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XXXI. The Solution of a Geometrical Problem in Magnetism 

 By T. H. Blakeslet, M.A* 



THE points in the field of a magnet usually chosen for 

 quantitative experiments, such as the determination of 

 H, or the control of a galvanometer-needle, lie either in the 

 axis of the magnet produced, or the equatorial plane. This 

 arises from the very simple expressions for the field in terms 

 of the moment of the magnet, and its distance from the point 

 considered, in these two cases. But in either of these cases 

 the exact value depends not merely upon these facts, but also 

 upon the distance between the poles ; and this latter can 

 rarely, if ever, be taken to be the entire length of the magnet. 

 Either some such rule as the lopping-ofF, in imagination, of a 

 fraction of the length, is applied, or the virtual distance 

 between the poles is expressed as an unknown quantity to be 

 determined by additional experiment. 



It is easy also to calculate the direction and magnitude of 

 the field at a point whose position relatively to the two poles 

 is given. But the following proposition is, at first sight, of 

 a more difficult order. 



" Given the two poles of a magnet, and a straight line inter- 

 secting at right angles its axis produced at a given point, to 

 determine at what point this line is parallel to the field. " 



The solution of this question may be of some scientific 

 interest ; because if we know the point experimentally, we can 



determine the length between the virtual poles. But the 



question is important practi- Fig. 1. 



cally from its bearing upon 



that of the deviation of a 



ship's compass in some cases. 

 Suppose A B a long uni- 

 formly magnetized rod having 



poles at A and B (say A is 



a north pole), and OP its 



equatorial plane. Then the . „ 



field at P is always parallel A c 



to A B, and in the direction 



of those letters, which call 



the positive direction. Sup- 

 pose a piece C D cut away 



so as to leave a gap having 



same equator. 



At C a south pole is developed, and at D a north pole. 



* Communicated by the Physical Society : read November 28, 1890. 



^ + 



D 



