104 M. G. Wiedemann on Torsion. 



torsion in its molecules, we will draw axes parallel with the 

 axis of the wire. Let the wire next be " accommodated " by 

 frequent rotations to and fro, and therein at last be tempo- 

 rarily twisted in the positive direction describing an angle 

 -f- a, while the molecules may be rotated so that the lower 

 ends of their axes, looked at from the axis of the wire, describe 

 an angle + a, say to the left. The direction of this rotation 

 follows even from my magnetic experiments *. If the wire 

 be slowly brought back into the permanent torsion-position 

 + b, the axes of the molecules will retain a portion + (3 of 

 their rotation to the left. If the wire now receives an impulse 

 in the positive direction, which again elongates it up to + a, 

 according to the laws of perfect elasticity it will swing back 

 again to the position + b. If it now swings beyond this po- 

 sition further to the right, and if the molecules in their rotation 

 had no friction on one another at all to overcome, it would arrive 

 at the elongation — a, since, according to § 6, the same force 

 that twists it from + b to + a twists it in the contrary direc- 

 tion from + b to — a, while the axes of the molecules would 

 be rotated just as far ( — a) to the right as previously to the 

 left. Again, with perfect elasticity the wire would go back to 

 the position — 5, in which the molecules would be rotated — /3, 

 and so forth. 



The to-and-fro motions of the wire, between ±a and ±b, 

 are perfectly elastic ; therefore the performances of work in 

 the swingings outwards and the swingings back again must, 

 within these limits, completely compensate one another. In 

 fact, however, there results a diminution of the amplitudes of 

 oscillation ; hence the loss of vis viva therein can only corre- 

 spond to the work which is expended for the alteration of the 

 positions of equilibrium, or the rotation of the molecules 

 from +/3 to — /3 which determines it. The above dimi- 

 nution may therefore be taken as a measure for this work. 



Since the shifting of the permanent torsion-position to accom- 

 modation is, within certain narrow limits, proportional to the 

 temporary torsion, and therefore the rotation of the molecules 

 therewith is likewise approximately so, the oscillation-ampli- 

 tudes must, within those limits, diminish according to the law 

 of a geometrical series. 



22. Oscillation-Experiments. — That, in proportion to the dis- 

 placement itself of the permanent position of equilibrium, the 

 resulting loss of vis viva may be relatively very little, follows 

 also directly from oscillation- experiments. 



The wire which had been made use of for the experiments 



* Pogg. Ann. cxvii. p. 203 (1862). 



