instant, taken in the proper sense, adding up to zero. 



For an alternating current circuit in which currents and potential 

 differences vary harmonically and can be represented by vectors, 

 algebraic addition is used for instantaneous values and vector addi- 

 tion for maximum or for effective values; hence, for maximum or 

 effective values we have the modified statement of Kirchhoff's Law: 



32. Law (/). Vector Addition of Electromotive Forces: Gen- 

 eral Law. In proceeding completely around any mesh or number of 

 meshes in an alternating current system of conductors, the vector 

 sum of all the differences in potential is zero; such vectors form a 

 closed polygon. 



For this vector addition, electromotive forces are represented by 

 arrows, the tip of one to the feather of the next, which must be in 

 sequence according to the direction in which we proceed around the 

 circuit. A coil xy may have an electromotive force represented by a 

 vector XY, as measured from x to y. Taken in the opposite sense 

 (by traversing the circuit in the opposite direction) the electromotive 

 force would be YX, the same vector with arrow reversed. 



To illustrate* further this addition, from a point on the side of 

 a hill, let two paths ascend: one to the point A (elevation 100) ; the 

 other to B (elevation 90). If a man starts at A, descends to O, 

 ascends to B and back to A, the ascents and descents add to zero 

 (100; +90; 4-io). 



To illustrate the special case of subtraction, if the sense or sign of 

 one quantity be reversed: let two men start from 0, one ascending 

 to A (-f- ioo) and the other to B (-{-90). The difference in their 

 level is now the difference between + ioo and +90, which illustrates 

 the following law: 



33. Law (2). Vector Subtraction of Electromotive Forces: 

 Special Law. In an alternating current system, if two electromotive 

 forces are separately measured away from a common point (as OA 

 and OB} the difference in potential between their outer ends (A and 

 B} will be the vector difference of the two electromotive forces (OA 

 and OB}. 



* For unvarying potentials or instantaneous values of varying poten- 

 tials this is a correct analogy; for the vector addition of varying quantities 

 it is merely an illustration. 



