12 

 APPENDIX 



A. GAGE FACTOR OF WIRE GAGE 



The increment in capacitance AC produced by a change in water height AA may be 

 computed from the formula, 



AC k 



— =0.555 ^/if per cm [1] 



AA r„ 



where k is tlie specific inductive capacity of the dielectric (enamel), 



In is the natural logarithm, 



r„ is the outer radius of dielectric, 



T. is radius of the conductor, in the same units as r^, and 



A is the change in water height in cm. 



The total capacitance presented by the gaging element is of secondary interest only, 

 as this capacitance may be considered as a part of the fixed capacitor in the bridge arm in 

 which the gage is connected. 



Formula [1], although exact, should be used to obtain approximate values only, owing 

 to the difficulty of accurately measuring the thickness of the insulation on the wire and de- 

 termining the dielectric constant k of the insulating material. For example, computed values 

 for AC (/xfif per in.) of the No. 28 enameled wire used was 53.5 /xfif per in., while the average 

 experimental value obtained by direct measurement was 56.0 /x^f per in. (This value was 

 used as a basis for selecting the internal calibrating condensers.) 



B. LINEARITY CONSIDERATIONS 



The degree of linearity obtainable from a conventional four-arm bridge is a function 

 of the ratio of the maximum change in impedance which will occur in the active bridge arm 

 and the impedance of the same arm at balance. 



The expression for the open circuit output voltage for a capacitive bridge with one 



active (variable) arm is 



ea 1 



e„ = volts [2] 



° 4 2+ot 



where e is the bridge driving voltage and a is the ratio of the change in capacitance of the 



AC 

 active arm to the capacitance of the arm at balance, i.e., . 



For example, in order to realize a linearity of one percent of full scale, the error 



factor — — in Equation [2] must not be numerically less than 0.99. Or stated otherwise, the 



2 +a 



