﻿to Illustrate Elastic Hysteresis. 515 



the area of the loop vanishes with p, and so violates the 

 facts. A combination of formulae (4) and (6) will suffer a 

 like disability. 



In view of the undoubted fact that when the strain range 

 is large enough, hysteresis exists, whether the. speed of 

 describing the cycle of strain change be quick or slow, the 

 author has felt it necessary to fall back on the rather primi- 

 tive notions of solid friction. It is not contended that the 

 ordinary ideas of fluid friction do not enter into the produc- 

 tion of elastic hysteresis at high speeds, but it is asserted 

 that with low speeds of describing a cyclical change, fluid 

 friction effects are neolioible. 



The author has found it possible, using the notions of solid 

 friction, to get results in good qualitative agreement with 

 many of the facts, and these notions enable mathematical 

 analysis of a simple character to be applied. The chief 

 factor in solid friction that is made use of in this paper is 

 the property according to which there is a marked discon- 

 tinuity between the limiting tangential force just required 

 to produce sliding (of one surface over another pressed 

 against it) in one direction as compared with the opposite 

 direction. If the tangential force available lies between 

 these limits, no slipping takes place. In fluid friction, as 

 usually understood, the frictional force will vary continuously 

 as the direction of relative motion or sliding is altered, and 

 at the instant at which the two surfaces have no relative 

 motion, the tangential force exerted by one on the other will 

 momentarily vanish. This behaviour is totally different to 

 that obtained with the agency of solid friction. 



§ 3. Description of a Simple Type of Model. 



In the model now to be described, the author conceives 

 that in a metal under stress there are groups of molecules 

 (or possibly crystals) which in some way are capable of 

 receiving and transmitting directly a portion of the stress 

 applied. There are also other groups of molecules which 

 may take up a portion of the stress, but this portion is deter- 

 mined by considerations of solid friction. The solid friction 

 is supposed to arise owing to the pressure of the first set of 

 groups acting normally on the second set. This pressure 

 may be considered as molecular in origin, and of the same 

 character as cohesive effects. Such pressures will doubtless 

 be large, and as a first approximation we may suppose that 

 this pressure is not materially altered even if slipping takes 

 place between members of the two sets of groups. It may 



2 L 2 



