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ON THE GEOMETRIC PROPERTIES OF THE MAGNETIC! 



CURVE, WITH AN ACCOUNT OF AN INSTRUMENT 



FOR ITS MECHANICAL DESCRIPTION. 



T 



BY P. M. ROGET, M.D,, SEC. R.S. 



HE properties of the magnetic curve being interesting to 

 the geometrician, as well as important in their connexion 

 with the theory of magnetism, I am induced to offer the follow- 

 ing demonstrations of the two fundamental propositions re- 

 specting them, derived directly from the law of magnetic 

 forces, as being more simple than any of those given by Pro- 

 fessors Robison, Play fair, or Leslie. I have also added an 

 account of a method I have devised for the mechanical de- 

 scription of these curves. 



The principal problem relating to the magnetic curves is to 

 find the direction, CT, Fig. 1. of the tangent to the curve 



Fig. 1 



which passes through any given point C, when the situations 

 N and S of the two poles are given. This direction indicates 

 the position which an infinitely small compass needle, placed 

 at C, and at liberty to turn freely round its centre, in a plane 

 passing through N and S, will assume by the action of the 

 magnet N S. This position must be such, that the rotatory 

 forces exerted on both poles of the needle by each pole of the 

 magnet shall exactly balance one another. 



The forces themselves, according to the established law of 

 magnetic action, are inversely as the squares of the distances 



