386 Mr Searle, On the Calculation of Capacities 



Capacity between two conductors. 



§ 12. In many, perhaps in the majority of cases, the relation 

 between two insulated conductors in the presence of other con- 

 ductors is in question. To lead up to the mathematical definition 

 appropriate to this relation, it will be convenient to consider the 

 manner in which this relation is examined in engineering practice, 

 in the case of a cable containing several conductors. Two of the 

 conductors, say [1] and [2], are selected and insulated ; the sheath 

 of the cable and some of the other conductors are earthed and 

 the remaining conductors are insulated. The conductors [1] 

 and [2] are then joined to the two poles of an insulated battery, 

 and thus receive equal and opposite charges — say + e and — e — 

 provided, as is the case in practice, that the charge upon the 

 battery itself be negligible in comparison with that on either 

 conductor. The charge on either conductor is then measured by 

 disconnecting the conductors from the battery and connecting 

 them through an insulated ballistic galvanometer, whose "throw" 

 measures e. Since e is proportional to the e.m.f. of the battery, 

 it is convenient to have a term to express the ratio of e to the 

 e.m.f. of the battery. We are thus led to speak of the capacity 

 between two conductors and to define it as follows : — 



Definition B. Let there be the n conductors [1], [2], ... [n] 

 in the field and let them all be initially uncharged. Then, if 

 the potentials of two insulated conductors [1] and [2] become 

 v x and v 2 when the equal and opposite charges e and — e are given 

 to [1] and [2], the ratio of e to v-i—v 2 is called the capacity between 

 [1] and [2} in the presence of [3], . . . [?i]. 



The capacity between the conductors [1] and [2], as thus de- 

 fined, depends, in general, not only upon the forms and positions 

 of the remaining n — 2 conductors, but also upon their electrical 

 conditions, and thus it is necessary to specify in each case which 

 of the conductors [3], [4], . . . [n] are insulated and which are kept 

 at the constant potential zero. 



If, initially, the insulated conductors have given charges, while 

 the other conductors are maintained at given constant potentials, 

 the definition would run as follows : — 



Let [1] and [2] be two insulated conductors with any initial 

 charges e l and e 2 , and let any number of the other n — 2 con- 

 ductors be insulated and have given charges, while the remainder 

 are kept at given constant potentials. Then, if the potentials 

 of [1] and [2] are changed from v x and v 2 to v x + V x and v 1 +V 2 , 

 when the charges are changed from e Y and e. 2 to e 1 + E and e x — E, 

 the ratio of E to V 1 — V. 2 is called the capacity between [1] and 

 [2] in the presence of [3], ... [n\. 



