158 BELL SYSTEM TECHNICAL JOURNAL 



above on the resistance will not exceed one part in 100,000, which is 

 quite satisfactory. The change in resistance (from the d-c. value) 

 due to energy dissipation in the insulation is, however, somewhat 

 larger than that due to the pure capacitance effect. This change is 

 given to a close approximation by the expression 



. „ Co:B? tan (j) 

 AR = 3 , 



where C is the total distributed capacitance between the wires of a 

 bifilar winding and is the phase angle of the capacitance.^ Clearly 

 both the capacitance and its phase angle should be kept as small as 

 practicable. An obvious and simple way of attaining the first object 

 would be by using the very finest wire available. To do this, however, 

 would in many cases result in excessive heating of the resistance. For 

 bridge tests on telephone apparatus the ratio arm current will rarely 

 exceed 25 milliamperes. The energy to be dissipated in a 1000-ohm 

 coil is then about 0.5 watt, requiring a radiating surface of about 25 

 sq. cm. for a maximum temperature rise of 10 deg., which is a desirable 

 limit. Since only the outer surface of such a coil is effective in 

 radiating the generated heat the question of the number of layers 

 requires consideration. Other factors being constant, it has been 

 found that of the various possible arrangements that are easily con- 

 structed and mounted, a sectionalized, two-layer winding gives mini- 

 mum capacitance. Hence one half of the winding is required to have 

 an exposed surface of 25 sq. cm. The gauge of wire is then determined 

 as a function of its specific resistance. A resistance alloy having a 

 suitably low temperature coefficient (such as manganin, advance, etc.) 

 will, on this basis, require that a wire no smaller than No. 38 A. W. G. 

 be used. This is the size of wire used by Curtis and Grover and in 

 the experiment covered by Table I. Using the data of this table, 

 it was calculated that a Curtis and Grover type of coil, except for 

 treatment, would have a change in resistance of not over one part in 

 50,000. The lower capacitance coils required from the phase-angle 

 standpoint would have even smaller changes. 



Summing up, then, the ratio arm coils were to be of approximately 

 1000-ohm resistance, wound with No. 38 A. W. G. double-silk-insulated 

 manganin, or advance resistance wire, dried, but not impregnated 

 with any moisture-resisting compound ; the winding was to be arranged 

 so that the true capacitances would not exceed 6.0 mmf. Besides 

 being balanced for d-c. resistance, the resultants of their capacitance 

 and inductance values were to be balanced to within 0.1 mmf. To 



' See Note 6. 



