22 BELL SYSTEM TECHNICAL JOURNAL 



CoLPiTTS Substitution Bridge Method, Fig. 2 



The unknown direct capacity is shifted from one side of the bridge 

 to the other, and the balance is restored by adjusting the capacity 

 standard so as to shift back an equal amount of direct capacity. 

 The method is therefore a substitution method, and the value of the 

 bridge ratio is not involved. Both the standard and the unknown 

 remain in the bridge for both settings, so that the method involves 

 transposition rather than simple, ordinary substitution. 



Details of the method as shown by Fig. 2 are as follows : To measure 

 the direct capacity Cn between terminals 1 and 2 connect one terminal 

 (1) to corner 5*of the bridge, and adjust for a balance with the other 

 terminal (2) on corner (^ and then on (?, while each and every one of 

 the remaining accessible terminals (3, 4, . . . ) of the electrical system 

 is permanently connected during the two adjustments to either corner 

 <^or (?. If the direct capacities in the standard condenser between 

 corners CF and S) are C, C" in the two balances, 



Ci2 = C" - C 



and if the bridge ratio is unity', 



Ci3 - Ci4 = C + C" - 2C°, 



where C^ is the standard condenser reading when the bridge alone 

 is balanced. 



Two settings are required by this method for an individual direct 

 capacity measurement, but in the systematic measurement of all the 

 direct capacities in a system the total number of settings tends to 

 equal the total number of capacities, when this number becomes large. 

 The number of settings may always be kept equal to the number of 

 capacities by employing an equality bridge ratio, and using the ex- 

 pression for the direct capacity difference given above. The same 

 remarks also hold for the group of direct capacities connecting any 

 one terminal with all the other terminals. 



In general, ground is placed upon corner C of the bridge, but is 

 transferred to corner 2), if it is connected to one terminal of the re- 

 quired direct capacity. The arbitrary distribution of the other 

 terminals between corners <^ and (? may be used to somewhat control 

 the amount of standard capacity required; or it may be helpful in 

 reducing interference from outside sources, when tests are made upon 

 extended circuits. The grounded capacity of a terminal or group of 

 terminals is measured by connecting the group to (?, and all of the 

 remaining terminals together to 2). 



• See appendix, section 2. 



