12 



M. Gr. Wiedemann on Torsion. 



Consequently, when the state of the wire, after repeated 

 torsions and detorsions, has become constant, an increase of 

 the loading, imparted to it during its detorsion, effects an 

 augmentation of the following temporary and permanent tor- 

 on the subsequent diminution of the load the final 



sions 



temporary and permanent torsions remain almost unaltered 

 (conf. § 14). If, however, we take the differences between 

 the temporary and the permanent torsions after the wire had 

 been once loaded, they remain almost perfectly equal. By 

 the loading, therefore, only the permanent position of equili- 

 librium is displaced (as above, § 5), reckoned from which the 

 transient torsions produced by the torsion- weight are constant. 

 In this sense the wire which has arrived at a constant state 

 possesses equal elasticity with different loads. 



12. Torsion of a Wire alternately loaded with different 

 Weights. — A similar action of different loading of the wire 

 is shown when it undergoes torsion by increasing weights w 

 at the same time that it is loaded with alternately lighter and 

 heavier weights W. The experiments were made on a brass 

 wire of the same dimensions as the former ones, and at the 

 temperature of 100° C. The results were as follows : — 



w. 



W. 



K 



T. 



Ti- 



Pr 



Tx-Px- 



AT,. 



AP X . 



A(Tx-Px). 



44 



3220 





470 



471 



3-2 



467-8 



113 



5-3 



107-7 



54 



9220 



3* 



583 



584 



8-5 



575-5 



105 



1-8 



103-2 



64 



3220 



6-5 



689 



689 



10-3 



678-7 



117 



6-7 



110-3 



74 



9220 



9-5 



804 



806 



17 



789 



111-5 



3-5 



107 



84 



3220 



16 



916-5 



917-5 



21-5 



896 



128-5 



183 



110 



94 



9220 



21-3 



1041 



104-6 



398 



1006-2 



115 



9-7 



111-3 



104 



3220 



38-5 



1161 



1167 



49 5 



11175 



150 



38-2 



115-8 



114 



9220 



48-5 



1311 



1323 



87-7 



1235-3 



148 



35-3 



120-0 



124 



3220 



84 



1459 



1468 



113 



1355 



220 



107 



140 



134 



9220 



111 



1679 



1715 



220-1 



1495 









The differences A show distinctly that the values r J\ and P x 

 constantly increase relatively more rapidly at the transition 

 from the unloaded to the loaded wire than in the opposite 

 case, while, on the contrary, the values T x — P x increase with 

 almost perfect regularity. 



13. Lastly, we notice the influence of different stretchings 

 with torsions in alternately different directions. A brass wire 

 of the former dimensions was, under alternately lighter and 

 heavier loading, turned both ways up to a determined tempo- 

 rary torsion ±T, and then the permanent torsion ±P was 

 observed. Thus : — 



