496 Prof. J. A. Fleming. On an Instrument for the [Jan. 26, 



is very useful in the laboratory for the determination of the coefficients 

 of coupling and mutual inductances of oscillation transformers. 



If there be two circuits inductively connected, forming an air core 

 transformer or oscillation transformer, and if these circuits have 

 respectively coefficients of self-induction L and N, and a coefficient 

 of mutual induction M, then we can determine L and N and M, if 

 these are not too large, by the instrument,_and also the " coefficient 

 of coupling " of the transformer, viz., M/v/LN. 



For this purpose we connect the two circuits of the transformer in 

 two ways. 1st, so that a current sent through the circuit flows round 

 in the same direction in the two coils ; and 2nd, so that it flows 

 in the opposite direction in the two coils. In the first position, the 

 effective inductance of the whole system is LI, where LI = L + 2M + N, 

 and in the second position it is L 2 , where L 2 = L - 2M + N. Hence, 

 LI + L2 = 2(L + N), and LI - L 2 , = 4M. Accordingly, we make four 

 inductance measurements with the instrument. 1st, that of the primary 

 coil alone, the secondary being open ; 2nd, that of the secondary alone, 

 the primary being open; 3rd, that of the primary and secondary 

 together joined up to assist ; and 4th, that of the primary and secondary 

 together, joined up to oppose. 



Twice the sum of the first two measurements should agree with the 

 second, and .one quarter of the difference of the last two gives the 

 mutual inductance. Having therefore L, M, and N, we can calculate 

 the coupling, Ml \/LN. 



In making measurement of this kind with high frequency currents it 

 is necessary to bear in mind that we cannot obtain the true separate 

 inductance of the primary coil simply by measuring it with the 

 secondary coil over it, even if that secondary coil has its terminals 

 open. There is a quite sensible dielectric current which passes from 

 turn to turn of the secondary coil when over the primary, even if that 

 secondary coil is open, and this dielectric current has the effect, in 

 accordance with well-known principles, of reducing the effective 

 inductance of the primary circuit. Nevertheless, in the above measure- 

 ment it is proper to take as L the inductance of the primary measured 

 in contiguity to the open secondary, and as the value of N the in- 

 ductance of the secondary measured in contiguity to the open primary. 



As an example of such a measurement the following figures may be 

 given. A certain air-core transformer had a primary consisting of 

 one turn of thick stranded copper wire, and a secondary of eight turns 

 of thinner stranded wire. Measuring as above described, the following 

 values in centimetres were found by the appliance here described : 



L = 695 cms., N = 45,700 cms. 



LI= L + 2M + N = 53,000 cms. 

 L 2 = L-2M + N = 40,120 



