OF ARTS AND SCIENCES. 179 



Projecting one circle upon the plane of the circle of greater radius, A, 

 we have 



^2 TT />2 T ^ a cos (<^ — 0') d<f) d(f)' 



_ P'"' P-" ^« cos(<^ — 0') d 



~ Jo Jo ^A^^ + ^^b'-2Aa 



cos {(f) — (f>') 



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

 from the case of mutual induction to that of self-induction between 

 two spires of a coil which may be considered approximately circular. 

 The form of J/ adapted for calculation is then 



M=i.VAu[{e-l)F+lJi:X, 



where c = ^^-P^ — r, and F and F are complete elliptic integrals to 



(A-\-a) 



modulus c. 



If we make A — a = Z), or ^ = Z) -f 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 centre to centre 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 indicated, to avoid 

 self-iuduciion. 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 movable 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 extension of the 

 various systems for transmitting power by electricity, especially the 

 electric car system, has led to great disturbances in the telephone 

 circuits. These disturbances are due both to leakage from the power 

 circuit into the telephone circuit, since the earth is used partially by 

 the electric power companies in their return circuits, and to actual 

 induction. The best remedy for these disturbances is doubtless the 



