STKUCTUEAL RESDLTS OF FAULTING. 171 



of tliu .subtanjTent, and the curve would cross the y-a\h at an angle of 4f)°; 

 but this is not the case when the equation is interpreted on oblicjue coor- 

 dinates. 



Fl(i. U. i/ = H)--'. 

 Point of minimum radius of curvature. TllG pOSitioU of tlie //-Mxis of tile logarith- 

 mic curve depends u[)on the unit chosen. There is, however, one fixed point 

 on the locus, that of minimum radius of curvature. "^I'liis must be deduced 

 from the general equation referred to rectangular coordinates (3), and the 

 value of X corresponding to it is 



_log (4 A In m) —log (\/8 + 9 tan- ;&— tan 5) 



Xc = 



log m 



From this formula the value of Xq for all simpler cases can easily be 

 derived. For the simplest equation, viz: 



ln2 J 1 



Xo = ^r- andy/o = 



Spacing of contours. — As tlic topographj of a country is usually represented 

 for geological purposes by contours, it would be interesting to discuss the 

 spacing of the contour lines on a map of a faulted surface. For an origi- 

 nally level surface and a vertical fault we have immediately 



Jx=z]og'ij — \og{y+Ji/) ; 



in which Jx is the variable hoi'izontal interval between contour lines and 



