8 M. Gr. Wiedemann on Torsion. 



from the temporary torsions produced by the above weights 

 W, the differences T — P will again be the same to whatever 

 value P M within the first limits P +m and P_ m the torsion 

 P +m has been reduced. They rise hardly quicker than corre- 

 sponds with the proportionality to the acting weights, and are 

 equal to the temporary torsions T m —V p produced by the same 

 weights in the ascendiDg direction. Within the limits P ±JW 

 and T ±m , therefore, the wire is almost perfectly elastic, if the 

 temporary deformations produced by the forces be reckoned 

 from the actual zero-position, and so the transient torsions 

 alone be taken into account. It is consequently only the dis- 

 placement of the position of permanent torsion toward one side 

 that conditions the deviation of the total (reckoned from the 

 original position of equilibrium) temporary torsions from pro- 

 portionality with the acting forces. Therewith the permanent 

 torsion P TC increases up to l J m , at first more quickly, and then 

 more slowly, with the rising forces. 



From the above-cited experiments it immediately follows, 

 further, that the wire which, after repeated torsions, has ac- 

 quired a permanent torsion P +m by forces W(_) acting in the 

 opposite direction to that of the last applied twisting force 

 W(+m) 7 receives stronger temporary torsions T ( _) than when 

 the forces W ( +) act repeatedly in the same direction as the 

 force W(+ m ). The difference corresponds to the shifting of the 

 position of permanent torsion in the negative direction. 



7. The Permanent Torsion of a Wire that is frequently 

 twisted as far as a determined Limit. — In other experiments a 

 metal plate directed vertically downwards was soldered in a 

 radial position to the horizontal disk borne by the wire ; and 

 horizontal screws were arranged so that at the torsion of the 

 wire the plate struck against them. When in this way a brass 

 wire of 2 millims. thickness, 450 millims. long, and loaded 

 beneath with 9200 grams, was repeatedly twisted by the tor- 

 sion-weights, the deflection amounting to T scale-divisions, its 

 permanent torsions P x were found to be : — 



I. II. 



1 2. 3 



T 1387 1387 1387 



P x 992 106-9 110 



1. 2. r 3 



2700 2661 2607 

 1056 1120 1136 



If the wire in experiment I. was again temporarily twisted 

 to 1387, struck gently with a flat wooden bar, and untwisted, 

 Prose to 115-2, F 1 to 115. 



Thus also with repeated equal (or, indeed, somewhat dimi- 

 nishing) temporary torsions of a wire the succeeding perma- 

 nent torsions increase. The latter also increase after agitation 

 of the temporarily twisted wire. 



