certain Apparatus for Distribution of Electricity. 293 



secondary coil of the induction-coils. It is easy to so con- 

 struct the induction-coils that the difference of potential 

 between the terminals of the secondary coils may be any 

 suitable number of volts, such as 50 or 100 ; whilst the 

 potential of the primary circuit, as measured between the 

 terminals of the dynamo machine, may be very great, e. g. 

 2000 or 3000 volts! If the electromagnetic action between 

 the primary and secondary coils, on which the useful effect of 

 the arrangement depends, were the only action, the supply 

 would be perfectly safe to the user so long as apparatus with 

 which he could not interfere was in proper order. But the 

 electromagnetic action is not the only one. Theoretically 

 speaking, every induction-coil is also a condenser, and the 

 primary coil acts electrostatically as well as electromagneti- 

 cally upon the secondary coil. This electrostatic action may 

 easily become dangerous if the secondary generator is so con- 

 structed that its electrostatic capacity, regarded as a condenser, 

 is other than a very small quantity. 



-fi — Earth 



D 



Imagine an alternate-current dynamo machine, A, its ter- 

 minals, B, C, connected by a continuous conductor, B D C, 

 on which may be resistances, self-induction-coils, secondary 

 generators, or any other appliances ; at any point is a con- 

 denser, E, one coating of which is connected to the conductor, 

 or may indeed be part of it, the other is connected to earth 

 through a resistance, E. Let K be the capacity of the con- 

 denser, V the potential at time t of the earth-coating of the 

 condenser, U the potential of the other coating, x the current 

 in resistance R to the condenser from the earth, being taken 

 as positive, and the earth-potential as zero. We have 



whence, since 



U=Asin27ntf, 



where A is a constant depending on the circumstances of the 

 dynamo circuit as well as the electromotive force of the 

 machine, and n is the reciprocal of the periodic time of the 



