348 THE CRYSTAL FALLS IRON-BEARING DISTRICT. 



Equation (2) is easily reduced to 



2&.H, ' ^^■> 



If, however, the dip needle is not balanced, but has, where there is no 

 local disturbance, a constant index error (measured from the horizontal), 

 it is readily seen that 



, „ 2b .Y—mga ,,, 



^""^^ 2&.H ' ■ • ^^) 



In an area of local disturbance the angle of dip a is given by equation 

 (3). Since V and V always act in the same line. 



Substituting this and the value of mga ft-om equation (4), equation (3) 

 becomes 



± V + H tan 9, ,^. 



tan a — == U^^ ^ (5) 



If the index error is 0', and the corresponding deflection a', we have 



tan a: _ ^ V' + H tan 9 

 tan a' "~± V + H tan 0' 



Therefore at the same station, the greater the index error the greater 

 is the angle of dip in the same or two similar instruments. It is also evi- 

 dent that the greater the vertical component of the pull of the rock, the 

 less will be the difference between the deflections in the two cases. 



Fi'om an inspection of equation (5) it is seen that tan arz:oo, or 

 ar=90° only when H,.rrO. H,. is, in general, given by the equation 



H,= Vff+H'^±2 H H' sin /?, 

 where /? is the strike of the rock measured from the north. H,. can there- 

 fore equal zero only when ^=^-^, or the rock strikes east and west, and at 



the same time H' is numerically equal to H, and acting in the op^josite 

 direction. Dips of 90° can not occur in other cases, no matter how strong 



