200 POLYPHASE CURRENTS. [Exp. 



force diagram is seen to be similar to the circuit diagram (b) of 

 Fig. i. 



8. If we take one outside line, say B, as our starting point 

 (imagining if we wish that it is grounded, but this is unneces- 

 sary), we have the electromotive forces EE and EA represented 

 by the vectors, BO and OA, in the direction shown by arrows in 

 Fig. 4. The sum of these two vectors is BA. 



9. If, as is common, we take the neutral O as the starting 

 point (say ground), the differences of potential between the side 

 wires and ground are OA and OB, the direction of the vectors 

 being from the starting point as in Fig. 5. The difference in 

 potential between A and B is now the difference between OB 

 and OA, Fig. 5; which is the same as the sum of BO (equal 

 -OB) and OA, Fig. 4. 



10. In general, if we take electromotive forces in sequence 

 as BO, OA they must be added (Fig. 4) ; if, however, we con- 

 sider each electromotive force in a direction away from a com- 

 mon joining point as OB, OA they must be subtracted 

 (Fig. 5). For the simple case at hand, involving only two elec- 

 tromotive forces connected to a common point, the difference 

 method may be readily applied. For more complicated networks 

 the addition method is used, as it is capable of more general 

 application; it is based on the statement of Kirchhoffs Law 

 ( 32, Appendix I.) that the differences of potential around any 

 mesh add up to zero. For this addition method, all arrows are 

 taken consecutively, from feather to tip. 



II. If each transformer has a secondary winding, consisting 

 of two equal coils, connect the secondary coils of the two trans- 

 formers so as to form a star-connected and a mesh-connected 

 quarter-phase system, as in (c) and (d) of Fig. I. Measure 

 all voltages and draw diagrams of voltages for the star and for 

 the mesh connection. 



In the mesh connection, the two secondaries of one trans- 

 former are connected as the opposite sides of a square, due 



