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



/increases with x (as it really does, though slowly) ju and c are 

 functions of/ If /is not uniform, the strain curve will be the 

 result of the combination of the logarithmic distribution of 

 energy with the varying coefficient of friction and will not 

 therefore in general be simply logarithmic. But were the rela- 

 tion of /to x logarithmic, so that/— v/ v beiug a constant 



It readily follows that y t is to y 2 in the same ratio for this case, 

 and therefore the strain equation would be 



y = A {fiv)~ x / c . 



Now according to Bochet the locus representing the relation of 

 the coefficient of friction to velocity is represented approxi- 

 mately by the equilateral hyperbola referred to axes parallel to 

 the asymptote.* 



For a series of velocities standing to one another in a constant 

 ratio and for a uniform total pressure at all contacts, the ratio 

 of successive values of the coefficient of friction will therefore 

 be nearly constant, or in other words v will vary very slowly for 

 the range of velocities for which Bochet's formula fairly repre- 

 sents the facts, and the locus of the edges of the sheets will 

 vary but little from a simple logarithmic curve. It will be 

 shown later that while this is true for very moderate velocities, 

 it is possible to experiment with velocities so low as to reveal 

 the variation of v. If/ varies at different contacts, of course the 

 ratio of successive values of w is not the same as the ratio of 

 successive values of y. 



Coefficient of restitution — If the strain is proportional to the 

 stress in a system of uniform sheets the strain equation may be 

 written 



y=As~ x / c =Api~ x , 



where p. is the ratio of the movement of two successive sheets. 

 The quantity c is therefore the length of the subtangent ex- 

 pressed in terms of the thickness of a sheet. If c is taken as 

 unity (making /*=s) and if the coefficient of restitution is zero 



dw _ 



dx 



* Ann. des Mines, 1861. If k is the statical coefficient, and k a> the value 

 of k for an infinite velocity and v the velocity in metres per second, Bochet's 

 formula may be written 



, A'o — kco , 



k = _ + kco . 



1 + 0. 3v 



To illustrate the statement made in the text, let k be 0-5 and kco be 0*1. If the 

 value of k is computed for «=tV, i, i, £, 1, 2, 4, 8, 16, 32, 64, and each of these 

 values is divided by the next following, the ratios or values of v obtained are in 

 the same order 101, 1-03, 1-06, 1-09, 1-17, 1-25, 1'27, ]'29, 1-23, L-17. 



