110 PROPERTIES OF CIRCULAR CURRENTS. 



751. COIL WITH THREE CIRCLES. A remarkable particular case 



is that in which m z i, from which follows m' 2 = - and p = ; 



7 49 



the two circles of radius r, merge then in the great circle of the 



sphere, and form a single coil having 64 windings, if the two small 

 circles have each 49, or 162 in all. 



The radius of the small circles is equal to a \/-> and their 



distance from the centre equal to a \/~- 

 The magnetic action at the centre is then 



(50) Go _ 



that is to say, 120 times that of the great circle. 



We know that a sphere, entirely covered with circular currents 

 situate in parallel planes, the successive distances of which are equal 



to - , produces in the interior a uniform field, the strength of which 

 n 



Q 



is - n^ (497). This arrangement would be difficult to realise in 

 practice, while that which we have investigated would give almost 

 the equivalent in the case of a complete spherical coil ; and in that 

 of a coil with three circles we should have 



90 



that is to say, the sphere must be covered with 180 windings. 

 For the sphere the total length of the wire will be 



f+a 



''J-f-* 1 



27ZVZ, rx = nfa i = go-n- 2 a = 2ira . 1 4 1 '4 



In the case of three circles we should have 



2 / 196' 



64 . 2Tra + 98 . 2ira j= = 2ira ( 64 + 7 ) = 2ira .138; 



