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February 12, 1835. 

 WILLIAM THOMAS BRANDE, Esq., Vice-President, in the Chair. 



Mr. Davies's paper, entitled " Geometrical Researches concerning 

 Terrestrial Magnetism," was resumed and concluded. 



The object of this paper is to exhibit methods of conducting the 

 mathematical inquiries which are applicable to the magnetism of the 

 earth, by the aid of the coordinate geometry of three dimensions. 



When a point on the surface of the earth is given by means of its 

 geographical coordinates, we can also refer it to any rectilinear co- 

 ordinates that may be found convenient, and the transformations 

 of the expressions can be made by known and familiar methods. 

 Also, since at a given point the needle is deflected a measured quan- 

 tity from the meridian plane, estimated on a tangent plane to the 

 earth at the given point, and is also depressed another measured quan- 

 tity below the same plane at that given point, its position is fixed by 

 means of these measures. It will hence become capable of reference 

 also to the same rectilinear coordinates as those into which the geo- 

 graphical coordinates were transformed. The equation of the line, 

 into which the dipping-needle disposes itself, becomes, therefore, ca- 

 pable of expression in terms of the measured quantities above referred 

 to ; viz., the latitude, longitude, dip, and variation. The method of 

 obtaining the constants which enter into the " equations of the nee- 

 dle" as referred to the equator, a given meridian, and the meridian 

 at right angles to it, are then detailed at length by the author and 

 these equations are calculated for six different places : Port Bowen, 

 Boat Island, Chamisso Island, Valparaiso, Paris, and Paramatta. 



With a view to bring the hypothesis of the duality of the centres of 

 magnetic force to a test, the author proceeds to reason, that as a free 

 needle subjected to the action of only two poles, will always dispose it- 

 self in the plane which passes through those poles and the centre of mo- 

 tion of the needle, the needle prolonged will always intersect the mag- 

 netic axis, or line which passes through the two poles. But when four 

 straight lines are given in space, a fifth line (or rather two lines) can be 

 so drawn as to intersect them all. If, therefore, we have the equations 

 of four dipping-needles calculated from correct observations, we ought 

 to be able to assign the equations of the two lines which rest upon 

 them j one or other of which, in such case, will be the magnetic axis 

 itself. This line ought to intersect every other needle • and hence 

 the constants in its equations and the constants in the equations of 

 any fifth needle ought to fulfill the algebraical test of intersection. The 

 author has calculated the equations of the magnetic axis for the needles 

 at Chamisso, Valparaiso, Paramatta, and Port Bowen, and made a 

 comparison of it with the Paris needle. Instead of intersecting, the 

 least distance between the said axis and needle is more than one 6th of 

 the terrestrial radius; and hence, could the observations themselves be 

 depended on, as being free from instrumental error and from local dis- 

 turbances, the question of the duality of the centres of force would be 

 at once settled in the negative j but, as the opinions of those philo- 



