ARAGO'S EXPERIMENT. 



571 



587. ARAGO'S EXPERIMENT. This method may be generalised. 

 Suppose that the pole describes a circle of radius , in the opposite 

 direction of the hands of a watch when looked at from above. 

 The action of the induced currents is that of two homogeneous 

 helices of contrary signs, or of a helicoidal ribbon BM' (Fig. 126) 



Fig. 126. 



coiled on the cylinder, with the axis of rotation for its axis, and 

 passing through the pole. Each element of this helix is magnetised 

 along a tangent to the cylinder, drawn perpendicularly to the axis, 

 and its action on the pole is equivalent to that of an infinitely 

 small magnet situate at a point M in the conducting plane. The 

 locus of the point M is the perspective curve of the helix seen 

 from the point A. If r is the radius vector MO, the angle 

 which it makes with the tangent at the point O, and observing 

 that the angle 6 is half the angle </> of the two planes passing 

 through the axis, and through the points B and M', we have, by 

 the triangles AMO and AM'K, 



__, T;r 20 sin . 



p M K 2 a sin 



c AK 2C + a<j> cota c+a6cota' 



This curve consists of a series of closed rings which have a common 

 tangent at the point O. 



