NOTES ON MAGNETISM*. 



No. I. 



A GEOMETRICAL construction, by means of which the action 

 of a small magnet on a distant particle of free magnetism may 

 be readily determined, is mentioned, in a memoir by Weber, 

 on the Bifilar Magnetometer (Scientific Memoirs, II. p. 270). 

 It is due to Gauss, but I do not know where he has demon- 

 strated it. A proof of it may be acceptable to some readers 

 of the Journal. 



I begin by enunciating the construction in question, which 

 will be easily understood without a figure. Let AB be a small 

 bar magnet, c its centre, P the particle of magnetism on which 

 it acts. Join cP, draw PD perpendicular to it, meeting cP 

 produced in D. Let cQ = JcD. Join PQ. Then PQ or QP 

 (according to the sign of the magnetism of P and the direction 

 of the poles of AB) is the direction of the action of A B on P; 



and p y is its magnitude, M being the measure of the mag- 

 netism of AB, m that of the magnetism of P. 



The dimensions of the magnet being small, and its length 

 in the direction of its axis being much greater than its breadth 

 or thickness, we may proceed as follows. 



Conceive the magnet to be composed of a series of intense 

 particles ranged along its axis. Let s be the distance of any 

 one of them from c, y^ds the measure of its magnetism. Also 

 let cP= r, and call the angle cP makes with cD, 6. 



* Cambridge Mathematical Journal, No. XX. Vol. iv. p. 90, February, 1844. 



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