of all known Substances to the Magnetic Influence y (J-c. 101 



Now these general resultants ought to be proportional to the 

 tangents of the angles of deviation produced by the magnet at 

 the respective distances. For, since the compass is acted upon 

 simultaneously by forces * in two directions, that is, at right 

 angles to each other, that of the earth, which may be considered 

 as uniform, and always in the direction of the magnetic meri- 

 dian, and that of the magnet varying as to intensity, but as to 

 direction, being always at right angles to the other, — the mea- 

 sure of the variable force will be fairly given by the tangents 

 of the angles of deviation produced in the needle. If, there- 

 fore, the law of the magnetic force as to distance be correct, 

 that the action of either pole diminishes in proportion as the 

 squares of the distance increase, then the tangents of the ob- 

 served angles of deviation applied inversely to the general result- 

 ants, ought, on this hypothesis, to give the same product for all 

 the different distances. 



In order to verify these deductions, and to obtain a practical 

 rule for determining the quantity of magnetic influence at all 

 distances, however remote, a careful series of experiments were 

 made with the two-feet bar magnet and one of Kater's five-inch 

 compasses at the several distances of one to ten lengths. 



The following Table contains the observed deviations, as pro- 

 duced by each pole of the bar, with the application of the tan- 

 gent of the mean of the observed deviations to the reciprocal of 

 the magnetic force acting on the compass at the respective dis- 

 tance, so as to produce the ratio, which was expected to be uni- 

 form, in the sixth column. 



• Though the forces are more in number than two, it is only necessary to 

 consider the resultants of the forces in each direction. 



