E L A S T I C I T Y 817 78. A question of great importance in the physical theory of the elasticity of solids, " What changes are produced in the moduluses of elasticity by permanent changes in its molecular condition," has occupied the attention, no doubt, of every " naturalist " who has studied the subject, and valuable contributions to its answer by experiment had been given by Wertheim and other investigators, but solely with reference to Young s modulus. In 1865 an investiga tion of the effect on the torsional rigidity of wires of different metals, produced by stretching them longitudinally beyond their limits of elasticity, was commenced in the physical laboratory of the university of Glasgow in its old buildings in 1865. The following description of experi ments and table of results is extracted from the paper by W. Thomson " On the Elasticity and Viscosity of Metals," already quoted (section 30), with reference to viscosity and fatigue of elasticity. " To determine rigidities by torsional vibrations, taking advan tage of an obvious but most valuable suggestion made to me by Dr Joule, I used as vibrator in each case a thin cylinder of sheet brass, turned true outside and inside (of which the radius of gravitation must be, to a very close degree of approximation, the arithmetic mean of the radii of the outer and inner cylindrical surfaces), 1 supported by a thin flat rectangular bar, of which the square-of the radius of gravitation is one-third of the square of the dis tance from the centre to the corner. The wire to be tested passed per pendicularly through a hole in the middle of the bar, and was there firmly soldered. The cylinder was tied to the middle of the bar by light silk thread so as to hang with its axis vertical. Each wire, after having been suspended and stretched with just force enough to make it as nearly straight as was necessary for accuracy, was vibrated. Then it was stretched by hand (applied to the cross bar soldered to its lower end) and vibrated again, and stretched again, and so on till it broke." The experiments were performed Avith great care and accuracy by Mr Donald M Faiiane. "The results, as shown in the accompanying table, were most surprising." The highest and lowest rigidities found for copper in the table are as follows : Highest rigidity 473 x 10 6 , being that of a wire which had been softened by heating it to redness and plunging it into water, and which was found to be of density 8 91. Lowest rigidity 393 4 x 10 6 , being that of a wire which had been rendered so brittle by heating it to redness surrounded by powdered charcoal in a crucible and letting it cool very slowly, that it could .scarcely be touched without breaking it, and which had been found to be reduced in density by this process to as low as 8 "674. The wires used were all commercial specimens those of copper being all, or nearly all, cut from hanks supplied by the Gutta Percha Company, having been selected as of high electric conductivity, and of good mechanical quality, for submarine cables. It ought to be remarked that the change of molecular condition produced by permanently stretching a wire or solid cylinder of metal is certainly a change from a condition which, if originally isotropic, becomes seolotropic as to some qualities, 2 and that the changed condi tions may therefore be presumed to be seolotropic as to elasticity. If so, the rigidities corresponding to the direct and diagonal distortions (indicated by No. 1 and No. 2 in fig. 14) must in all proba bility become different from one another when a wire is permanently stretched, instead of being equal as they must be when its substance is isotropic. It be comes, therefore, a question of extreme interest to find whether rigidity No. 2 is not increased by this process, which, its is proved by the experiments above described, diminishes, to a very remark able degree, the rigidity No. 1. The most obvious experiment, and indeed the only practicable experiment, adapted to answer this question, for a wire or round bar is that of Cagniard- Latour, in which an accurate determination of the difference produced in the volume of the substance is made by applying and removing longitudinal traction within its limits of elasticity. With the requisite apparatus, which must be much more accurate
- It is exactly the square root of the mean of their squares.
" For example , see paper " On Electrodynamic Qualitiot; of Metals," Philosophical Transactions, 1850, by W. "Thomson. No.2, o than that of Cagniard-Latour. a most important and interest ing investigation might be made. The results, along with an accurate determination of the Young s modulus for the particular case, give (sec. 47) the modulus of compression, and the rigidity No. 2. liegnault suggested the use of hollow instead of solid cylinders, to be subjected to longitudinal pull, and (after the manner of the bulb and tube of a thermometer) a capillary tube to aid in measuring changes of volume of the hollow; and Wert heim, adopting this excellent suggestion, obtained seemingly very accurate results for brass and glass, which are given in the tables of section 77. Substance. Length of Wire in centi metres. Volume in cubic centi metres. Density. Moment of Inertia of Vibra tor Wi 2 . Time of Vibration one wav or (half period) in seconds. T. Rigidity in grammes weight per square centimetre 27r 3 mv* ?T2V2 . Alumi- ) nium J ij 3 1-1845 2764 31771 1-14 241 x!0 c Zinc 2 304-9 2-351 7-105 31896 4-31 359-6 xlO 6 Brass 2377 4-76 410-3 xlO 6
248-3 5-456 354-8 xlO 6
261-9 1-703 8 : 398 5-96 350-1 xlO 6 Copper 2435-0 15-30 8-91 38186 16-375 448-7 xlO 6 )> ,, ,, 61412 20-77 448-4 xlO 6 Copper s 214-4 1-348 8-864 31771 5-015 433-0 xlO 6
>! ,, ) J 61412 6-982 431-8 xlO 6 Copper 4 143-7 9096 8-674 3-381 393-4 xlO 6 Copper 5 286-8 20612 4-245 442-9 xlO 6 ,, 291
4-375 435-6 xlO 6 > 293 4-417 436-2 xlO 6
- >
296-1 4-500 433-8 xlO 6 >} 300-0
4-588 434-0 xlO 6 ,, 303-4 4-646 437-8 xlO 6
309-3 ? ? 4-833 428-6 xlO 6 313-2 4-931. 427-5 xlO 6 317-4 1-962 8-835 5-040 425-9 xlO 6 Copper 6 315-6 81771 8-155 442-3 xlO 6 ,, 235-5 ? j 9-425 432-2 xlO 6 j; 251-9 827 8 -872 j j 10-463 428-6 xlO 6 Copper 7 253-2 1-580 8-91 5-285 472-9 xlO 6
262-8 5-640 464-3 xlO 6
270-4 5-910 460-4 xlO 8
- ,
278-7 6-20 458-5 xlO 6 287-9 6-5325 455-0 xlO 6 >) 297-5 6-8195 451-0 xlO 6
308-8 7-3075 448-9 x!0 c Copper 8 256-5 1 -6145 8 -90 4-2226 463-5 xlO 8 j> 267-9 4-5625 453-3 xlO 6 )> 280-1 4-915 446-2 xlO 6
- >
292-2 5-240 445-5 xlO 8 ,, 301-9 5-532 438-2 x!0 c Soft Iron 9 316-8 6-655 791-4 xlO 6 > 322-1 6-88 778-3 xlO
- >
335-1 7-301 779-0 xlO 6 ,, 347-4 7-768 766-6 xlO 5 366-0 1-357 7 : 657 8-455 756-0 xlO 6 Platinum 39-4 1745 20-805 20612 2-05 622-25x10 Gold 65-9 1825 19-8 10902 281 xlO 6 Silver 75-7 1185 10-21 10967 270 x,10 c Remarks. 1 Only forty vibrations from initial arc of convenient amplitude could be counted. Had been stretched considerably before this experiment. 2 So viscous that only twenty vibrations could be counted Broke in stretching. 3 A piece of the preceding stretched. 4 The preceding made red-hot in a crucible filled with powdered charcoal and allowed to cool slowly, became very brittle : a part of it with difficulty saved for the experiment. 6 Another piece of the long (2435 centims.) wire ; stretched by successive simple tractions. 6 A finer gauge copper wire ; stretched by successive tractions. 7 A finer gauge copper wire, softened by being heated to redness and plunged in water. A length of 260 centimetres cut from this, suspended, and elongated by successive tractions. 8 Another length of 260 centimetres cut from the same, and similarity treated. y One piece, successively elongated by simple tractions till it broke.
VII. 103