282 Mr. T. H. Blakesley on the Solution of 



These two poles produce a field at P parallel to D C, and 

 in the negative direction. 



If the point is in the neighbourhood of 0, the two inner 

 poles w r ill be dominant and the field negative ; but if P is very 

 remote from 0, the poles A and B w T ill be dominant, and the 

 field positive. There must therefore be some position where 

 the field vanishes, and the two rods AC, DB would produce 

 no deviation on a compass at that point, in whatever direction 

 the head of the ship carrying the system pointed. 



Such permanent magnets w r ould produce what is called 

 semicircular deviation on a compass situated at any distance 

 but this critical one from 0; that is, through one semicircle 

 the deviation would be easterly, and through the remaining 

 semicircle westerly; but these semicircles would each have 

 the deviation produced in it changed in sign if this critical 

 point is transgressed. If, however, the rods AC, DB are of 

 soft iron, liable to magnetization by the action of the hori- 

 zontal component of the earth's field, the general effect is 

 that the direction of the deviation changes sign after every 

 quadrant, each pair of opposite quadrants having one kind of 

 deviation, easterly or westerly; and in this case the actual 

 sign for each pair of opposite quadrants depends upon the 

 position of the compass relative to this critical position. 



This application may serve to excuse me for bringing 

 forward an easy method of practically finding this point. 



It is clear that the point is one for which the field due to 

 either magnet, A C or D B, alone, would be entirely along 

 P, i. e. at right angles to the axis of the magnet. 



The Solution. 



Let n m be the position of ^ Fig. 2. 



the poles of a magnet, and P 

 a point situated at distance 

 d from 0, being in the axis 

 of the magnet produced, and 

 P being perpendicular to cl 

 Own. 



Let the distance 



On =n, 



Om = m. 



Let p be the numerical value of the poles m and n. 

 Then, writing down the condition that the component parallel 

 to the magnet of the field produced at P by p at m shall be 



