G. F. Becker — Impact Friction and Faulting. 123 



Case of the atmosphere. — A peculiar case arising under the 

 general equation is that in which the passive body,_ though of 

 finite mass is of infinite volume, and therefore, in its uncom- 

 pressed state, of infinite tenuity. Here the value of a being 

 infinite, the coefficient B disappears and the equation assumes 

 the simple logarithmic form. The value of the energy at the 

 contact, however, cannot be affected by the fact that there is no 

 limit to the expansion of the material. A therefore assumes 



the value 



_?nvW 1 \_ m„v 2 



and the base of the equation diminishes in such proportion as 

 to give the correct integral. IE c 2 is the exponential constant 

 for this case 



m v 3 mv 3 en 

 -c =- 



2 2 2 ra+1 



»+l 



c„= — — c 



" n+2 



- (a+2)» _ 



m„v 2 „/ r mv 2 ?i(n4-2) ^ +1)c 

 2 2 (n+iy E 



For a perfect gas under the compression produced by the 



impact of a body of its own weight n=l. The value m 2 is the 



actual mass of the unit volume at the contact of the masses, 



and c 2 is one-half the length which the volume of gas would 



have if uniformly compressed to m r 



The average stress, due to the elasticity of a solid, when 



strained from its' natural condition to that of a given strain, is 



just half the stress required to keep it in this state of strain.* 



If the energy potentialized in the passive mass by an impact 



Mv 2 

 at the moment of maximum compression is the effect of a 



constant force of corresponding intensity would be to potentialize 



Mv 2 v 



an energy -~ where v^— . It a column of uncompressed 



gas possessing the mass of a column of the atmosphere of the 

 same section, were to strike the earth at a velocity g, the average 



M<7 a 



potentialized would be —^—. This is four times of the energy 



actually potentialized in the atmospheric column. In general 

 if the energy diagram for the impact of a mass 2M moving at 

 a velocity v and impinging upon a mass 2raM is reduced to half 

 its dimensions, or if it is interpreted in terms of a unit twice 

 that used in plotting it, the result is the distribution of energy 



* Thomson & Tait, Nat. Phil., § 674. 



