﻿to Illustrate Elastic Hysteresis. 537 



between the cases of direct and shear stresses shall be made 

 numerically, it is quite clear that such a model will lead to 

 exactly the same type of results in the two cases. A com- 

 parison of the preceding theory with the results of Mr. F. 

 E. Rowett's experiments is satisfactory in many ways. 

 These experiments dealt solely with shear stress hysteresis 

 (see Proc. Roy. Soc. A. vol. lxxxix. p. 528 et seq.). 



§ 15. Time Effects. 



It is quite clear that the model and its accompanying 

 theory do not explain what may be called time effects in 

 elastic solids. By this phrase is meant here the changes 

 which take place in a solid with lapse of time, with or 

 without the application of external stress (kept constant). 

 Some account can be rendered of these effects by assuming 

 that when slip takes place, the frictional force of slipping is 

 not a constant as in the model of § 3, or a function of the 

 slip as in the modification of § 10, but depends also on 

 the velocity of slip, not on the rate of change of the strain. 

 The difficulties arising out of time effects have been avoided 

 in the above discussions as far as possible. They are re- 

 garded as arising out of change of fju with velocity. This 

 " coefficient of friction " will doubtless depend not only on 

 the velocity of rubbing, but also on temperature, which in 

 turn is a function of the number of hysteresis cycles 

 described, etc. In this connexion, it should be observed 

 that the introduction of //, into the argument of the paper 

 is essentially an artifice which brings out the striking 

 analogy which seems to hold between the every-day phe- 

 nomena of solid friction, and the more subtle friction 

 obtained in elastic hysteresis experiments. 



Conclusion. 



In this paper the author has described a simple model 

 which would seem in many ways to bring out, at least quali- 

 tatively, many of the general effects observed in connexion 

 with elastic hysteresis. The ultimate standpoint is that such 

 effects are due to something analogous to the ordinary solid 

 friction of every-day life. The model enables some simple 

 deductions to be drawn of a mathematical character, but no 

 attempt is made here to stress these deductions unduly, as 

 the model (involving one dimension of displacement) can 

 only but roughly represent what is essentially a question of 

 statistics, involving slippings in all conceivable directions. 



