M. G. Wiedemann on Torsion. 5 



Thus the temporary torsions increase, as was previously 

 found, at the first operation of the increasing weights, at first 

 more slowly, and then always more rapidly, up to a deter- 

 mined value corresponding to the maximum loading. This 

 latter value rises on the repeated employment of the maximum 

 loading, at first more rapidly, then more slowly, up to a cer- 

 tain maximum*. 



The permanent torsions exhibit the same behaviour ; only 

 they rise, on the operation of increasing weights, as already 

 mentioned, more rapidly than the temporary torsions ; they are 

 also more increased, on repeated torsion by the same maxi- 

 mum weight, than the latter. 



The result previously observed, with alternately directed 

 torsions is here confirmed — that the limits up to which oppo- 

 sitely acting forces temporarily twist wires always become 

 narrower with repeated torsions, and gradually approach a 

 constant minimal distance. In the present case those forces 

 are the temporarily twisting maximal weight and the force nil, 

 and the distance between the limits is the corresponding value 

 Ti— Pi. 



At the same time, with repeated torsions the differences 

 Ti — Pi that obtain for the various twisting weights become 

 constantly more proportionate to the twisting weights ; they 

 rise a little with increasing weights, as the differences A of 

 the consecutive values T x — P x show. 



'4. Repeated Torsion in opposite Directions. — In order to 

 pursue this latter relation within wider limits, especially when 

 the wires are not only unilaterally (wisted repeatedly in one 

 determined direction, but their molecules are turned aside by 

 alternately acting forces in opposite directions, a wire of the 

 same dimensions as the former ones was loaded with 8175 

 grams, repeatedly put into oscillation, and thereupon twisted 

 ten times hither and thither by the weights ±114, when its 

 temporary and permanent torsions no longer perceptibly 

 altered ; their amounts, in scale-divisions, were : — 



W=+80 T3753 P 1486-2 T-P = 2267 

 \y = -80 T1122 P 1387'5 T-P= -1265-5 



Upon this the wire was twisted by increasing weights 

 ( — )W; and then the numbers were : — 



W= 44 64 84 104 124 



T 943 740 533 331-6 124-5 



P 1387-5 1387-5 1387-5 1387-5 1387*5 

 T-P 444-5 674-5 854-5 1056 1263 

 A 203 207 201-5 207 



Finally the wire was twisted in the opposite direction by 

 * See an analogous observation on stretching : Thalen, I. c. p. 682. 



