meter (T and t). Through the cork in D a glass tube A also passes, the end reaching nearly to the bottom of the thimble. The tube AD is connected by means of the tubulure, which fixes it to the stand, and an india

rubber tube with an aspirator G. Some ether is placed in the thimbles, and after the instrument has had time to reach the temperature of the air, the two thermometers are read, giving the temperature of the air, . The aspirator is now started, and draws air through the tube A into the instrument. This air bubbling through the ether causes evaporation, which cools the ether and thimble, which in turn cools the air in its immediate vicinity. When a film of dew is deposited on the thimble D, indicating that the dew-point has been reached, the aspirator is stopped, and the temperature

of the thermometer T read. It is again read when the dew disappears from the thimble, and the mean of these two readings gives the dew-point fo

In the chemical hygrometer a known volume of air is drawn, by means of an aspirator, through a series of tubes containing substances, such as anhydrous calcium chloride or phosphorous pentoxide, which readily absorb moisture. From the difference in the weight of these tubes before and after the passage of the air and the volume which has passed, the absolute hygrometric state of the air (w) can be obtained, and W can be got from tables, if the temperature of the air is taken.

The wet and dry bulb hygrometer depends for its action on the fact that the drier the air is, the more rapid will be the evaporation from a wet body exposed to the air. Since evaporation requires the supply of heat (latent heat of evaporation), it follows that the extent to which a wet body is cooled by evaporation will depend on the hygrometric state of the surrounding air. Two similar thermometers are fixed on a stand, the bulb of one of them being covered with muslin kept moist by means of a piece of lamp-wick which dips in a ves.el of water. Unless the air is saturated, evaporation will take place from the muslin, and hence the wet bulb thermometer will indicate a lower temperature than the other, the difference being greater the greater the evaporation, that is, the drier the air. By comparing the readings of the wet and dry bulb thermometers with the

humidity, as obtained by other hygrometers, a table has been drawn up, by means of which, from the reading of the dry bulb thermometer, and the difference between the dry and wet bulb thermometers, the dew-point can be obtained. The indications of this instrument are, however, considerably influenced by its environment, also by the action of draughts, &c.

222*. Effect of the Curvature of the Surface on the Vapour Pressure. The form of the surface separating a liquid from its saturated vapour has an influence on the vapour pressure, which Lord Kelvin was the first to point out, and which has important applications in explaining the condensation of vapour into liquid in such cases as occur in clouds.

Suppose we have some liquid, such as water, contained within a vessel C (Fig. 177), from which all air has been exhausted, so that we have only to do with the liquid below and its vapour above. Further, let a fine capillary tube AD of radius dip in the liquid. If the liquid wets the glass it will rise in the capillary, and let the height of the curved surface A above the plane surface B be h.

σ

B

A

C

r

-D

FIG. 177.

Now the pressure within the vapour at the level of A will exceed the pressure at the level of B by the weight of a column of vapour of height h, or, if o is the density of the vapour, by ohg dynes per square centimetre. Hence, if the whole is at the same temperature, and if the vapour pressure at the concave surface A is the same as at the plane surface B; then when the pressure at B is equal to the vapour pressure at the existing temperature, the pressure at A will be less than the vapour pressure, and so evaporation will still take place from the surface A. involve a continuous circulation of the liquid up the tube, for the height h depends on the surface tension, and must remain constant. Such a continuous circulation could, theoretically, be made to do external work, say by turning a small turbine placed in the tube; and since the temperature is maintained constant, we should thus manufacture energy, which is contrary to the law of the conservation of energy. We therefore conclude that the liquid and its vapour must be in equilibrium both at A and at B, or that the vapour pressure, p, at the plane surface must be greater than that, C, at the concave surface A by an amount equal to the weight of a column of the vapour of height h, or p-c=ohg.

This would

If the density of the liquid is p, the weight of the column of liquid of height his pgh. The difference in pressure between the surface A and a point D within the tube on a level with the surface is equal to the weight of the column of the liquid of density p, less the difference of pressure between A and B, due to the weight of an equal column of the vapour of density σ. Thus the difference of pressure between A and D is gh(p-o). If the liquid wets the tube, so that the angle of contact is 180°, it has been shown in § 160 that the difference in pressure between A and D is equal to

2T
r

where T is the surface tension of the liquid-vapour surface.

Hence, equating the two values we have obtained for the difference of pressure, we get

2 T
r

=gh(p=σ),

Now the curved surface of the liquid is, as shown at the side, very nearly a hemisphere of radius r, and we see from the above expression that the decrease of vapour pressure with curvature is inversely proportional to the radius of the spherical surface. If, instead of being concave, the surface had been convex, such as is the case in a raindrop, the vapour pressure at the curved surface would be greater than that at a plane surface, and this increase would increase with the decrease in the radius, r, of the drop. Thus, in the case of very small drops, the vapour pressure may be very considerably greater than that corresponding to a plane surface at the same temperature. The result is that although the air may be saturated, as measured in the ordinary way with a plane surface, very small drops, so far from increasing in size by the condensation of vapour, are actually evaporating.

The above reasoning explains why it is that if air is perfectly free from suspended solid matter, or dust, it may be cooled to a temperature considerably below the dew-point, without the formation of drops of water or mist. A very small drop-and at first, in such a dust-free air, all the drops must be small-will have a high vapour pressure, and will again evaporate. If, however, there is dust in the air, the dust particles will act as nuclei, so that the water which condenses first on them, instead of being in the form of an excessively small spherical drop, may be spread out into a surface of comparatively small curvature, so that re-evaporation will not take place. The formation of large drops is also explained, for the vapour tension at the surface of a small drop will be greater than that at the surface of a larger drop, and hence evaporation will take place from the small drops, and condensation on the large.

state.

223. Sublimation.-Hitherto we have exclusively considered the passage of a solid to the liquid state, and that of a liquid to the gaseous Under certain conditions it is possible, however, for a solid to pass directly into the gaseous state without passing through an intermediate liquid condition. This change from solid to vapour is called sublimation, and is very clearly marked in the case of camphor and iodine. These bodies, when gently heated, readily pass into vapour, although the temperature has not been sufficiently high to melt them.

Although to a much less marked degree, ice exhibits the same phenomena. Thus at a temperature of 1° C. the vapour tension of ice amounts to 0.42 cm. of mercury, and a piece of ice kept at this temperature will sublime till the pressure of the vapour in the surrounding space is 0.42 cm. of mercury, when equilibrium will be set up.

224. The Triple Point.-In Fig. 174 we have given the curve of maximum vapour pressure for a liquid (water), or, in other words, the boilingpoint for different pressures. This curve gives the pressure corresponding to any temperature at which both the liquid and the vapour can exist in contact one with the other without their relative proportions altering-i.e. they are in stable equilibrium-and is called the steam line.

As has been seen in § 210, the melting-point of a solid depends on the pressure, so that a similar curve to the steam line can be drawn, giving the melting-point at different pressures. Such a curve will indicate the pressure corresponding to any temperature to which a mixture of ice and water must be subjected, in order that the two states may be in stable equilibrium. This curve is called the ice line. Finally, we may have, as has been mentioned in the previous section, a solid in stable equilibrium with its vapour, and may therefore draw a third curve showing the pressures at which, under various temperatures, a solid and its vapour can exist simultaneously. This curve is called the hoar-frost line.

The general form of these curves for water is shown in Fig. 178. The three curves meet at the point P, which is called the triple point. Since the steam line gives the conditions under which the vapour and liquid may exist simultaneously, the ice line those under which the liquid and solid may exist simultaneously, and the hoar-frost line those under which the vapour and solid may exist simultaneously, it is obvious z that at the triple point all three, solid, liquid, vapour, can coexist in stable equilibrium. The ice line in the case of water, which expands on solidifying, so that increase of pressure lowers the melting-point, slopes

and

PRESSURE IN CM. OF MERCURY

9

TEMPERATURE

FIG. 178.

downwards towards the right. Since, however, the lowering per atmosphere increase of pressure is only o°.co75, the slope is too small to be indicated on the figure. In the case of a body like paraffin, which contracts on solidifying, the ice line would slope downwards and towards the

left. The triple point for water corresponds to a pressure of 0.046 cm. of mercury, and a temperature a very little above o°.

225. Freezing-Point of Solutions-Cryohydrates. It has long been known that the freezing-point of sea water is lower than that of pure water, and generally that the presence of a salt dissolved in water lowers the freezing-point. Of late years, however, great attention has been directed towards the effect of a dissolved salt on the freezing-point of the solvent, and the results are of very great interest, both from a physical and a chemical standpoint.

The first to make anything like a complete investigation of this subject was Raoult, and he found that the depressions produced by equimolecular quantities of different substances dissolved in the same solvent were approximately the same, so long as the solutions were not too concentrated. By equi-molecular quantities is meant quantities of the different substances proportional to their molecular weights, so that the solutions contained equal numbers of molecules of the dissolved substances in the same volume. For fairly dilute solutions the depression is proportional to the quantity of salt dissolved. In the following table, the molecular depressions are given, i.e. those which would be produced if the molecular weight in grams of a body was dissolved in 100 grams of the solvent. These values are calculated, on the supposition that the depression is proportional to the concentration, from experiments made on much more dilute solutions, although with such concentrated solutions this proportionality no longer exists, and, even if it did, it would in many cases be impossible to obtain such concentrated solutions at such low temperatures. It is, however, convenient to reduce all results to some standard number of molecules of the dissolved substance to a given volume of the solvent, and the molecular weight in grams is in many ways a convenient number. The same kind of convention is employed when stating the density of a vapour, in that the density is given for a temperature of o° and a pressure of a standard atmosphere (§ 217), although in most cases, under these conditions, the vapour would have condensed to a liquid.

MOLECULAR DEPRESSIONS FOR SOLUTIONS IN ACETIC ACID.