20 Trowbridge and Sheldon — Neutralization of Induction. 



be estimated as follows. Taking Maxwell's discussion for the 

 induction between parallel circuits of radii A and a, we have 

 the coefficient of mutual induction, 



C r cos e ds ds' 

 M =JJ r 



Projecting one circle upon the plane of the circle of greater 

 radius, A, we have 



_ /* 2 7t r*7t Aa cos( cp— q)') dcpdqJ 



~Jo K ^/A* + a? + b' 2 — 2 Aa cos (<p—qj) 



Making b the distance between the planes of the circles == 0, 

 we pass from the case of mutual induction to that of self-induc- 

 tion between two spires of a coil which may be considered 

 approximately circular. The form of M adapted for calcula- 

 tion is then 



%\/l[a 

 where c = ,—: v , and F and E are complete elliptic integrals 



to modulus o. 



If we make A — a = D, or A = D 4- a, in which D is the 

 distance between the spires at which the self-induction becomes 

 insensible, the most perfect minimum can be attained. We 

 have found that copper wire of 2 mm. diameter, wound in a 

 flat loose spiral, the spires of which from center to center of 

 the wire are 4 mm. apart, gives no sensible self-induction for 

 spirals of eight to ten spires. On turning a movable coil of 

 this form so that its axis may be perpendicular to the axis of 

 the fixed coil, a perfect minimum can be obtained. A slight 

 movement to the right or left of this position is quickly made 

 evident by the note of the interrupted circuit which is heard 

 in the telephone. It is evident that, if four coils are employed, 

 as in Hughes's form of induction balance, the two coils in the 

 telephone circuit should be wound in the manner we have in- 

 dicated, to avoid self-induction. On placing a plate of metal 

 between one set of the coils of this balance, the movable .coil 

 no longer gives a minimum at the position where its axis is at 

 right angles to that of the fixed coil, but at some point removed 

 a few degrees from this. By placing a mirror upon the mova- 

 ble coil, and by observing its deflection with a telescope, a 

 greater refinement of reading is possible. 



This instrument in its modified form suggests the possibility 

 of neutralizing induction upon telephone circuits. The exten- 

 sion of the various systems for transmitting power by elec- 



