Physics. “On the Theory of Hysteresis according to VorrerRA”’. By 
Dr. W. Koster Dz. (Communicated by Prof. W. H. Junius). 
(Communicated at the meeting of June 26, 1920). 
§ 1. In chapter VI of his ‘‘Lecons sur les fonctions de lignes” 
Vourrrra treats elastic hysteresis. By the method developed by him 
there the equations expressing the components of the elastic tensions 
as functions of the quantities that determine the state of the elastic 
medium, are revised. In the classical theory of elasticity these 
equations have the general form: 
Component of tension = linear homogeneous combination of the 
quantities of deformation. (Law of Hooke). VoLTERRa substitutes for 
this relation the equation: 
t 
tin (t) Dihfrs Yrs (t) fz Wih/rs (tt) Yrs (t) dt. 
0 
In this ¢, represent the elastic tensions at the moment ¢, y‚s (4) 
representing the quantities of deformation at that moment and jy, (t) 
the same quantities at a variable moment r. Further the 6’s and 
the w’s are coefficients; VoLTERRA calls the w’s coefficients of heredity. 
We shall show in what follows that dissipation of energy may 
ensue from these suppositions of VorTERRA’s; i.e. in the case that 
his suppositions have physical meaning. 
We further point out that the idea on which VorrTErra’s hypothe- 
sis is founded, is that of distance action in time. For the contribu- 
t 
tions to this f= Witirs (tt) Yrs (©) dt are supplied by deformations y‚s, 
0 
which existed at moments t in the past. This distance action in time 
is somewhat unsatisfactory, we ought to be able to manage with- 
out it. If at a given moment the condition is completely determined, 
the principle of causality tells us, that what will follow is also 
entirely fixed. Only with a definite previous history there will be 
another deformation at a fixed point of time than when the 
previous history had been different. We shall later on try to deal 
with elastic hysteresis without assuming distance action in time. 
