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BELL SYSTEM TECHNICAL JOURNAL 



and calculating the potentials of i and k and then allowing the direct 

 capacity between j and k to become infinite, the direct capacity 

 between terminals i and j is dj = — Lim {Qk Vk /Vi). This gives 

 the above formula for C,-^, with — C„- as a special case. This method 

 is an electrostatic counterpart of the ammeter method shown in 

 Fig. 8 on page 29. 



If there is but one ignored terminal the determinant solution takes 

 on a simple form from which Rules 1 and 2 and Fig. 1 may be checked. 



If all but two terminals are ignored the equivalent direct network 

 is reduced to a single direct capacity. When, for each pair of termi- 

 nals, this capacity dj is known, from measurements or from calcu- 

 lations, the direct capacities between the terminals may be derived 

 by means of the following formulas 



r - 1^ 



Gi = -Cn= -2^ 



where Dij is the cofactor of the element in row i column j of the 

 determinant 



D = 



which has zeros in the main diagonal, a border of ones in the last 

 row and column, while the other elements are 5^ = 1/C,-,-, that is, 

 the reciprocals of the given capacities. The 5's form a complete 

 symmetrical system of network constants; Maxwell's coefficients of 

 potential pa with the two sufifixes the same are the same quantities, 

 but he employs only those coefificients of this type which are associ- 

 ated with the earth, his system being completed by adding the co- 

 efficients with different suffixes. By starting with Maxwell's results 

 the above formula may be deduced, but more direct proofs, both 

 physical and mathematical, will be given in the theoretical paper 

 referred to at the end of the present paper. 



The purpose of this section of the appendix is achieved if the de- 

 terminant solutions are made so clear as to be available for use in 

 any particular case. 



(2) Starting with the bridge alone balanced at reading C** the other 

 two settings involve, in the capacity standard, increases in the direct 



