APRIL 4, 1921 hersey: irreversible time effects 151 



In equation (2) with its A^ separate quantities y, R, t,Ci,. . .C^ there 

 are N - 1 degrees of freedom, but Buckingham has shown^ that di- 

 mensional requirements diminish this number by k, where k is the 

 number of fundamental units needed for measuring the original N 

 quantities. Now in treating irreversible processes where the physical 

 state is held constant, x, X, and t are sufficient for fundamental units 

 so that k = 3. Consider for example a body whose properties are 

 fixed by J/ = o drift constants Bo, n, and /3 (defined by equations (7) 

 and (13)). The dimensions of the original six quantities are [y] — 

 [x], [R\ = [X], [t] = [t], [Bo] = [xX-H-''], [n] = [1], and [3] = 

 [A"-i]. Therefore (2) becomes 



y = BoRt" funct (J3R, «) (3) 



and it is clear that there are now only two independent variables, (3R and 

 «, instead of five. The procedure for model experiments can also be 

 illustrated by equation (3), letting primed symbols refer to the model, 

 others to the original. The condition for similarity is that the model 

 be made from a substance having the same value of n, and loaded over 

 a range R' such that R'/R = /:^//3'. The yield y at any time t can now 

 be computed from the yield y' observed at time t' by the relation 



y Bo' R' v) ^ 



The load history diagrams for the model and original are to be kept 

 geometrically similar. 



Superposition theory. Direct calculation of the yield y at time / is 

 possible on the basis of an assumption which may be called the prin- 

 ciple of the superposition of elements of drift. By drift is meant the 

 increase of displacement while the load is held constant. Imagine a 

 small load AA' applied instantaneously to a body which is in a normal 

 state; that is, to a body which has rested undisturbed for a sufficient 

 time so that all previous effects have sensibly died out. What hap- 

 pens? It is a matter of observation that the displacement does not 

 stop with the immediate or elastic part x , but keeps on increasing. 

 Under these circumstances, the yield ^y observed after a lapse of time 

 T reckoning from the instant when the load was applied is termed the 

 drift due to instantaneous loading. It can be written 



^y = AX- F{T) (5) 



This equation serves to define the drift function F{T), which is a 

 purely empirical characteristic of the body. 



» This JouRNAi. 4: 347-353. 1914. 



