The expansions of the other liquids examined by Kopp are given in the following table, the volume of each liquid at 0° C. being taken as unity. The densities (= d) reduced to 0°, and the boiling points under a pressure corresponding to 760mm or 29.92 inches of the barometer are also given at the heads of the respective columns. T.

01-00000 100000 100000 100000 100000 100000 100000 100000 1.00000

51-00576 1-00523 1.00454 1.00750 1-00790 1.00680 1.00529 1-00497 1-00529 10 101154 101052 1.00911 101518 1-01616 1.01387 101190 101000 1.01060 15 1-01734 1-01585 1.01373 1·02308 1.02476 1.02035 1.01796 101505 1.01588 20 1-02319 1-02128 1.01840 1-03122 1.03372 1.02810 102410 1.02016 1.01129

70 1-07785

1.08391

1.09007

1.09631

90 1-10266

1.10910

60

1-00000 100000 1·00000 100000 100000 1.00000 1-005251-00707 1.00683 1-00649 1.00642 1-00603 1-00592 1-00565 10 1-01052 101428 101369 1-01317 1.01297 101216 101193 101108 15 1-01583 1-02162 1-02062 1·02004 1·01964 1-01837 101800 1 01721 20 1-02117 1-02916 102766 1-02710 1-02644 102471 1-02417 1-02315

1-026591-036921-03481 1-03435 1.03340 1-03113 1-03042 1.02919 30 1-03203 104495 1-04211 1-04179 1-04050 1-03776 1.03678 1.03532 35 1-03754 1-05326 | 1·04960 1.04940 1-04778 1.04449 1-04325 1-04158

40 1.04309

45 1.04871

50 1.05439 551-06013

1.06596

65 1.07187

1-05730 1.05719 1-05521 1.05135 1-04983 1.04794 1-06525 1.06517 1.06283 1-05836 1.05654 1.05444

1-07347 1.07331 1.07064 1.065541-063381-06105 1-08199 1-08161 1.07865 1.07287 1.07035 1.06779

1.08686 1.08037 1-07747 1-07467 1-09529 1.08806 1.08474 1.08168 1-10395 1-09594 1-09216 108884

1-11284 1-10400 1-09975 1-09615

1-11226 1-10753 1-10360 1-12074 1.11548 1.11122

1.12944 1-12361 1·11898 1-13835 1-13193 1.12691

1-14750 1-14407 1.13503

1.00000 1.00000

1-14921 1-14330

1.15816 1.15175

1-16914 1-16038 1.16920

160 1.20399

Linear expansion of Solid bodies when heated from 0° to 100° C.*

*The linear expansion of a solid multiplied by 3 gives the expansion in volume, very

Crystals not belonging to the regular system exhibit when heated an unequal expansion in the direction of their axes, in consequence of which the magnitude of their angles becomes altered (Mitscherlich, Pogg. 1, 125; 10, 137). In crystals belonging to the right prismatic system the expansion is different in the direction of all three axes; in arragonite, on raising the temperature from 0 to 100°, the inclination of the lateral faces increases by 2' 46", and that of the terminal faces diminishes by 5 29"; gypsum is, according to Fresnel (Bull. des Sc. Mathem. 1824, 100; also Pogg. 2, 109), more expanded by heat in the direction of the principal axes than in that of the lateral axes.-In crystals belonging to the rhombohedral system the expansion is the same in the directions of the three secondary axes; but different from that according to the principal axis. The obtuse angles of the primitive rhombohedron of calespar diminish by 8 when the crystal is heated 100°, and the acute angles increase by the same quantity. Hence it may be calculated that the relative expansion of the principal axis (compared with the secondary axes) amounts to 0.00342; moreover since, according to Mitscherlich and Dulong, the cubical expansion of calcspar between 0° and 100° is only 0-001961, it may likewise be determined that calcspar, when thus heated, does not expand in the direction of the secondary axes, but contracts by 0.00056, and that the absolute expansion of the principal axis may be estimated at 0.00286.-In bitter-spar, the obtuse angle of the primitive rhombohedron diminishes when the temperature is raised from 0° to 100° by 46"; in ferruginous bitter-spar, by 3' 29"; in iron spar, containing a considerable quantity of manganese, by 3' 31"; and in pure iron spar, by 2' 22". Since now, among all these minerals, calcspar forms the least, and ferruginous bitter-spar the most obtuse rhombohedron, it follows that the expansion in the direction of the principal axis does not increase in the same proportion as the relative length of the axis itself diminishes. (Mitscherlich.)

The alloy of 2 parts bismuth, 1 part tin, and 1 part lead, expands when heated from 0° to 44° C.; when still further heated it contracts, so that at 56° its density is the same as it was at 0°, and at 69° still greater; beyond this temperature, expansion again takes place; at 87.5° the alloy has once more the same density as at 0°; and at 94°, at which it fuses, the same as at 44°. (Erman, Pogg. 9, 557.)

For an account of H. Schröder's attempt to discover a relation between the equivalent volume and the expansion of bodies, see Pogg. 52, 282.

¶ Messrs. Playfair & Joule have lately made some experiments on the expansion of salts and other solid bodies. (Qu. J. of Chem. Soc. I. 121.) The results are as follows:

paper.

The

Of the three specimens of sulphate of copper mentioned in the preceding table, the first and third were prepared for experiment by pounding the salt finely and pressing it between folds of bibulous second was in small crystals, obtained by stirring the cupreous solution while cooling: it contained rather more than 5 equivalents of water. The expansion of oxalic acid appears to be greater and that of peroxide of tin less than that of any other solid yet examined. ¶.

Since elastic fluids are in so many respects-particularly with regard to their combination in equal proportions by volume-the most normal substances in existence; since they appear to possess no cohesion, which

force probably exerts a disturbing action on the expansion by heat of liquids and solids; since again they all expand in the same ratio between the same limits of temperature, it may in all probability be supposed that their expansion is likewise uniform; that is to say, if the addition of any given quantity of heat has produced an expansion of 0.001 for example, the addition of a second equal quantity will produce an increase of exactly 0.001 of the first volume. This being admitted, it is found that all other bodies, when their expansion is compared with that of air, exhibit a variable expansion, inasmuch as the expansion produced in them by equal increments of heat is greater at higher than at lower temperatures. If the increase in volume which different bodies undergo between the temperatures of freezing and boiling water be divided into 100 equal parts or degrees, it will be found that when these several bodies are further heated, their expansions will be expressed by different numbers of such parts, and in the following proportion:

Dulong and Petit estimated the expansion of air at 0.375 (page 224); Rudberg (Jahresber. 19, 44), from his own experiments, determined it to be 0-364; this however will not explain all the deviations. (Comp. Pambour, Compt. rend. 12, 655; also Pogg. 53, 234.)

Expansion by heat serves as the basis of most Thermometers which are used to measure the lower degrees of temperature, and of Pyrometers by which higher temperatures are indicated. Since gases and vapours are the only bodies whose expansion is uniform, the ordinary thermometers, which are filled with mercury or spirit, cannot give the true teinperature exactly, but, on the contrary, always make the higher temperatures too great; moreover, they do not agree among themselves. (The reduction of the degrees of a mercury, platinum, copper, or iron thermometer is, to a certain extent, given in the preceding table.) Again, in using fluids, the expansion of the glass in which they are contained must be taken into consideration, since it makes their apparent less than their real expansion; and since, according to the above table, the expansion of glass at high temperatures increases much more rapidly than that of gases, the error of the mercurial thermometer is to a certain extent corrected by this circumstance. Bellani (Brugn. Giorn. 15, 268; 16, 217 and 294) has likewise shown that the bulbs of mercurial thermometers generally contract in the course of time, so that when they are immersed in melting ice, the mercury stands from 4° to 1° R. above the freezing point previously marked; an effect which-as observed by Flaugergues (Ann. Chim. Phys. 21, 333) and by Aug. de la Rive & F. Marcet (Bibl. univ. 22, 265)—may be attributed to the pressure of the external air on the bulb of the thermometer, inasmuch as there is a