of Duplex Telegraphy. 541 



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 r = s", and we 

 have at last 



A"l' _ 1 

 Ml" ~ 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 thick- 

 ness of the b coil d ff , and the diameter of the iron core 2r } we 

 have 



A^_cf 

 A!~ d /} 

 l / =(2r + d / )7r y 

 l /, = {2(r + d')+d // \>jr; 

 (lr + d f )d" = 2d'(r + d f ). 

 This equation fixes the relative dimensions of the two bob- 

 bins and their cores in order to have v= \ / -. 



Suppose, for instance, we make d f = d /f arbitrarily f, we get 

 2r = 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 de- 

 pends of course on the absolute dimensions of the bobbins, and 

 on the resistance of the line for which the instrument is to be 



* 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 mag- 

 netic 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's relay, an instrument so well considered in all its details of con- 

 struction, the diameter of the coil is about three times the diameter of 

 the core. In the absence of any thing else on the subject I thought my- 

 self justified in using this proportion. Hence the substitution of d'=d", 

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

 the diameter of the iron core. 



