NOTES ON MAGNETISM. 189 



We suppose the magnet and needle to be in the same plane. 

 In the figure let be the centre, SON the line of the axis of 



the magnet, C the centre of the needle. Project on ON 

 in D, take OE 2 OD, draw EN' perpendicular to SN meet- 

 ing ON', which is at right angles to OC in N', CN' is the 

 line in which the axis of the needle must be placed, its north 

 pole being turned towards N'. 



In order to prove this, we have only to remark that the 

 angle 6 or CON is constant, the position of C being given ; 

 consequently the condition to be fulfilled, in order that the 

 moment of rotation L may be a maximum, is 



3 cos 6 cos & cos (j> = 0. 

 Now as (j> is the angle between N' C and 8N 9 we have 



ED = CN' cos <, 



and therefore OD = J- CN' cos <j>. 



Again, 00 = CN' cos & and OD=OC cos 0. 

 Hence 0Z> = CN' cos cos 0'. 



Consequently 3 cos cos & cos < = 0, 

 or the required condition is fulfilled. 



There are three particular cases worth noticing : 



(1) = 0. In this case C lies in the axis ON, D coincides 

 with it, and ON' is perpendicular to ON, and therefore parallel 

 to EN'. Consequently the point N' is removed to an infinite 

 distance, and CN' is therefore perpendicular to ON. The 



, T . 2MM' . . .. 

 corresponding value of L is - _j , and is the maximum 



maximorum. 



(2) = 0'. In this case the magnet and needle are parallel 



