﻿528 Mr. S. Lees on a Simple Model 



increase of |F |, was generally quite similar in character to 

 the static stress-strain loops referred to in § 6. 



The limits just referred to correspond to P] and N x of our 

 fig. 7. If we take the static elastic limits for zero hysteresis 

 loops given by Smith & Wedgwood's fig. 14 as 9*5 tons 

 per in. 2 , and consider the case indicated in the same authors' 

 fig. 15, viz. [FjI = 7'65, we ought by (a) of this section to 

 get for the point N x of our fig. 7 a value of 



F = 9-5-7-65 = 1-85 tons per in. 2 . 



The actual value indicated in Smith & Wedgwood's fig. 15 

 would appear to be about 1*6 tons per in. 2 . 



A difficulty arises in connexion with the differences in the 

 stress limits for zero hysteresis loops as shown in Smith & 

 Wedgwood's figs. 2 and 14. The two results of these figures 

 can be to some extent reconciled by assuming that repeated 

 slip causes some change in the value of /j, in the model, 

 e. g. by temperature change, etc. Ultimately, of course, the 

 explanation is molecular, but the fact that rest causes the 

 material to go from a state corresponding to Smith & 

 Wedgwood's fig. 2 to a state corresponding to their fig. 14, 

 is a good reason for taking this simple explanation. 



There are certain outstanding differences between the 

 results obtained from the model of § 3, and the actual results 

 of Smith & Wedgwood. The first is that the mean-stress- 

 strain loop is not a parallelogram in actual experiment. 

 This has been already noted. Further, when the loop does 

 not reduce to a straight line, it is found experimentally that 

 for a given |Fi|, variation of |F | causes the points of maxi- 

 mum F (corresponding also to points of maximum strain) 

 to lie on a curve like N'h' of fig. 7 b. According to the 

 present theory, this curve should be a straight line (parallel 

 to KL of fig. 4). 



In an attempt to meet the objections just raised to the 

 model of § 3, and those mentioned at the end of § 6, 

 the author now puts forward a slightly modified theory 

 and model. 



§ 10. Modified Model. 



Fig. 8 shows a modification of the model described in § 3. 

 It will be noticed that the contacts for A^ with C^ and B : 

 are point (or line) contacts ; similarly for A 2 with C 2 and B 2 . 

 The rubbing surfaces of A x and A 2 are now taken as curved, 

 instead of straight (or plane). 



