476 SCIENCE PROGRESS 



form occurs, all that can be happening is an internal rearrange- 

 ment of the particles of which the body is composed— a fact 

 which has caused the method to be much used in later research. 

 The next theory of importance was that published by Boltz- 

 mann 1 in 1878. The total after-effect was taken as being due to 

 a whole series of after-effects resulting from applications of stress 

 at all times previous. He assumed, and afterwards verified by 

 experiment, that if a body were acted upon by a stress for a very 

 short space of time t, then the resulting after-effect, after any 



time t, was proportional to -, and also to the magnitude of the 



stress. The total after-effect in a body subjected to stress for a 

 considerable time will be made up of all the elementary after- 

 effects due to the application of stress during the series of short 

 times into which the total time may be divided. Further, he 

 assumed that these short durations of stress produce in the 

 aggregate the sum of the effects they would have produced 

 individually. This principle has been called the " Principle of 

 Superposition." Kohlrausch has shown, however, in the case of 

 a silver wire, that this principle is somewhat removed from the 

 truth, and that the calculated after-effect, on this assumption, is 

 always greater than that actually observed. That is to say, 

 the small durations of stress produce less effect when existing 

 together than the sum of their individual effects. Notwith- 

 standing this fact, however, Boltzmann's final results are in 

 close accordance with observation. The chief results are the 

 following : 



1. That if a wire is suddenly twisted, then the couple necessary 

 to maintain it at this initial torsion may be represented by — 



D -<■{«.-* log (-')}, 



where D is the couple and t the time reckoned from the moment 

 of twisting ; a, c, b and p being constants. The restriction is 

 imposed that the formula holds neither for very small nor very 

 large values of t. The four constants shown can in reality be 

 reduced to three, for log p may be added to the constant a, giving 

 it a new value. 



2. That if a wire is suddenly acted upon by a constant couple 



1 L Boltzmann, Wiener Sitzungsberichte, October 8, 1874 ; Wied. Ann. 5 

 (1878). 



