152 JOURNAI, OF THE WASHINGTON ACADEMY OF SCIENCES VOX,. 11, NO. 7 



The fundamental physical assumption of drift superposition may 

 now be stated in this way : The yield y at any time t is the algebraic 

 sum of all the elements of drift generated by each previous load incre- 

 ment. 



If this assumption is true, the general problem of irreversible time 

 effects can be solved mathematically without further physical informa- 

 tion than is already contained in the function F. The ' assumption 

 implies that if two bodies have the same drift function F, they cannot 

 differ in any of their remaining effects; and while this assumption is 

 probably not precisely true even for moderate loads, it is certainly 

 true as a first approximation, and therefore practically useful. 



The following two-constant expressions have been used in aneroid 

 barometer work : 



, F{T) = Ail - r-'"'") (6) 



F{T) = BT" (n<l) (7) 



") (8) 



(9) 



has been proposed by Michelson ' for the drift due to torsion in a large 

 number of substances. The coefhcients A, B, C, K, m, n, a may 

 depend on temperature and other physical conditions, including the 

 load X itself; but are required by the superposition assumption to 

 be independent of the load increment AX. 



The principle of the superposition of elements of drift may be ex- 

 pressed mathematically thus, 



y = Z AX. Fit - t) (10) 



in which y is the yield at the present time /, while A A' denotes a load 

 increment applied at some previous time r. For convenience the 

 argument T of the drift function has been replaced by its equivalent, 

 t — T. Equation (10) can also be put into the form of a time-integral.'^ 



t 



= C^ Fit - r)dr (11) 



* Laws of elastico-viscous flow. Proc. Nat. Acad. Sci. 3: 319-323. 1917. 



^ The time-integral was made possible by suggestions of Dr. F. B. Silsbee. Acknowledg- 

 ments are due also to Dr. L. B. Tuckerman and Prof. P. W. Bridgman for valuable sug- 

 gestions. The first attempt at a general solution was completed in 1916 in connection with 

 work on elasticity at Harvard University. It led to a formula which is equivalent to (10) 

 but which was to be applied by the summation of series instead of by integration, and 

 which also differed in that F (T) represented the drift following a gradually applied load. 



