in the Branches of a Wheat stone } s Bridge. 171 



The point C always lies on the semicircumference OCA. 

 Hence the points H and D move on similar circles, their 

 distances from always being proportional to OC. 



For experimental purposes four coils were constructed 

 approximately alike, of the following dimensions : — The spools 

 were 44 centims. long, 2*5 centims. in diameter to the wind- 

 ings ; the round hole through the centre 2*3 centims. in 

 diameter ; the wire No. 22 B. and S. single cotton in 8 layers 

 of 492 turns per layer, making a total of 3936 turns. Four 

 iron cores were made alike of soft iron wire No. 16, insulated 

 with single cotton, 'and cut into uniform lengths of 44 centims. 

 The mass of each core was 407 grains. The resistance of 

 each coil was measured to be about 16*2 ohms. The reactances 

 and inductances were also measured for each coil both when 

 the iron cores are removed for minimum reactance, and when 

 they are in the central position for maximum reactance. 

 When no iron core is inserted, the induction of each coil is 

 •0166 henrys, and with a value of w = 876 this gives the react- 

 ance = 14*5 ohms. Combining the resistance and the reactance 

 we have 21*6 ohms impedance. When the iron core is inserted 

 the current with a constant potential source falls rapidly owing 

 to the increased impedance. When the core is in the central 

 position, the inductance becomes 1*084 henrys, corresponding 

 to a reactance of 950 ohms, and an impedance the same 

 as the reactance to within 0*15 of an ohm. It is interesting 

 to note that the inductance is increased 65 fold by inserting 

 the iron core. 



Fig. 6 represents to scale the case when no iron is in either 

 coil, and shows the variation of the points as two cores are 

 inserted one into each coil, until they are entirely in. The 

 angle AOC is laid off for no iron, equal to 



, SLo) 29 n 



arc tan ^ = » 9 .q-« = '9 approx. 



Hence 0=42° approximately. The E.M.F. OC is there- 

 fore 222*9 volts, and as the resistances are approximately 

 equal, the point H (the letters of all the figures denoting- 

 corresponding points) bisects OC. As the reactances of all 

 coils are approximately equal the point M also bisects AC, 

 and hence P lies at the middle point of OA. The current OD 

 is 6*9 amperes, in each circuit, making a total of 13*8 amperes 

 in the main line. Any change made by introducing the two 

 iron cores has the effect of moving the points upon the heavy 

 portions of their respective circles in the directions of the 



P2 



