346 



THE OKYSTAL FALLS lEON-BEAEING J)ISTRICT. 



belt would act along- the line P N, drawn througli P perpendicular to the 

 strike of the rock. Since there is as much material on one side of this 

 line as on the other, the components perpendicular to it will balance each 

 other, and the instruments at P will be affected exactly as if all the attract- 

 ing material were concentrated along this line. The horizontal needle will 

 take a position in the line of the resultant of the two forces which act upon 

 it, namely, the horizontal component of the earth's magnetism (which acts 

 in the line of the magnetic meridian) and the horizontal component of the 

 material within the circle of attraction (which acts along the line P N). 



The force which de- 

 flects the needle from 

 its general local direc- 

 tion is the component 

 along P N, and it is 

 evident that the great- 

 er this component the 

 greater will be the de- 

 flection of the needle, 

 since the direction in 

 which it acts always 

 remains the same at 

 all stations for any 

 given direction of 

 .strike of the rock. 

 For if /? is the strike 

 of the rock measured 

 from the north, and H and H' are the horizontal components of the earth's 

 and the rock force respectively, it is readily shown that S, the angle of deflec- 

 tion of the horizontal needle at any station, P, is given by the equation: 



Fig. If).— Circles of attraction. 



tan S :^ 



COS /? 



H 



(1) 



H' 



^ ± sin /? 



From this equation it is easily seen that, no matter how great may be 

 the horizontal component of the force of the magnetic rock, the horizontal 

 needle can not be deflected past the normal. 



