2 M. Gr. Wiedemann on Torsion. 



relations of this sort, first to investigate the positions of equi- 

 librium of bodies deformed by forces, or the torsions of their 

 molecules which then takes place. 



With this intention I have already, in the years 1858- 

 1862*, published a series of treatises both on torsion and 

 bending considered apart, and also on the analogies between 

 mechanical and magnetic phenomena, as well as the reciprocal 

 actions between the two. 



I had endeavoured inter alia to determine in general out- 

 lines the ratio between the permanent deformations of a body 

 and the temporary deformations occurring during the action 

 of the deforming force, and had shown that, as Wertheim f 

 had already observed, the former occur even after the slightest 

 temporary deformations, so that in a body not previously de- 

 formed a limit of elasticity does not properly exist, but bodies 

 which have sufficiently often been deformed within certain 

 limits by determinate forces, on the repeated action of the 

 same or less forces in the same direction as that last applied, 

 constantly again receive the same permanent deformation. 

 With this agrees the result subsequently (1865) communi- 

 cated by Thalenf , that by repeated stretching of rods a raising 

 of the limit of their elasticity, increasing with it, takes place §. 

 Moreover, with the first deformation the permanent alterations 

 of form increased much more rapidly than the temporary, 

 which is not the case in an equal degree with repeated defor- 

 mations. I had in like manner shown that, when left longer 

 in a state of rest after repeated deformations, bodies partially 

 return to their previous condition ||, and behave similarly 

 under deformations which exceed the limits of the first. I 

 have also studied the behaviour of bodies under consecutive 

 oppositely directed deformations^, &c. 



In addition to these experiments I take leave to communi- 

 cate some older and newer observations by which their results 

 should be extended. 



2. Apparatus. — The influence upon a wire of repeated tor- 



* Pogg. Ann. ciii. p. 563 (1858), cvi. p. 161 ; Basle Verhandlungen, ii. 

 Heft 2, p. 169 5 Pogg. Ann. cvii. p. 139 (1859). 



t Ann. de Chim. et Phys. xii. p. 385 (1842) : Pogg. Ann. Ergbd. ii. 

 p. 70 (1848). 



\ Pogg. Ann. cxxiv. p. 600 (1865). 



§ Similar results also by Tresca, Compt. Rend, lxxiii. p. 1153 (1874) ; 

 Uchatius, Beibl. i. p. 273 ; Bauscliinger, ibid. p. 380 (1877) ; and others. 



|| Similarly Bauscliinger, /. c. (1877). 



51 A series of the results of torsion and bending obtained by me have, 

 certainly without mention of them, been confirmed by W. Voigt {Disser- 

 tation d. Univ. Konigsberg, 1874?) in the bending of sticks of rock- 

 salt. 



