Ill 



Between the coils, M and S, with its center on their common axis, a piece 

 of soft iron wire is suspended at an angle of 45° to the axis of the coils. 



In the instrument with which the following observations were made, 

 the coil M consisted of 72 turns of No. 22 copper wire wound in two 

 sections having 48 and 24 turns respectively. 8 was similarly wound 

 with No. 28 manganin wire and had a resistance of 668 ohms. Each was 

 made adjustable along their common axis for a distance of 13 centimeters. 



The needle was suspended with a fine phosphor-bronze torsion fiber. 

 The deflections were measured with mirror and scale. 



If an alternating current is sent through either of the Coils, the needle 

 becomes a magnet acted upon by a couple depending upon the instan- 

 taneous value of the current. The couple will be in the same direction 

 whatever the direction of the current. In short, it will vary as the sine of 

 twice the angle theta and as the mean of the square of the current values. 



Since the couple varies as the sine of twice the angle theta, it will 

 be a maximum for theta = 45°. Here also will be the position for the 

 least sensitiveness to change in the zero. 



In order to use the instrument as a phasemeter, readings of the deflec- 

 tion produced by the current in M, and the fall of potential in 8 are taken 

 independently. Then, usually, two readings of the deflection produced by 

 the currents in both coils simultaneously are taken — one in which both 

 couples act in the same direction, the other when they act in opposite 

 directions. The values of these two latter readings depend upon the 

 angle of lag, and together with the reading for the currents, independ- 

 ently, give sufficient data for its computation. 



The calculatiou may be made in two ways: 



(1) Analytically. 



(2) Graphically. 

 In the first method, 



Ci^ = A2.4- B2 + 2AB cos <? 



Cz" = A2 + B2 — 2AB cos <l> when 



A* is the deflection with M acting independently. 



B^ is the deflection with S acting independently. 



Cf and C| is the deflection with M and S acting simultaneously. 



<p may be found from either equation. 

 In the second method, two triangles are laid off with their sides proportional 

 to the square roots of the readings. The angle of lag, <{>, is given in either case as 

 shown in Fig. II. 



