764 Dr. Fleming on the Determination of the 



Strictly speaking we should add to the value o£ the ex- 

 pressions (1) and (3) for the inductance of a rectangle and 

 a square a term equal to B//27ra, where B/ is the high 

 frequency resistance corresponding to a frequency n. The 

 formulae (1) and (3) as they stand give the inductance for 

 infinite frequency. The value of R'/27rn is, however, generally 

 negligible compared with the other term, and the expressions 

 given may be taken to be the inductances for any frequency 

 of the order of 10 G . 



In the next place, we may employ the same instrument 

 to determine the coefficients of coupling of the circuits of 

 an air core-transformer such as an oscillation transformer 

 used in wireless telegraphy. Suppose the inductance of the 

 primary circuit to be denoted by L, that of the secondary by 

 N, and the mutual inductance by M. Then M/ v^LN is 

 called the coefficient of coupling, and is a quantity of im- 

 portance in the theory of high-frequency transformers. 



We may join the two circuits of the oscillation transformer 

 into one circuit so that they assist or oppose each other in 

 creating co-linked flux. In one case the effective inductance 

 is equal to L + *2M + N, and in the other case it is L — 2M + N. 



Hence if we treat the oscillation transformer so joined up 

 in the two ways, and measure as above its effective induct- 

 ances, and call them Lj and L 2 , we have 



Lx = L + 2M + N, 



L 2 = L-2M + N. 



Hence ->»- _ Li — L 2 



and x , at L x + L 2 



4 



L + N = 



We can then determine directly and independently the larger 

 of the two inductances L or N, and hence we can calculate 

 the value of M/y^L.N or the coefficient of coupling of the 

 circuits. As an instance of such a determination we may 

 give the measurements made with a form of oscillation trans- 

 former used in wireless telegraphy. The primary circuit 

 consisted of one single turn composed of 8 turns of 7/22 

 insulated copper wire in parallel wound round a square 

 wooden frame. The secondary circuit consisted of turns, of 

 the same stranded wire wound over the primary circuit. 

 The resultant inductances were measured by the cymometer 

 with the circuits joined up to add and oppose each other. 



