16 L. Schwendler — On the General Theory of Duplex Telegraphy. [No. 1, 



As we have supposed that the magnetic action of any one cylindrical 

 coil is proportional to the magnetic action* of an average convolution it is 

 also consistent to put s' = a", and we have at last 

 A" V _ 1 

 A' l'~ 2 

 If now the two bobbins of the coils a and b are taken of equal length, 

 and if the thickness of the a coil be d', the thickness of the b coil d", and 

 the diameter of the iron core 2 r, we have, 



jr_ d" 



A 7 ~ d' ' 

 V =(2r+ d') rr 

 I" = (2 (r + d') + d''] it 

 (4 r + d') d" = 2 d' (r + d') 

 This equation fixes the relative dimensions of the two bobbins 



ve v == v o 



and their cores in order to have v = v 2 



Suppose for instance we make d' = d" arbitrarilyf we get 2 r = d, 

 and from it can be easily calculated that the diameter of the wire of the b 

 coil should be about 19 per cent, larger than that of the a coil. The 

 absolute diameter of the wire depends of course on the absolute dimensions 

 of the bobbins, and on the resistance of the line for which the instrument 

 is to be used. But this question, although of practical importance, has 

 nothing to do with the Theory of Duplex Telegraphy. This settles the 

 solution of the 1st problem of the compensation method. 



* Lenz and Jacobi have experimentally proved that, •within certain limits, the 

 magnetic force exerted by a convolution on its centre (iron core) is almost independent 

 of the diameter of the convolution. These limits are generally fulfilled in Telegraph 

 Construction. Hence the magnetic action of a coil can be put proportional to the 

 magnetic action of one convolution. Theoretically this can of course not be true, for the 

 magnetic force exerted by a convolution necessarily extends on both sides of the plane in 

 ■which the convolution is situated. Therefore the wider a convolution is the less of its 

 total force exerted will be made use of for producing magnetism in the iron core, and, 

 consequently, the force exerted by a convolution on its centre 'must decrease with the 

 diameter of the convolution. It appears, however, that this decrease is exceedingly slow, 

 and in the present investigation it is considered unnecessary to be taken into account. 



t I have not been able to find anywhere a definite law which connects the diameter 

 of a coil with the diameter of the core acted upon. In Siemens' relay, an instrument 

 so well considered in all its details of construction, the diameter of the coil is about 

 three times the diameter of the core. In the absence of anything else on the subject 

 I thought myself justified in using this proportion. Hence the substitution of d' = d", 

 which gives d=2r, or total diameter of the a coil equal to three times the diameter of 

 the iron core. 



