the temperature at which this change takes place can be noted with considerable accuracy. Raise the temperature a little above the melting point, and allow the bath to cool slowly. When the paraffin solidifies it becomes opaque. By alternately heating and cooling within narrow limits, a series of values of the melting point which only differ very little can be obtained; the mean of these may be taken as the melting point of paraffin. K. Effect of Dissolved Salts on the Freezing Point. For the more accurate determination of the freezing point of a solution, and of the effect of dissolved salts in altering the freezing point, the following apparatus, described by Beekman, may be used. The glass tube A (fig. xxi) contains a delicate thermometer s' T, a stirrer of stout platinum wire, and the liquid to be experimented on. The salt whose effect it is wished to study can be introduced by a side tube B, sealed on to A, or more simply through a glass tube passing through the cork which closes the upper end of A. The tube A is placed inside a wider tube c, passing through a cork in the open end of c. This tube merely serves as an air-jacket. c passes through the lid of a wide glass vessel D, which contains water or a freezing mix A T FIG. xxi. B D ture, the temperature of which should be some 5° below the freezing point of the liquid in A. The bath also contains a stirrer. A weighed quantity of liquid is placed in a and the whole allowed to cool slowly, being kept at the same time well stirred. The liquid in A is probably thus cooled below its freezing point, freezing then takes place, and the thermometer rises suddenly to the melting point as the solid separates out. The freezing point of the solvent-water, or whatever it may be that separates out on freezing-is thus determined. A known quantity of the substance whose effect is required is introduced through the side tube B, and the experiment is repeated. The effect of the salt in modifying the freezing point of the solvent is thus found. It has been shewn by Raoult and others that, for a large number of substances, when a mass of the substance, grammes, is dissolved in a solvent, the mass of the solution being w, then the product of the molecular weight of the substance multiplied by the depression of the freezing point is proportional to p/w, so that, if m be the molecular weight of the salt, A the depression of the freezing point, and ka constant, then for a large class of salts This law may be verified by finding the depression of the freezing point produced by the addition of various amounts of the same salt, and then by comparing the depression produced by dissolving equal quantities of different salts so as to form solutions of equal volumes. The quantity k is the product of the molecular weight of the salt, the depression of the freezing point produced by the solution of one gramme of salt and the mass of the solution. The results are generally stated on the supposition that m grammes of salt are dissolved per litre of the solution. We then have p = m, w = mass of one litre of solution; m A is the depression produced when m grammes of salt (m being the molecular weight) are dissolved in 1 litre of the solvent. Thus, according to the law, A should be constant. It is found to have the value 18° C. approximately. According to Raoult there is a relation between the constant k, the absolute temperature of solidification T, and the latent heat L. By supposing a small quantity of the liquid taken round a thermodynamic cycle at the temperature of solidification, he shews that k 2T2/L. This result may be verified if the latent heat of fusion of the substance be known. = Experiment. Shew that the lowering of the freezing point of a solvent due to the presence of a salt is proportional to the mass of salt dissolved, and inversely proportional to its molecular weight. COEFFICIENTS OF EXPANSION. For any ordinary substance, with the exception of water, the changes of volume for equal increments of temperature are so nearly equal that the expansion may be calculated. from a coefficient approximately constant for each substance, which may be defined as follows: Definition. A coefficient of expansion by heat may be defined as the ratio of the change of a volume, area, or length per degree of temperature to the value of that volume, area, or length at zero centigrade. In solids and liquids the expansion is so small that in practice we may generally use, instead of the value of the quantity at zero, its value at the lower of the two temperatures observed in the experiment. For solid bodies we have the coefficients of linear, superficial, and cubical expansion depending on the alteration of length, breadth, or thickness (linear), of surface (superficial), and of volume (cubical) respectively. γ Let a, B, y be these three respectively, and suppose the body to be isotropic, i.e. to have similar properties in all directions round any given point; then it can be shewn that ẞ=2a, y=3 a. For consider a rectangle the sides of which are a and b. When the temperature is raised by the sides increase respectively by a at and bat, so that their new values are a(1+at) and b(1 + a t). Thus the area is a b(1+a t)2, or, since a is very small, a b(1+2a). But if ẞ be the coefficient of superficial expansion, the new area is a b(1+ßt). Thus we have ẞ=2 a. In a similar way considering the expansion of a cube. we may shew that y=3 a. For liquid bodies we have to deal only with the coefficient no of cubical expansion. Any measurement of expansion is attended with considerable difficulty. A liquid requires to be contained in some vessel, and thus we have to consider the alteration in volume of the vessel as well as that of the liquid itself. In the case of a solid, any cause which changes the temperature of the body to be measured probably changes that of the measuring apparatus and causes it to expand also. Our measurements wi' therefore give the expansion of one substance relatively another. Thus, we should find, mercury and most liqui expand considerably as compared with glass, while t metals expand greatly in comparison with wood or stone. Methods, it is true, have been devised for determining the absolute expansion either of a liquid or a solid, but tl ese are too complicated for an elementary course. We shall explain how to determine (1) by means of reading microscopes, the coefficient of linear expansion of any solid which can be obtained in the form of a long rod, and (2), by means of the weight thermometer, the coefficient of expansion of a liquid and also that of cubical expansion of a solid. In the case of a gas we may consider either the alteration of volume under constant pressure or the alteration of pressure at constant volume. We shall describe experimental methods of measuring these two. 16. ase re 36. Coefficient of Linear Expansion of a Rod. We require to measure the length of a rod, or the disor, ance between two marks on it, at two known temperatures, Osay 15° C. and 100° C. t). be The highest degree of accuracy requires complicated apparatus. The following method is simple, and will give very fair results. A thick straight rod is taken, about 50 cm. in length, nt and a glass tube of 4 or 5 cm. bore and somewhat greater ength than the rod. The tube is closed with a cork at n- .ch end, and through each cork a small piece of glass tubing passed, and also a thermometer. Two fine scratches are us made on the rod, one close to each end, at right angles to sel its length, and two other scratches, one across each of the d, former, parallel to the length. The glass tube is clamped to in a horizontal position and the rod placed inside it, resting two pieces of cork or wood in such a manner that the atches are on the upper surface and can be seen through glass. The whole should rest on a large stone slabone window-sill serves admirably. -1 The piece of glass tubing in one of the corks is connected vith a boiler from which steam can be passed into the tube, the other communicates with an arrangement for condensing tthe waste steam. A pair of reading microscopes are then brought to view the cross-marks on the rod, and are clamped securely to the stone. The microscopes, described in § 5, should be placed Iso that they slide parallel to the length of the rod; this can be done by eye with sufficient accuracy for the purpose. If microscopes mounted as in § 5 are not available, a ir with micrometer eye-pieces, or with micrometer scales in the eye-pieces, may be used. For convenience of focussing on the rod which is in the lass tube, the microscopes must not be of too high a power. heir supports should be clamped down to the stone at S |