PHYSICS: A. A. MICHELSON 
321 
mately proportional to the stress and independent of time.* A closer 
approximation is given by 
Si = CrPey 
The Elastico -viscous Displacement. — This is manifested in a slow re- 
turn vifchen the stress is removed ; and it is assumed that the same forces 
are brought into play during the direct motion. 
This displacement is represented by the formula ^2 = ^2(1 — ^"^^O 
where A2 = C^Pe^'^. 
The Viscous Displacement. — Here the elastic force is absent or very 
small in comparison with the viscous resistance. The specimen does 
not return to zero even after a long time interval. f The viscous dis- 
placement is given by ^3 = (Ft + T^o^o)^ - {F^oY in which F =CzPe^'^ 
and Fo the corresponding value, when P has the value Po during the 
time, /o. 
For a specimen which has not been subjected to previous strain the 
formula reduces to Sz = {FtY . Experiment gives p = i approxi- 
mately, until the specimen is near the rupture point when p approaches 
the value unity. 
The Lost Motion. — If the stress be applied for a short time (even a 
small fraction of a second) the specimen does not return to the original 
zero. The difference between the original and the new zero is the lost 
motion, L. 
It seems probable that the lost motion may be considered as a function 
of / such as f , where r is very small (less than 0.02 for zinc). 
If this be considered as part of the viscous term 
Sz = Azf{t) 
then the total viscous yield may be represented by 
Sz = Az[f{t)-\-Cf] 
(If the actual stress is between the limits 0 and Po, C = 0) 
The Return. — If after a time, t^ the displacement has reached the 
value, S, and the stress is released, the specimen promptly returns to a 
displacement short of zero, and continues much more slowly in the 
same direction. 
If the elastico-viscous displacement at the time, t^ is given by 
S2 = A2{\~e-<^<T,) 
* Doubtless there is some viscous resistance to this displacement, but it is very small, 
t In some cases it may be made to return to the original position by heating, or by alterna- 
tion (alternate positiv^e and negative diminishing stresses). 
