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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 calcspar 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 rhombobedron diminishes when the temperature is raised from 0° to 100° by 4' 6"; 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 87.5o the alloy has once more the same density as at 0°; and at 94°, at which it fuses, the same as at 44o. (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.

1 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:

Name.

Formula.

Expansion for 180° Fah.

KO,

Copper (reduced by hydrogen)

Cu

0.0055

0.00767 Red oxide of mercury

Hg 0

0.005802 Protoxide of lead...

Pb o

0.00795 Red oxide of manganese

Mn' 04

0.00522 Peroxide of tin

Sn 08

0.00172 Sulphuret of lead

Pb s

0.01045 Chloride of potassium.

КСІ

0.010944 Chloride of barium ..

Ba Cl + 2HO

0.009873 Chloride of ammonium

N H+ Cl

0.0191 Nitrate of soda

Na 0, NOS

0.0128 Nitrate of potash....

KO, NOS

0.01967 Ditto (in large crystals).

0.017237 Ditto (finely powdered)

0.019187 Nitrate of lead......

Pb 0, N O

0.00839 Nitrate of baryta..

Ba O, NOS

0.004523 Chlorate of potash

KO, CIOS

0.017112 Chromate of potash

KO, Cr 03

0.01134 Ditto (in fine small crystals)

0.011005 Bichromate of potash..

2Cr 03

0.0122 Bichromate of chloride of potassium

K CI, 2Cr (3

0.015902 Oxalic acid ..

H 0, C* 0 + 2H 0

0.027476 Oxalate of potash

KO, C'08 + HO

0.01162 Binoxalate of potash

KO, 2CoO3 + 3H O

0:011338 Quadroxalate of potash

KO, 4C° 03 + 7H ()

0.015916 Oxalate of ammonia

N H+ 0, Co 08 + H )

0.00876 Binoxalate of ammonia

N H+ 0, 2C* 03 + 3H 0 0.013718 Quadroxalate of ammonia

N H+ 0, 4C 0 + 7H 0 0.014347 Sulphate of potash ..

KO, SO3

0.010697 Bisulphate of potash

KO, SO3 + HO, S OS 0.012287 Sulphate of ammonia

N H+ 0, s 0 + H 0

0.010934 Sulphate of copper.

Cu 0, SOS + 5HO

0.009525 0.005315

0.00812 Sulphate of iron

Fe O, SO3 + 7HO

0.01153 Sulphate of magnesia

Mg O, SO3 + 7H O

0.01019 Sulphate of copper and ammonia Cu O, SO3 + NHO, SO3 + 6H O 0.0066113 Sulphate of copper and potash Cu (), S ()3 + KO, SO3 + 6H O 0.009043 Sulphate of magnesia and potash MgO, S OS + KO, S03 - 6H O 0.009372 Chrome alum

Cr2 (3, 3S 03 + KO, SO3 -- 24H O 0.005242 Potash alum

Alo 03, 3S (+ KO, SOS 24H O 0.003682 Sulphate of zinc and potash

Zn 0, S ()3 + KO, SO3 + 6HO 0.008235 Sulphate of magnesia and ammonia MgO, SO3 + NHO, SO3 6H 0 0.007161

C12 H" on

0:011160 Sugar of milk

C2H112

0.009111

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Cane sugar

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 fively and pressing it between folds of bibulous paper. The 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. 1.

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 inay 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 increnients 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:

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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 tou great; moreover, they do not agree among themselves. (The reduction of the degrees of a mercury, platinum, copper, or iron thermoineter is, to a certain extent, given in the preceding table.) A gain, 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 thernioneters generally contract in the course of time, so that when they are immersed in melting ice, the mercury stands from 1 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

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Tbeter the fire to which the XLR-setity of air driven out of

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320 100 752 | 210 300 572 || 160 200 392 316 395 743 | 236 295 563 156 | 195 383 312 390 734 | 232 290 554 152 190 374 308 385 725 228 285 545 148 185 365 304 380 716 | 224 280536 144 180 356 300 375 707 || 220 275 527 140175 317 296 370 698 | 216 270 518 136 / 170 338 292 365 689 212 265 509 132 165 329 288 360 680 208 260 500 128 160 320 284 355 671 204 255 491 124 155 311 280 350 662 | 200 250 482 120 150 302 276 315 653 | 196 245 473 116145 293 272 340 644 192 240 464 112 140 284 268 335 633 188 235 455 108 | 135 275 264 330 626 184 230 446 104 130 266 260 325 617 180 225 437 | 100 125 257

320 608 || 176 220 428 96 120 248 252 | 315 599 | 172 215 419 92 115 239 248 310 590 || 168 210 410 88110 230 24+ 305 581 164 205 401 84 105 221

80 100 212 4

5
76 95 203 8 10
72 90 194 12 15
68 85 185 14.32 17.78
64 80 176 16 20
60 75 167 20 25
56 70 | 158 24 30
52 65 149 28 35
48 60 140 32 40

55 | 131 36 45
40 50 122

50 36 45 113

55 32 40 104 48 60 28 35 95 52 65 24 30 86 56 70 20 25 77 60 75 16 20

64 80
12 15 59 68 85

10 50 72 90
5 41 || 76 95
0 32 80 100

40

13 22 31 40 49 58 67 76 85 94 103 112 121 130 139 148

256

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e.

b.

c.
d.

f.
1°R. = 1.25° C. = 2-25°F. 1°C. = 0.89 R. 1.8° F. 1°F. - 0:55° C. 0:44°R.
2 = 2:5 = 4.5 2 =1:6 = 3.6 2 =1:11

= 0.88
3 = 3.75 = 6.75
= 2:4 =5.4 3 =1:67

=1:33
= 3.2
= 7.2

= 2.22 =1.77
5 — 2.78 = 2.22
6 = 3:33 = 2.66
7 = 3.89 = 3:11
= 4:44

= 3:55

How many degrees Fah. = 273° Cels.? According to the table, 270° C. = 518° F. ; the 3° C. over are equal by d. to 5.4° Fah.; and these added give 518° + 5:4° = 523.4 Fah. - How many degrees of Cels. = 676° Fah.? By the table, 671°F. = 355° C.; and by d. 5° F. = 2.78° C., therefore together 671° F. = 355° + 2.78° - 357.78° C.

Wedgewood's Pyrometer depends upon the contraction of cylinders of clay at high temperatures. The first degree W. corresponds, according to Wedgewood, to 598° C., and each degree W. is equal, according to the same authority, to 72° C. According to Guyton-Morveau, on the other hand, the first degree W. corresponds to 270° C., and each degree W. is equal to only 34°C. This pyrometer appears to give but very uncertain indications, the inaccuracy arising chiefly from this circumstance—that the clay cylinders contract as much at a low red heat continued for some time as at a more powerful heat sustained but for a short time.

Prinsep (Ann. Chim. Phys. 41, 247) makes alloys of silver and gold, ten parts of which contain 1, 2, 3, 4, 5, 6, 7, 8, or 9 parts of gold;-and for very high temperatures, alloys of gold and platinum containing 99, 98, 97, &c. per cent. of gold; they are made into flattened buttons. These alloys he places in separate cupels in the fire whose strength is to be determined, and ascertains which of them are fused. From a compa

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