TRANSACTIONS OK SECTION A. 



575 



obtained when the mirror was present, (/>) with that obtained when, the mirror 

 being absent, the geometrical position of the coil was occupied by an actual coil of 

 the same magnetic moment as the ' image.' 



Iron in thin sheet as used for tin-plate is not thick enough to form a perfect 

 mirror. A piece of boiler-plate, | inch thick and rather less than 3 ieet square, 

 formed a perfect plane mirror for poles placed not more than 4 or 5 inches away 

 from its centre. A long solenoid 200 centimetres long, 15 centimetre diameter, 

 uniformly wound with twelve turns per centimetre with a wire capable of canning 

 15 amperes without overheating, was used in one series of experiments to produce 

 a pole. 



In the case of a convex spherical surface of iron of infinite magnetic permea- 

 bility, and of radius of curvature r, the object being a pole of strength m situated 

 at a point at a distance a from the middle of the mirror surface, tlie image is a 



pole of strength -m . Its distance .r behind the surface is equal to r — —"- 



« + ?• 



a + r 



or 



a + r 



If a = 



.r = 



.v=hr 

 X = )• 



The image of an infinitely distant pole is at thai centre, not as in the case of the 

 optical image half-way between surface and centre. 



The following simple construction gives the position of the image of any point- 

 pole outside. 



Let P be the position of the point-object, and O the centre of the spherical 

 surUce Join PO, and with P as centre describe the arc OS. Then witli centre 

 a and OS as radius describe arc OQ, cutting PO in Q. Q is the ima"-e of P 



J<'or a concave mirror the construction is reversed by finding successively the 



centres of the arcs. The image is a pole having strength = -m"^- '", where a is 



r 



the distance of the image from the surface 



r.v 

 r — X 



Both formiilfe show that as r increases to infinity a = x. 



The whole of the experimental work has been carried out for me by Mr. Miles 



Wallcer, 



