Error in the Use of a Ballistic Galvanometer 



577 



of capacity C must be charged in order that its discharge 

 through a galvanometer may produce a throw 0, is 



27T<i(j' 



where t is the time of oscillation of the galvanometer-needle 

 and H is the strength of the controlling held. When this is 

 put for E in (2) it becomes 





(*) 



showing that for galvanometers with magnetic systems exactly 

 alike and moving in fields equally strong, the percentage 

 error under consideration is inversely as the galvanometer- 

 resistance, the capacity of ihe condenser discharged, the 

 extent of the throw produced and the initial displacement 

 of the needle being supposed fixed. 



Magnitude of Krror when a Condenser is charged through 

 the Galvanometer. — The magnitude of the error which occurs 

 on charging a condenser through a galvanometer in the 

 usual way is given by (2). We may, however, arrange the 

 circuit as in fig. 1, and charge the condenser by opening the 

 key K. In this Ccise when the key is closed a current I flows 



B 

 L 



£ 



Fiff. 1. 



Fi 



round the circuit KLB which we shall suppose is of inconsi- 

 derable resistance but possesses considerable self-inductance L. 

 If the opening of the key occasions no spark, then the energy 

 dissipated in the process of charging is equal to that stored 

 magnetically in the field of the current I at the commence- 

 ment, together with that stored electrostatically in the con- 

 denser at the end ; that is, it is equal to 



i(LP + EQ). 



If the galvanometer be a high-resistance one ; practically 



