EXPERIMENTS OF GAUSS. 585 



their distance to the point P. The angle* of these two directions 

 being w, we have 



cos co 



The components of the force one perpendicular and the other 

 tangential to the sphere of radius r are 



3V M 

 Z = -- =n cos w , 



~br r n + l 



i>V ' M 



H = - = sm oj . 



r Do> r n + l 



We shall see again, as before, that for any two masses, and 

 therefore for a symmetrical magnet, the components of the field at 

 a point, developed as functions of its distance from the middle of 

 the magnet, will have the same expression, excepting terms of cor- 

 rection only containing even powers of the length of the magnet 



Let us observe, as a particular case, that for a great distance R, 

 the values F p and e of the field of a magnet, on the line of the 

 poles and in the plane of the equator, are 



F. M 



the ratio of these two expressions is equal to the index n of the 

 power which defines the elementary action. 



1158. EXPERIMENTS OF GAUSS. In a series of experiments, 

 made with a view to verify the law of magnetic actions, Gauss * 

 acted on a movable magnet by a second one, placed at varying 

 distances of 1-3 to 4 metres. 



The deflecting magnet was always perpendicular to the magnetic 

 meridian, and the line of the centres perpendicular or parallel to 

 the meridian. For each distance the deflection of the movable bar 

 was obtained by the means of four readings, relative to two positions 



* GAUSS. Intensitas vis Magnetics Terrestris, etc. Comment. Soc. 

 Gotting., Vol. vni. 1841. Gauss' Werke, Vol. v., p. 81. 



