DIRECT CAPACITY MEASUREMENT 



33 



merit of networks has been simplified. In another paper the terminol- 

 ogy for admittances and impedances will be still further considered, 

 together with their analytical correlation. 



APPENDIX 



In explaining the different methods of measuring direct capacities 

 it is necessary to start with a clear idea of what direct capacities are, 

 and to make use of the additive property, but it is not necessary to 

 go into any comprehensive discussion of direct capacities. Accord- 

 ingly, the mathematical treatment of direct capacities has been reserved 

 for another paper, but it seems desirable to append to the present 

 paper proofs of the analytical results given in this paper, since the 

 method of approach giving the simplest proof is not always perfectly 

 obvious. 



(1) Reducing the number of terminals which are considered 

 accessible, by ignoring terminals p, q, r, . . . , changes the direct and 

 grounded capacities from (Qy, G,) to (Qj , G,'), the latter being ex- 

 pressed in terms of the former as follows: 



Cy L-ip Cjg 



— Cjp Cjp Cpq 



CIj = 



Gp 



— Cpq 



Cpq 



Gi — — Cu 



where C/,- is given by formula above and G,- = — C^. 



To check these formulas note that on substituting (G,-, — Gy) for 

 Maxwell's (9,-,-, qij) in his equations (18)'* the coefficients form an 

 array in which the grounded capacity G,- is the ith element in the main 

 diagonal and — Cij is the element at the intersection of row i, column 

 j. The array may be supposed to include every terminal symmetrically 

 by considering the earth's potential as being unknown and writing 

 down the redundant equation for the charge on the earth. Let the 

 charge be zero on terminal j and on all concealed terminals; let there 

 be a charge on terminal i and an equal and opposite charge on all the 

 remaining accessible terminals, connected together to form a single 

 terminal k. Now taking the potential of j as the zero of reference 



"76tV/., p. 108. 



