STRIJCTITRAL RESULTS OF FAULTING. 161 



to move tliroiigli ;i (listiincft />, /'„ , , would move tlirough ii (listaiice />,. Hence 



lln ^ h^ 

 .IJn+l fh 



and 



or the movements of any two successive slieets are in tlie same constant ratio; 



Hence, too, 



K 



Locus of the edges of sheets. — If BC is taken as the r-axis of the locus of the 

 edges of the slieets and WP^ as the v/-axis, 



or 



"^ rr 1 — m'^-' rz — In mdx; 



y 



whence 



yzriAm'"^ (2) 



which is the ordinary logarithmic curve and the equation of the locus of 

 the projecting edges of the sheets. The locus of the other edges found at 

 the reentrant angles is 



Modification for case of a finite number of sheets. — 111 auy uatural Or experimental 

 case the number of movable sheets will necessarily be finite. The locus 

 which will be formed if P„ is fixed, can be obtained by supposing that after 

 the infinite curve 



jf rr A m~'' 



has been formed, 1\ and all its successors are forced back to their original 

 position on the line AB. Each sheet from W to P„_i would then be drawn 

 down through a certain distance, which can leadily be shown to be given 



by the equation 



y" zz. b„)if~" — Aii(''~-'\ 



The locus actually assumed will therefore be 



y :^l/' — ji" — A nr'' — A)n,^~-" zz Anr^i 1 — /«-<'■""'), 



Comparison of the two loci. — Tlu' Variation ol' this ei|Uation Irom the logarith- 

 11 r; I, 



