THE POLYPHASE CIRCUIT. 307 



the lines. The case of a non-inductive load and also of 

 an inductive load are shown. Imagine the series coil of a 

 wattmeter to be inserted in one line, carrying the current 

 Ci, for instance, in the right-hand diagram. Suppose also 

 that the volt coil of the wattmeter is connected so as to 

 read the voltage between the same line and one of the 

 others, so as to read the voltage E l} for instance. The 

 wattmeter reading will then be C l E l cos E l C^ that is 

 C E cos (30 <). Now imagine the volt coil thrown over 

 to read the voltage between the line in which the current 

 flows and the other line, and suppose this to be "._,. The 

 watts read will now be C l E% cos E 2 C 1} or C E cos 

 (30 -f 0). Thus the two readings of the wattmeter will 

 be respectively C E cos (30- 0) and C E cos (30 + 0), 

 i.e. C E (cos 30 cos <f> + sin 30 sin 0) 

 and C E (cos 30 cos - sin 30 sin *) 

 The sum of these is 2 C E cos $ cos 30 = \/3~C E cos 0, 

 which is the value in watts of the power in the circuit. 



We have, therefore, the following rule for determining 

 the power in an equally loaded inductive three-phase circuit. 

 Connect the wattmeter with its current coil in one of the 

 line wires, and join the volt terminal alternately to the 

 other two line wires. The sum of the two readings thus 

 obtained gives the total power on the circuit. The load 

 and power factor on the three lines are of course assumed 

 equal. 



Incidentally it is worth noticing that the difference 

 between the two wattmeter readings when divided by the 

 line voltage gives the idle current directly. 



The difference of the readings is 2 C E sin 30 sin <t>. 



= ZCE $sm<l> = E. C sin*, 



and C sin is the wattless current in the line. (See page 

 74). 



The method just given, although simple in use for 

 occasional measurements, or when arranged with a throw- 

 over switch, has the disadvantage that it requires two 

 readings to be taken and to be added together. It is 

 therefore not a direct reading method suitable for switch- 

 board use. 



The next method to be given is suitable for permanent 

 connection in the circuit for obtaining direct readings. 



