DIRECT CAPACITY MEASUREMENT 19 



sary to accurately measure, and have admittances overwhelmingly 

 larger than the direct conductance, which is often the most important 

 quantity. This is the interesting problem of direct capacity measure- 

 ment, and distinguishes it from ordinary capacity measurements 

 where isolation of the capacity is secured, or at least assumed. 



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 general- 

 ized so as to include both the capacity and conductance components 

 of direct admittances, and the inductance and resistance components 

 of direct impedances. 



Definition of Direct Capacity 



It is a familiar fact that two condensers of capacities Ci, Ci, when 

 in parallel or in series, are equivalent to a single capacity (Ci + d) 

 or Ci C-i.l{C\ -f C2), 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 I. 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 con- 

 cealed 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 are then 

 eliminated one after another by applying these two rules; the final 

 result is independent 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 



* See appendix, section 1, for a discussion of determinant solutions. 



