612 REPOKT— 1887. 



where c^ is the primary current, c^ the secondary, I the length of the wires 

 opposed to each other, d the distance separating them, r^ the resistance of the 

 secondary circuit. When these quantities are represented in C. G. S. units 

 M equals 'OOS. 



The current induced by one mile of one ampere at one mile distant is 

 1'3 X 10"^' amperes. A current is still perceptible at 1'9 miles distant; hence 

 we can calculate that a bell telephone requires six ten-thousand millionths of a 

 milliampere, or in figures -0000000006 milliampere to be audible. 



One curious result of these inquiries is that the disturbances are transmitted 

 equally well through water and the earth as through air, and hence our cables are 

 disturbed as well as our land wires. Communication with coalpits is possible, 

 though nothing but the earth intervenes. 



10. On the Coefficient of Self-induction in Telegraph Wires. 

 By W. H. Preece, F.B.S. 



The value of the coefficient L is given in terms of 10~* centimetres per mile. 

 It is very easily obtained on automatic circuits worked on the duplex system at 

 high speed. It is so small in copper that it may be neglected. 



The value of L in iron wire was found to be 



By the duplex method ... -00498 

 By direct measurement ... '0051 

 The mean result being ... '00504 



Hence L for iron wire, such as is used for telegraph circuits, may be taken as 



■005 X 10"' centimetres per mile, 

 while that for copper is less than 



■00001 X 10~'centimetres per mile. 



11. On the General Theory of Dynamo Machines} 

 By Edward Hopkinsox, B.Sc. 



A dynamo consists essentially of two closed circuits or ' tubes,' in both of which 

 there is a displacement of the nature of a flux dependent upon the relative motion 

 of the two circuits. We may call one of these the ' magnetic circuit,' and the other 

 the ' electric circuit.' Either or both of these may be in motion ; but as we are 

 concerned only with the relative motion of the two, we may for convenience (as, in 

 fact, is usually the case) regard the magnetic circuit as fixed, or displaced only by 

 the reaction of the electric circuit upon it, and consider the latter only as moving 

 under external forces, whether electrical or mechanical. The flux along the magnetic 

 circuit is called the ' magnetic induction,' which is a vector or directed quantity, 

 requiring for its definition reference to co-ordinate axes. It is subject to the fun- 

 damental condition known as the ' solenoidal condition,' or ' equation of continuity.' 

 The flux along the second circuit is called the ' electric current,' and is also a 

 vector quantity, subject to the solenoidal condition. Neither circuit is necessarily 

 bounded by tlie limits of the machine, and both may be and generally are subdivided. 

 Both these fluxes are produced by corresponding forces, called respectively ' mag- 

 netic force ' and ' electromotive force,' which likewise are vector quantities, but are 

 de6ned by reference to a line instead of by an area, as is the case with the flaxes. 

 (Maxwell, 'Treatise on Electricity and Magnetism,' vol. i. p. 10.) We now re- 

 quire to know the relation between each force and its corresponding flux. Let us 

 fir.st inquire into the relation between the magnetic induction (B) and the magnetic 

 force (H). Such a relation may be expressed by the general equation 



B=/-'(H)" (a) 



The form of the function depends upon the medium in which the tube is drawn, 



' For paper in full, see The Electrician, vol. six. Sept. 9, 1887. 



