304 ANOMALOUS EXPANSION OF WATER. [142. changes of temperature, in the course of twenty-four hours, to an elongation and contraction varying from half an inch to three inches (from 12 to 76 millimetres), and a roller bed is provided to allow this expansion to occur freely. Brittle substances, such as glass and cast-iron, often crack on the sudden application of heat, because a sudden dilatation is produced upon the surface before the heat has time to reach the interior, and thus the cohesion is destroyed. The thicker the plate the greater is its liability to fracture. Sudden cooling, by inducing unequal contraction, has a similar effect. A knowledge of these effects of expansion explains why the wires of certain metals, such as iron and platinum, may be soldered into glass; whilst other metals, such as silver, gold, or copper, separate and crack out as the joint cools. The expansion of iron or of platinum differs from that of glass by only a very small amount, whereas other metals vary from it greatly, and contract far more in cooling. (143) Anomalous Expansion of Water.-A remarkable exception to the law of contraction by the lowering of temperature, exists in the case of water. Water follows the regular law until it reaches a temperature of about 4° C. (39°2 F.); then, instead of contracting, it begins to expand, and continues to do so until it reaches the freezing point. About 4° it is at its point of greatest density, and just before it freezes it occupies the same volume as it did at 9° C. If water at 4° C. be taken as 1000, it has a density, at o° C., of 999'88 (Pierre). From 4° C. water expands regularly as the temperature rises: so that 1000 parts at 。° C. become More recently Kopp (Pogg. Ann. 1847, lxxii. 48) has determined the expansion of water with the following results: By dissolving common salt in water, the point of maximum density is lowered, and the solution goes on contracting regularly at temperatures considerably below 4o, until, in sea-water, the anomaly disappears, the maximum density occurring according to Despretz at 25°38 (− 3°.68 C.), a temperature below its point of congelation, which the same observer estimates at 28°-62 (-1°88 C.). Various other salts besides common salt (sodic chloride) have the effect, when dissolved in water, of lowering its point of maximum density; but amongst the numerous liquids examined by Pierre, no other liquid besides water was found thus to expand whilst the temperature was falling. 144.] CORRECTION OF GASES FOR TEMPERATURE. 305 (144) Correction of Volume of Gases for Temperature.—It has been already mentioned that aeriform bodies expand for equal rise of temperature more than either solids or liquids, and that the rates of expansion for all gases and for vapours, at a sufficient distance from their boiling points, may be assumed to be equal and uniform, at all degrees of temperature and under all variations of pressure. It becomes, therefore, a matter of importance to estimate the amount of this expansion in all experiments where the quantities of gases require to be determined, and where their density is to be inferred from measurement of their volume. Provided that the temperature of the gas be known, the calculation is easily made. Experiment has shown that for every degree of temperature upon Fahrenheit's scale, an amount of expansion takes place equal to of the volume that the gas occupied at o F.; that is to say, that a quantity of any gas which, at the temperature of o°, occupies 459 volumes, for every additional degree increases in volume by 1; so that at 1° it will become 450 volumes, at 2° 461, at 40° 499, at 60° 519 volumes. England, all comparisons of gases are usually referred to the temperature of 60°. Suppose it be required to ascertain the volume which 92 cubic inches of coal gas, measured at 70°, would have when reduced to 60°:-Since 459 volumes of any gas at o° would at 70°, have increased in volume by 70, it would have become 459 +70, or 529 volumes. Again, a gas, which at o occupied 459 volumes, would, at 60°, occupy a volume equal to 459+60, or 519. The volume, therefore, of any gas at 70° would bear the same ratio to the volume which it would occupy at 60° as 529 does to 519. And hence : 529 519 9'2 : x (=9°026 cubic inches). In If the gas, instead of being measured at 70°, had been measured at 50°, and it were desired to reduce the 9'2 cubic inches to the standard temperature of 60°; the gas, which occupied 459 volumes at o°, would have expanded to 459+50, or 509 volumes at 50°. The ratio to the volume at 60°, which would, as before, be 519, is given as follows :— 509 51992: x (=9'381 cubic inches). In this case, the observed volume is less than the corrected one; before, it was greater.* An additional and independent correc The correction to o° C. is made on the same principle with equal facility. Suppose the volume of the gas (say 153.) to have been measured at 15° C.; required its volume at o° C. Since the expansion for each 1°C. is of the 306 MODE OF TAKING DENSITY OF GASES. [144 tion of the volume of the gas for the deviation of the barometric pressure from the standard (41) is needed after the correction for the temperature has been made. (145) Liquids and gases immediately adjust their volume to the alteration of temperature; but, according to observations made in the Arctic Expedition, solids do not immediately do so in all cases it was frequently observed in the metallic scales of many of the instruments, that full contraction did not occur until a concussion had been given to the apparatus; the metal then contracted suddenly and completely. (146) Process for taking the Density of Gases.—The principal corrections required in the delicate operation of taking the density of a gas with accuracy have now been pointed out. Regnault, in his elaborate researches (Ann. Chim. Phys. 1845 [3], xiv. 211), has reduced the number of corrections ordinarily required, by counterpoising the globe in which the gas is to be weighed by a second globe of equal size, made of the same glass; a practice which had previously been adopted by Prout, in his careful investigations on the density of the atmosphere. The film of hygroscopic moisture which always adheres to the glass is equal in both globes; and as the volume of air displaced is also equal in both cases, the calculations for its buoyancy may be dispensed with. volume at 0° C., 273 volumes at o° C. would become 273 + 15 = 288 at 15° C. ; consequently 288: 273: 153 : x ( = 145 ̊03). Or expressing the whole in general terms; for the English standards, if T' be the observed temperature° F., V the corrected volume at 60° F., V' the observed volume, then V= 519V 459+ T For the French standards, if T be the observed temperature in ° C., V the corrected volume at o° C., then in which 0.003665 is the coefficient of expansion of gases for each degree C.; that is, I volume of gas at o° C. becomes 1003665 at 1°; 103665 volumes at 10°; and so on. 146.] DENSITY OF GASES. 307 The following is a brief description of the method adopted by Regnault:A balance capable of weighing 1 kilogramme, and sufficiently sensitive to turn with half a milligramme when loaded, is placed upon a chest provided with folding doors, within which the glass globes, each of the capacity of about 10 litres, attached to the scale-pans, are freely suspended. The globe, B, fig. 121, is hermetically sealed; the globe A, for weighing the gases, is provided with a stopcock; the air is exhausted from A as perfectly as possible, and it is connected with an apparatus which supplies the gas to be weighed, the gas having been carefully purified and dried. The globe is again exhausted very completely, the last portions of air being thus displaced by the gas, and it is a second time filled with the gas; this process must be B FIG. 121. repeated a third time, and the gas may then be considered to be free from atmospheric air. To avoid the need of any correction for temperature, the globe is this time placed in a vessel with melting ice (fig. 122), in order to cool the gas to o° C. When the globe is filled with gas, and sufficient time has elapsed for it to acquire the temperature of the ice, the vessel of mercury, x, into which the escape tube dips, is removed, so as to equalize the pressure within the globe with that of the air; the stopcock is closed, and the globe withdrawn, wiped carefully with a damp cloth, to avoid rendering the surface electric, and it is then suspended to the scale-pan. It is not weighed, however, until after the lapse of a couple of hours, by which time the equilibrium of its temperature with that of the atmosphere is restored, and the produc tion of currents (152) around it is obviated. The weight, W, is then accurately noted; the globe is again plunged in ice, the gas removed by the air-pump, and the pressure of the gas which still remains in it is measured accurately by the gauge attached to the air-pump. The empty globe is again withdrawn from the ice and weighed as before, representing its weight as w; the difference of the two weights (or W-w) will give the weight of a volume of gas the pressure of which is equal to that of the atmosphere, as marked by the observed height, H', of the barometer at the time of the experiment, diminished by the pressure, h, of 308 DENSITY OF GASES. [146. the remaining gas, as measured by the gauge. If the capacity of the globe has been previously accurately determined, the corrected weight of the gas will be obtained by the following proportion: : Regnault (Recherches, etc., Mem. de l'Institut, 1847, xxi. 158) has in this manner determined the weights of 1 litre of each of the following gases, at o° C., and under a pressure of 760mm. of mercury at o° C. :— From these data it is easy to determine the weight of 100 cubic inches of each gas in grains. The litre has a capacity of 6102704 cubic inches; the gramme is equal to 15'43235 grains; and the expansion of air between 32° and 60° F. by heat is such, that 1,000,000 parts become 1,057,007. The barometric pressure of 760mm. at o° C. would be equal to a column, at 60° F., of 30'006 inches of mercury. Calculating from these numbers, the weight in grains of the under-mentioned gases under a pressure of 30 inches of mercury (the column being measured at 60° F.) is as follows: If the amount of condensation which the constituents of a compound gas undergo in the act of combination be known, it is easy to check the experimental determination of its density, and *The difference between the highest and lowest of these results did not amount to more than of the entire weight of the air employed. Extreme variation, go of the whole. 1 Extreme variation, ooo of the whole. S Extreme variation, || Extreme variation, |