ELASTICITY 815 ... M JKp Dividing p by thia expression we find for the kinetic M = Heuce _ JKp M M 1- 76. For any substance, fluid or solid, it is easily proved, without thennodynamic theory, that M _K "M~N ; where K denotes the thermal capacity of a stated quantity of the substance under constant stress, and N its thermal capacity under constant strain (or thermal capacity when the body is prevented from change of shape or change of volume). For permanent gases, and generally for fluids approximately fulfilling Boyle s and Charles s laws as said above, k is proved by thermodynamic theory to be approxi mately constant. Its value for all gases for which it has been measured differs largely from unity, and probably also for liquids generally (except water near its temperature of maximum density). On the other hand, for solids whether the stress con sidered be uniform compression in all directions or of any M K other type, the value of ~ or ^ differs but very little N from unity; and both for solids and liquids it is far from constant at different temperatures (in the case of water it is zero at 3 9 Cent,, and varies as the square of the difference of the temperature from 3 9 at all events for moderate differences from this critical temperature, whether above or below it). The following tables show the value of ^r or ^ , and the value of 6 by the formula of sec. 74, for different fluid aud solid substances at the temperature 15 Cent. (289 absolute scale). The first table is for compression uniform in all directions ; the second, necessarily confined to solids, is for the stress dealt with in " Young s Modu lus," that is, normal pressure (positive or negative) on one set of parallel planes, with perfect freedom to expand or contract in all directions in these planes. A wire or rod pulled longitudinally is a practical application of the latter. THEKMODYNAMIC TABLE I. Pressure equal in all directions Ratio of Kinetic to Static Bulk- Modulus. Temperature 15 C. (289 absolute] J = 42400 centi metres. Elevation Substance. Density. Thermal Capacity per unit Expan sibility of Tempera ture pro duced by a pressure of one Static Bulk- Modulus in grammes Deduced value of M K M or N mass = e. gramme per = K. per square square (i^JIX- 1 centimetre centi JK~ / te metre r =M. = J~K~p Air . . . Distilled 001220 2375 00346 0824 1033 water Alcohol Ether . Mercury Glass, flin Brass, 1-000 795 7005 13-56 2-942 1-000 6148 5157 0330 1770 00016 00106 00155 00018 000026 000011 OOU0148 0000292 0000274 000000340 22-63 XlO 6 11-4x10 8-07 xlO 6 552-5 X 106 423 XlO 6 1-0040 1-22 1577 1-375 1-00375 drawn Iron Copper 8-471 7-677 8-843 09391 1098 0949 0000545 0000d95 0000545 000000466 000000319 000000443 1063x106 1485 xlO* 1 717 x 10 s 1-028 1-319 1-043 THERMODYNAMIC TABLE II. Pressure parallel to one direction in a solid Ratio of Kinetic tc Static Young s Modulus. Temperature 15 C. (289 absolute}. 1 Lowering jThermal of Tempera ture pro duced by a Static Young s Modulus Deduced value of Substance. Density Capacity per unit Expan sibility pull of one in grammes per M N Si or K P* mass = . gramme =K. per square square (<e 2 M-i centimetre te centi - metre JK J =M. Zinc 7-008 0927 0000249 000000308 873x106 1-0080 Tin . . 7-404 0514 000022 000000394 417x10 1-00362 Silver . 10-369
- 0 r 57
000019 000000224 736x106 100315 Copper 8-933 0949 000018 000000145 1245x106 100325 Lead 11-215 0293 000029 000000602 177x106 1-00310 Glass 2-942 177 0000086 000000113 614-4x106 1-000600 Iron 7-553 1098 000013 000000107 1861x106 1-00259 Platinum 21-275 0314 -0000086 OOOOOOo77,-> 1704 x lO 8 1-00129 77. Experimental Results. The following tables show determinations of moduluses of compression, of Young s modulus, and of moduluses of rigidity by various experi menters and various methods. It will be seen that the Young s moduluses obtained by Wertheim by vibrations, longitudinal or transverse, are generally in excess of those which he found by static extension ; but the differences are enormously greater than those due to the heating and cooling effects of elongation and contraction (section 76), and are to be certainly reckoned as errors of observation. It is probable that his moduluses determined by static elongation are minutely accurate; the discrepancies of those found by vibrations are probably due to imperfections of the arrangements for carrying out the vibrational method: TABLE OF MODULUSES OF COMPRESSIBILITY. Substance. Moduluses of com pressibility in grammes per square centimetre. Tempe rature. Authority. Distilled water 22-63 xlO 6 15^ Alcohol 12-4 xlO 6
Amaury and ... 11-4 xlO 6 15 Descamps, Ether . 9 5 xlO 6 - Cmnptes Ren- ,,.... 8-07 xlO 6 14 dus, tome xvii. Bisulphide o,f carbon 16 3 xlO 6 14 p. 1564(1869). Mercury 552-5 xlO 6 15 . Glass Another specimen . Steel .... Iron .... Copper .... 423 x 10 6 354 x 10 6 1876 xlO 6 1485xlO 1717 xlO 6 ...1 ". Everett s Illus trations of the Centimctrc- Gramme- Second System of Units. Brass, different speci- ) mens . . . ) Mean 1063 xlO 6 Wertheim, Ann. de Chim., 1848. TABLE OF MODULUSES OF RIGIDITY. Modulus of Rigidity Substance. in grammes per Authority. square centimetre. Wertheim, Glass, different specimens . Mean 150x]0 6 Annalcs Brass, different specimens . Mean 350 x 10 6 de Chimic, 1848. Glass 243 x 10 6> ) Another specimen 240 xlO 6 Everett s III. Brass, drawn . . 373 xlO 6 of the Centi Steel 834 xlO 6 } metre- Grajmne- Iron, wrought . 785 xlO 6 Second Si/stem Copper . . . 542 xlO 6 of Units.
456 x 10 s J