1G8 



GEOLOGY OF THE COMSTOCK LODE. 



drauiilit with great care, the locus 



can be produced on such a scale that both its elements are sensible. 



Bfdudion and interpretation of the equation. — A few data as to the com- 

 putation and representation of the logarithmic curve may be of use to 

 those who have to do with special cases- of faulting, either technically or 

 geologically. 



Equation referred to the cropping as origin. In tllC fomi of tllC eqUatloU dcduCcd, 



!J-Am-% (1) 



the curve is referred to its asymptote and the fault line as axes. In ascer- 

 taining the value of the constants applicable to any given surface, however, 

 it will be more convenient to refer it to the fault line and a line perpendic- 

 ular to the latter at the point where it reaches the earth. If the fault dips 

 at 90°, and if the original surface was level, the equation will then be 



y—A{m-''—\) (2) 



If the original surface was not horizontal, but formed an angle S with 

 the iC-axis, then retaining the same axes each // will be diminished b}' x tan 9, 

 and the equation becomes 



y^A ()»-^ — 1 ) - ./• tan i> ; (3) 



and in this case the asymptote of the curve would still cut the^-axis at — A, 



l)ut would make an angle S 

 with the ,r-axis or would be 

 parallel to the original sur- 

 face. Since the angle S 

 merely expresses the rela- 

 tive directions of the .r-axis 

 and the oi'iginal surface, this 

 equation is general, and a})- 

 plies, whatever may be the 

 dip of the fissure and what- 



FlG.5.-,=J(m-_l)-xtau--. ^^,^^, ^^^ j^.^^^ ^^^g^^ ^j^^ 



slope of the original surfiice. If fi is tlie dip of the fissure and S is the 

 slope of the original surface, we also have 



5 — f|0o_/y_t-(5, 



