Page:The Bell System Technical Journal, Volume 1, 1922.pdf/19

Rh sary to accurately measure, and have admittances overwhelmingly larger than the direct conductance, which is often the most important quantity.

The substitution alternating current bridge method, suggested to me in 1902 by Mr. E. H. Colpitts as a modification of the potentiometer method, has been in general use by us ever since in all cases where accuracy and ease of manipulation are essential.

After first defining direct capacities and describing various methods for measuring them, this paper will explain how this may all be generalized so as to include both the capacity and conductance components of direct admittances, and the inductance and resistance components of direct impedances.

It is a familiar fact that two condensers of capacities C$1$, C$2$, when in parallel or in series, are equivalent to a single capacity (C$1$ + C$2$) or C$1$ C$2$/(C$1$ + C$2$), respectively, directly connecting the two terminals, These equivalent capacities it is proposed to call direct capacities. The rules for determining them may be stated in a form having general applicability, as follows:

Rule 1. The direct capacity which is equivalent to capacities in parallel is equal to their sum.

Rule 2. The direct capacity between two terminals, which is equivalent to two capacities connecting these terminals to a concealed branch-point, is equal to the product of the two capacities divided by the total capacity terminating at the concealed branch-point, i.e., its grounded capacity.

These rules may be used to determine the direct capacities of any network of condensers, with any number of accessible terminals and any number of concealed branch-points. Thus, all concealed branch-points may be initially considered to be accessible, and they were are then eliminated one after another by applying these two rules; the final result is independedt of the order in which the points are taken; all may, in fact, be eliminated simultaneously by means of determinants ; a network of capacities, directly connecting the accessible terminals, without concealed branch-points or capacities in parallel, is the final result. Fig. 1 shows the two elementary cases of direct capacities and also, as an illustration of a more complicated system, the bridge