124 G. F. Becker — Impact Friction and Faulting. 



due to the action of a constant force Mv on the mass 2nM. If 

 p is the pressure at any point and s the strain, we have in general 



dw =2xls. 

 If the stress aod strain are in a constant ratio, say k, ds=kdp 

 and 



If p is the value of p for the contact plane of the masses, and 

 w the value of the energy for the same surface, 



w : 10=1? :p*. 

 For the atmosphere therefore 



— x/2c 2 



2>=Po £ _ 

 Here c 2 , as already pointed out, is half the height which the 

 atmosphere would have were it uniformly compressed to the 

 density at the bottom of the column ; 2c 2 is therefore the 

 familiar "height of the homogeneous atmosphere," and the 

 equation is the barometric formula, introduced here merely as a 

 check upon the reasoning. 



Case of a rivet. — If the coefficient B is positive instead of 

 negative the entire energy will be potentialized within finite 

 limits. This is possible only when the passive mass is sub- 

 jected to two impacts in opposite directions, or when it rests 

 against an infinite mass which may be regarded as rigid. In 

 this case one-half of the entire energy will be potentialized in 

 the finite passive mass. The general equation shows that the 

 energy is to be considered as imparted to the passive mass 

 from opposite directions, and it is evident that the result is 

 the same as it would be if the energy were first distributed 

 over an infinite mass, and the energy potentialized beyond 

 x=a were then restored to the finite cylinder from the opposite 

 direction. The equation may therefore at once be written for 

 the contact as origin 



This curve must be horizontal at some point, say x=a, and if 



dvj/dx is made equal to zero B=£~ 2a ' c . According to the 

 preceding 



r £ -2a/ c s x/c dx= r € -x/c dx _ 



v o */« 



which gives 



s 2a / c = e a / c (e a//c —l). 



ISTow in a former paragraph it was shown that 

 £ a/d _ £ na/c{n + 1 ) _ n + ^ 



