﻿516 



Mr. S. Lees on a Simple Model 



further tentatively be assumed that whether or not slipping 

 takes place, the two sets of groups will behave elastically, so 

 far as each set is concerned. These points are involved in 

 the model shown in fig. 3. In this diagram, A x and A 2 

 represent two groups of molecules of the first kind referred 

 to. Aj and A 2 are directly connected up to the agency pro- 

 ducing the stress (represented in the diagram by forces 

 F, F), and are shown joined together elastically by a spring- 

 marked with tension T x in the diagram). As typical of the 

 groups of the second kind referred to, we have the items 



B 1? B, 



Oi, 



and C 2 . Here B x and C t are between them 



squeezing A x with a pressure N. B 2 and C 2 are performing 



Fiff. 3. 



Springs to produce 

 compression A/ 



a like office for A 2 . Bj and B 2 are shown joined together 

 elastically by a spring (represented as being in tension T 2 ). 

 Cx and C 2 are similarly connected together by a spring (also 

 shown in tension T 2 ). The diagram is intended to represent 

 a state of affairs such that when F is zero, the tensions T 2 

 and the tension T 1 all vanish. Such a state of affairs 

 may be called the neutral state. For such a state, the dis- 

 placements of Ai, Bj, and Ci from their equilibrium positions 

 are all equal, and (measured with 00! taken as unaffected) 

 may be denoted by x. Similar remarks apply to A 2 , B 2 , and 

 C 2 . Since we shall have under these circumstances 



Ti = \ Y x v , T 2 = \ 2 x, (8) 



where \i and X 2 are appropriate elastic constants, it follows 

 that 



F = (X 1 -f2X 2 ).r 



(9) 



