JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. U April 4, 1921 No. 7 



PHYSICS. — On the theory of irreversible time effects A Mayo D. 

 Hersey, Massachusetts Institute of Technology. 



The study of irreversible phenomena has never been carried far 

 in comparison with other aspects of physics. This paper aims to 

 formulate the problem of time effects — meaning transient or re- 

 coverable effects as distinguished from permanent changes — and to 

 develop methods of analysis for use in subsequent research. The 

 writer's attention was directed to the importance of this subject in 

 consequence of aneroid barometer investigations- at the Bureau of 

 vStandards in 1911. 



General formulation . When a load A' is suddenly applied to an im- 

 perfectly elastic body, a certain amount of displacement, x^, takes 

 place at once, if ordinary inertia effects are excluded. This may be 

 termed the elastic part of the displacement and written x^ = X/E, 

 where E denotes the stiffness of the body. But the actual displace- 

 ment X at any time t differs from this by some small amount y which 

 may be termed the inelastic yield, so that 



X = X/E + y (1) 



The yield, y, depends on the whole past history of the loading of the 

 body and so the displacement at any present time t depends on the 

 load history X = funct (r) for all previous times t < t. 



An absolutely general formulation of the problem of irreversible 

 time effects is, therefore, having given the load-time curve, to deduce 

 the displacement-time curve. When the problem has been solved 

 in this general way the solution will be found to embrace, as particular 

 cases, all such special effects as the discrepancy between static and 

 dynamic modulus ; residual displacement after removal of load ; phase 

 difference between a periodically varying load and the corresponding 

 displacement; time needed for approaching the cyclic state — a state 



' Received February 26, 1921. 



- Described in Phys. Rev. 6: 75-76. 1915. It is hoped opportunity will be available 

 later for a more extended report on irreversibility, including a detailed discussion of experi- 

 mental data already collected. The present paper is intended only as a brief abstract of 

 the principles involved. 



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