818 ELASTICITY 79. The following tables show the effects of differences of temperature on the Young s Modulus, rigidity-modulus, and modulus of compressibility of various substances : Substance. Density. Young s Modulus in million grins, per square centimetre. iy 173 558 715 979 1052 1552 1728 1956 2079 100 200 Lead 11-232 18-035 10-304 11-225 8-936 21-083 7-622 7-919 7-757 163 531 727 938 1418 2129 1901 2188 548 637 786 1296 1928 1792 1770 Gold Silver Palladium Copper Platinum Steel, drawn, English.. Cast steel Iron, Berry The above results are from Wertheim s " Mcmoires" on Elasticity, Ann. de Chim. et Phys., torn xii. (1844). The change in the rigidity-modulus produced by change of temperature was investigated by Kohlrausch. He found that it is expressed by the formula n = ?? (1 - at -fit*), where ?? denotes the value of the rigidity-modulus at C., n its value at temperature #, and a, (3 coefficients the values of which for iron, copper, and brass are as follows: ft Iron.. 0-000447 0*00000052 Copper 0-000520 0-00000023 Brass 000428 00000136 Moduluscs of Compressibility of Water, Alcohol, and Ether at Different Temperatures. 1 Modulus of compressibility in grammes per Temp. square centimetre. Authority. Water. Alcohol. Ether.
20-6 xlO 6 12-4xl0 6 9 5xl0 6 For water, 1-5 20-2 x 10" Grassi, Ann. 41 20 7 x 10 s de Chim., tome 10-8 21-5xl0 5 xxxi. (1851). 13-4 21 -JxlO 8 14-0 8-07x1 j 8 For other and 15-0 11 -4 xlO 8 alcohol, 18-0 22-4x10" A ma my and 25-0 22-6x10" Descamp, 34-0 2-2-8 xlO 6 ... Comptes Rcn- 43-0 23-3 xlO 15 dus, tome xvii. 53-0 23-5x10" p. 1564 (1SC9). 80. Tempering soft iron by long-continued stress. Preliminary experiments by Mr J. T. Bottomley towards the investigation promised in section 5 above have dis covered a very remarkable property of soft iron wire respect ing its ultimate tensile strength. Eight different specimens, tested by the gradual application of more and more weight within ten minutes of time in each case until the wire broke, bore from 43 J to 46 Ib (average 45 -2) just before breaking, with elongations of from 17 per cent to 22 per cent. Another specimen left with 43 Ib hanging on it for 24 hours, and then tested by the gradual addition of weights during 25 minutes till it broke, bore 49} Ib before breaking, with elongation of 15 per cent. Another left for 3 days 11 hours 40 minutes with 43 Ib hanging on it, and then tested by the gradual addition of weights during 34 minutes till it broke, bore 5H fi> just before breaking, with elongation of 14 4 per cent. Another specimen of the same wire was set up with 40 ft hanging on it on the 5th of July 1877, on the Gth of July 3 ft> were added, on the 9th 1J Ib more, and on the 10th f Ib more, making in all on this date 45} Ib. Thenceforward day by day, with occasional intervals of two days or three days, the weight 1 The modulus seems to be a minimum near the temperature of maximum density. was increased first by half a pound at a time, and latterly by a quarter of a pound at a time, until on the 3d of Sep tember the wire broke with 57 Ib (elongation not re corded). This gradual addition of weight therefore had increased the tensile strength of the metal by 26 7 percent. ! 81. Experiments made for this article.- There are many subjects in the theory of elasticity regarding which information to be obtained by experiment only is greatly wanted. Several of these have been pointed out above (section 21), and while this article was being put in type, experiments were made in the physical laboratory of the university of Glasgow with a view of answering some of the questions proposed. Mr Donald M Farlane, besides making the experiments referred to in sections 3 and 21, in vestigated the effects of applying different amounts of pull to a steel pianoforte wire which had been twisted to nearly its limits of elasticity, and which was kept twisted by means of a couple. The results proved a deviation from Hooke s law by showing a diminution of the torsional rigidity, of about 1 G per cent., produced by hanging a weight of 112 Ib on the wire. Of this 1 -2 per cent, is accounted for by elongation and by shrinkage of the diameter, leaving P 4 per cent, of diminution of the rigidity-modulus. It was also found that when the wire was twisted far be yond its limits of elasticity, and then freed from torsional stress, a weight hung on it caused it to untwist slightly. When the weight was removed and reapplied again and again, the lower end of the wire always turned in the same direction as the permanent twist when the weight was re moved, and in the opposite direction when it was applied. This result shows the development of reolotropic quality in the substance of the wire, according to which a small cube cut from any part of it far out from the axis, with two sides of the cube parallel to the length, and the other two pairs of sides making angles of 45 with the length, would show different compressibilities in the directions perpendicular to the last-mentioned pairs of sides. Another very interesting result, discovered in the course of these experiments, was that when a length of live metres of the steel wire, with a weight of 39 Ib hung upon it, was twisted to the extent of 95 turns, it became gradually elongated to the extent of y^Vo f the length of the wire ; when farther twisted it began to shorten till, when 25 turns had been given (in all 120 turns), the weight had risen from its lowest position through nearly ^oVo f ^ha length of the wire, so that the previous elongation had been diminished by about } of its amount. Experiments were also made by Mr Andrew Gray and Mr Thomas Gray for the purpose of determining the effects of various amounts of permanent twist in altering the rigidity-modulus and the Young s modulus of wires of copper, iron, and steel. A copper wire, of 3 15 metres in length and 154 centimetre diamster. No. 17 B.W.G., which had a rigidity-modulus of 442 million grammes per square centimetre to begin with, was found to have 420 after 10 turns, showing a diminution in the modulus of -^ of its own amount. The diminution went on rapidly until 100 turns of permanent twist had been given, when the modulus was as low as 385. The diminution of the modulus continued with further twist, but very slowly, up to 1225 turns, when the modulus was found to be 371, showing a diminution to the extent of ^ of its original value ! There was little farther change until 1400 turns had been given, when the modulus began to increase. At 1525 turns its value was 373, and at 1625 it was 377. Twenty turns more broke the wire before the torsional elasticity had been again determined. A pices of iron wire of nearly the same length, about three metres, but of smaller diameter ( 087 centimetre),
ahowed continued diminution of torsional rigidity ac far as
