STRUCTURAL RESULTS OF FAULTra(}. 163 



is dependent only upon E. If w is tlie work done on any contact, 



^^'„=./;(/;„ — /VO. 

 and if L denotes the work done on the first contact, TFP,, the o-eneral 

 equation for the work on all contacts is 



or the' distribution of energ-y is log'arithniic however the friction may vary, 

 so long as the material composing- the sheets is the same tliroiigh(»nt the 

 system, and supposing- friction independent of velocity. 



Morin's law is merely an approximation, but should an exact i-elation 

 be discovered between friction and velocity it would be an easy matter to 

 give the variation of the friction its proper weight in the equation for a 

 faulted surface. 



Locus of edges of sheets when the friction varies regularly. CaSeS may readily arisS in 



which the friction varies regularly from contact to contact, as would hap- 

 pen for example in a system of sheets between which the pressure was pro- 

 duced by the weight of the sheets themselves. Suppose the case of friction 

 increasing from/ at the contact TFPby asmall increment./?. Then for 

 any distance x from the origin, the frictional resistance will be/(l+ xt). 

 If dx is the thickness of a sheet, the relative motion at x will be dy and the 

 work done/ (1 + xt) dy. If the friction were constant and equal to/ the 

 work done on the same contact would be derivable from an eqiiation, say 



and would amount to 



fdy^-zz — fA In mm~^dx; 



and since it has been shown that the work on any contact is independent 



of the frictional resistance, 



f(\-^x()dyz:.—fA In mm~''dx; 



or 



rmr'^dx 

 ,,/z=-.4ln«,j j^-, 



which is not integrable when m > 1. 



Approximate equation. — If tlic pressurc is produccd by the weight of the 

 sheets and if these are numerous, / is a very small quantity and its square 



