350 THE GEYSTAL FALLS lEON-BEAEING DISTEIOT. 



By differentiating- tlie riglit-liand side of (7), with respect to x, it is 

 easy to show that V has a maximum vakie when x=0. When the rock 

 strikes north and south, this also corresponds to a minimum value of H„ as 

 has already been shown; and, therefore, by a reference to equation (5) it 

 is readily seen that a point of maximum dip coinciding with a point of no 

 horizontal deflection is in that case found over the middle plane of the ■ 

 buried magnetic rock. 



Where the strike is inclined to the meridian, the points of maximum 

 dip and zero deflection will not coincide, since the maximuna value of V 

 does not occur at the same station as the minimum value of H^. As has 

 already been shown, H^ is a minimum when H'=H sin /? (^ being the angle 

 of the strike), and this is in general on the side of the rock on which the 

 angle made with an east and west traverse is obtuse. The point of maximum 

 dip will be situated on the same side of the rock between this station and 

 the point of no horizontal deflection, and will approach the latter as the 

 strike approached the meridian, and also as V increases relatively to H'. 

 With strongly magnetic rocks the points of no deflection and maximum dip 

 practically coincide on maps platted to the scale of 4 inches to the mile, 

 except where the strike is nearly east and west. 



5. HORIZONTAL AND VERTICAL COMPONENTS WHEN THE MAGNETIC ROCK 



DIPS AT AN ANGLE. 



Under the last heading it was assumed that the magnetic rock dips 

 vertically, and that it continues indefinitely downward at this angle. In 

 consequence of this assumption, and also of the conception of the manner 

 in which magnetism is distributed through magnetic rocks, it has been con- 

 cluded that the north poles of the rock, which repel the north end of the 

 compass needle, are situated so far below the surface that their effect may 

 be neglected. Therefore we have taken into account only the south poles, 

 which are situated at the rock surface. 



In the case of rocks which do not dip at high angles this assumption 

 can not safely be made, and the influence of the bottom poles must be 

 taken into account. Since the force of these poles acts in opposite direc- 

 tions from that of the upper poles, and since they are more deeply buried, 

 it would seem that their influence in genei'al must be to diminish the total 

 force which acts upon the needles at any station, and therefore that the 



