164 GEOLOGY OF THE COMSTOCK LODE. 



may sometimes be to the senses a vanishing quantity. When this is the 

 case the equation 



sensibly represents the hicus. For the value of w may be written 



Ji/f{l-{-xt)=f(b-b,)m-^ 

 or 



•' \.-\-xt \l+xt \+xty 



while the approximate equation gives 



^ \l-\-xt ^ , xt J 

 and since 



1+,— +-^ = l+J'<, 



the two equations give the same results, if 4 is inappreciable. 



It has already been pointed out that, since the distribution of energy 

 is logarithmic, the sum of the relative movements is dependent on the vari- 

 ation of the friction. If therefore the friction is a minimum at the contact 

 W Pj, a greater amount of energy will be required to move W through a 

 distance A than if the friction were constant. The total energy required 

 will be the same as it would be if each relative movement took place by 

 itself Assuming the appi'oximate equation deduced for this case, it can 

 readily be shown that, if W moves a distance A, the total energj^ required 

 by the system is 



■^<' + 'f7|i> 



Since there is nothing essentially positive in the nature of t, all the 

 foregoing equations become applicable to the case of a decreasing frictional 

 resistance by merely reversing the sign of t. Landslides might furni.sh 

 cases of this character. Suppose a mass of material divided into sheets 

 resting on a hillside, and that through weakened coherence the mass de- 

 scended such a distance ns might be necessary to do a work /A on tJic 



