﻿to Illustrate Elastic Hysteresis. 517 



Thus regarding F as representing externally applied stress, 

 and x as the corresponding strain, we get the usual Hooke's 

 law holding for stresses which do not disturb the neutral 

 state. This remark, of course, holds for either tension or 

 compression. 



If fi denote the coefficient of solid friction between Aj and 

 both B 2 and C b the same value holding for A 2 and both B 2 

 and C 2 , slipping will take place when 



T 2 = /xN (10) 



This will correspond to a value of x given by 



T 2 = \ 2 # = yU,N. 



Thus the value of F at which the linear proportional relation- 

 ship between F and x breaks down will be 



F = (X 1 + 2\ 2 > = 



(Xi + 2X 2 ) 



x*N. 



(11) 



Fig. 3 a. 





1 1 



1 



i 



v r 







£/ — ^S | r 2 <r- \b 2 1 | 





F 



' i'i 



m _Ji j r /c 



i ^i 



— -i*- 



F 





| | C, —*>T 2 T 2 ^— C 2 







, 



i 







If F be increased beyond this limit, slipping will take 

 place, of amount (say) y, between Aj and B 1 and Ci ; also 

 (see fig. 3 a) between A 2 and B 2 and C 2 . The tensions T 2 

 will remain constant during such an increase of F, and we 

 shall now have 



F = X 1 x+2fil$ = \ l x + 2\ 2 (x-tj). 



(12) 



This, though a linear relationship between F and #, has a 

 different slope from (9), and F is no longer proportional to x. 



