DIRECT CAPACITY MEASUREMENT 31 



the slide wire and the direction of the motion of the slider as oblique 

 asymptotic axes.'^ L = GS/g = 4 G/p(G^ — g^), where G is the 

 total conductance and {G =*= g)/2 the limiting direct conductance on 

 either side. 



If an ordinary slider replaces the hyperbolic arc slider, and the 

 scale reading is made non-uniform so as to give one-half of the differ- 

 ence between the direct conductances C? to 3) and C to 3), the con- 

 ductance standard will still give absolutely correct results with the 

 Colpitts method, provided the bridge ratio is unity. This simplifica- 

 tion in connection with the balancing capacity / of Fig. 6 would, 

 however, not be strictly allowable. For improvised testing we have 

 found it sufficient to use two equal resistances {R) with a dial re- 

 sistance {r) in series with one of them, and take the defect of con- 

 ductance introduced by the dial resistance as equal to r/F? or to 

 10~2r, 10~V, r, micromho according as R was made 10000, 3162, 

 or 1000 ohms. 13 



For a step-by-step conductance standard. Fig. 9 shows a set of 

 10 equal resistances, connected in series between corners ^, (?, to 

 the junction points of which there is connected a parabolic fringe of 

 resistances, the largest of which is 2.5 times each of the ten resistances. 

 With this arrangement the direct conductance in CFS) may be ad- 

 justed by ten equal steps, beginning with zero, whi'e the conductance 

 in (?2) is decreased by equal amounts to zero. The total res'stance 

 required for this conductance standard 's only 21/25 of the res'stance 

 required to make a single isolated conductance equal to one of the 

 ten conductance steps; the ratio may be reduced to 1/2 by doubl ng 

 the number of contacts, ^^ and using onsfringe resistance for all posi- 

 tions. Resistance may be still further economized by using as high a 

 total conductance as is permissible in the bridge, and securing the 

 required shift in conductance from a small central portion of the 

 parabolic fringe. 



Fig. 9 shows the variable capacity standards as well as the variable 

 conductance standards and a few practical points connected with the 

 capacity standards may be mentioned here. 



The revolving air condenser standard has two fixed plates connected 

 to <^ and (?, so that the capacity will increase as rapidly on one side 

 as it decreases on the other side. Since perfect constancy of the total 

 capacity is not to be expected, on account of lack of perfect mechanical 

 uniformity, the revolving condenser should be calibrated to read 



1* See appendix, section 8. 

 " See appendix, section 9. 

 " See appendix, section 10, 



