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most of the reactions begin and finish in a fraction of a minute, the slowest not lasting longer than a very few minutes; and as the temperature of the liquid during the reaction passes from T-T, about 1° to T-T, about 0°.1, it is evident that under these experimental arrangements the heat evolved or absorbed can be safely neglected. We arrive at the same conclusion by a calculation of the total heat absorbed or given off by the liquid in each individual

dt dr

case, using the equation =C(T,—t), given above.

E. Some Further Details.

a. A large copper bath (Ba) with double walls was used for the investigation of the separation of salts from supersaturated solutions. The space between was filled with petroleum and the outer walls were covered with sheets of asbestos, a círcle below being left uncovered for the burner. One thermometer (1) was in the petroleum, the other in the air-chamber (2). The beaker with the liquid and stirrer were placed in the inner chamber on thick felt. The rod of the stirrer was then fixed to the guide (9) which was moved by an electromotor, separated from it by a ring of asbestos, in order to bring to a negligible quantity the heat passing from the stirrer to the guide during the time of the reaction. The number of ups and downs of the stirrer was 36 per minute. The temperature of the inner chamber being kept as far as possible constant, the velocity of cooling of 4 litres of a solution, almost saturated at the temperature of the airchamber, was measured and the convergence-temperature for the given experimental conditions determined. (In this case the conditions were:-36 stirrings per minute, temperature of room T, temperature of the petroleum T', of the airchamber T", 4 litres of liquid, &c.) A solution saturated above the convergence-temperature was then prepared, so that the temperature of the liquid after the separation of the salt should be as near to the convergence-temperature as possible, 4 litres of it were poured into the beaker, and the separated crystals dissolved by stirring the liquid and warming it a few degrees above the temperature of the solution. With this solution the final experiment was made. The beaker with the solution was replaced in the air-chamber and stirred. As the temperature of the liquid approaches the point of saturation stirring must cease, and the liquid be allowed to cool without any disturbance. A very slow and cautious movement of the stirrer may be occasionally made to equalize

the temperature of the liquid. Even with such precautions. salt crystals easily separate from the solution, and it becomes necessary to redissolve them. Sometimes half a dozen expeperiments must be made, before a solution sufficiently supersaturated (without crystals, or with so few crystals that they may be neglected) is obtained. For this reason it is always absolutely necessary to examine the liquid by illuminating it in the inner chamber from time to time, and to begin the experiment as soon as a few crystals have separated. The crystals seem not to separate so readily from the supersaturated solutions when the inside of the beaker and the stirrer are covered with a thin layer of indiarubber, which was easily done by means of an indiarubber solution.

b. This difficulty does not exist at any rate for some overcooled liquids, e. g. water and unsaturated aqueous solutions from which the solvent (e. g. ice) is to be separated. We can easily overcool water or an aqueous solution one degree, or even more, below the freezing-point without any ice separating, if the necessary precautions be taken. On the other hand, it is very difficult, with some solvents like benzene, to get a sufficiently great overcooling. The investigation of such liquids presents great difficulties; the velocity of separation being here very great, so that it can only be carried out between smaller limits of overcooling. The precautions to be taken in overcooling water and aqueous solutions are the following: The liquid bath in which the liquid is cooled down must not be too cold, and a continuous stirring of the liquid must be kept up to prevent the formation of too cold layers at the sides of the beaker, the stirrer should not touch the sides of the beaker. The general arrangements of the experiment are those described in the paper of the late P. B. Lewis "On the Freezing-Point Method" (Chem. Soc. Trans. 1894). The number of stirrings was 36 per minute. The convergence-temperature and other constants were determined by the methods given given in the paper already quoted (Phil. Mag. Dec. 1897).

c. The investigation of the velocity of ice melting was carried out with the arrangements used for ice separation (b). Cubes of ice were used. A cage in the form of a cube was fixed to the stirrer, each side of it consisting of three rods, covered with indiarubber tubes to prevent the formation of grooves in the ice. The ice cube was placed in the cage, closed up in it by the upper lid, and was taken of such a size as not to be able to rotate, and kept under the surface of the water while stirring was going on. They were prepared in the following way:-A cube of ice was cut by a saw from a pure transparent block of ice which had been exposed for some

time to the temperature of the air. Holding the cube with a thick perfectly smooth sheet of indiarubber, it was polished on a heated thick smooth iron plate, and measured by a wooden cm. ruler until the correct shape was obtained. The 'cube was then quickly weighed on a sufficiently sensitive balance (placed on very smooth and thick sheets of indiarubber) and rapidly brought into the cage for the experiment. From its weight we know very accurately its surface at the beginning of the reaction, and from the quantity of the liquid, the weight of the beaker and stirrer and their initial temperature Tou, and their temperature t at the time 7, the surface of the ice cube at the time T can be calculated. At the end of the reaction the ice was again weighed. It was found that a considerable part can be melted before the ice loses its cubic shape. Experiments were at first made, without success, with a view of obtaining the ice in the form of a sphere, either by compressing pure ice, or by freezing water in two Magdeburg hemispheres or in glass balls, allowing the water from the inside to escape through a tube, or by turning the ice on a lathe, &c. The number of stirrings was about 60 per minute.

IV. The Results obtained.

By the method given above the velocity of ice separation, ice melting, and of the separation of salts from supersaturated solutions were investigated, and the equations concerning the total length of the curves were found. All these reactions prove to be regulated by one and the same general law, which is given in the following differential equation:

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Since all reactions were investigated within limits of less than one degree, we can very well assume that the velocity constant K' remained during the reaction the same.

In Plate II. two photographic curves (reduced to half their size) are given-one representing the velocity of separation of ice from an NOK solution, the other the velocity of separation of solid NO3K from a supersaturated NO3K solution. The velocity of reaction is very different in the two cases, being very much slower in the case of the separation of salt. The nature of the curve, however, is in both cases the same, as is to be seen from II'., which represents II. when instead of the actual 1 cm.=1 second, 1 cm.=10 seconds is taken. The same result was found in the case of about sixty other curves, to be published later. The results obtained from these curves are given in the following Tables I. and II

TABLE I.-Velocity of Separation of Ice from a NOK Solution.

Beginning of June 1898. Freezing-point on the Pt-thermometer=- -0°.2255.

to-tov=6.2 cm. on the photographic curve 14 cm. of the bridge (derived from the calibration of the curve)=0°.3670 (on the Pt-thermometer).
Ice-bath=-2°.4. Calibrated in 8 points. The values to-t, t-tov, t-tov+K are given in the table not in degrees C., but in centimetres
of the photographic curve, as they have been obtained, since dealing with differences of logarithms we thus get the same result. To get
the absolute value of (K') or K' of the differential equation for t-tov=1°, T-T1 =1 minute, the values (K'). 1000, and K'. 1000 must be
600 × 2.3026
multiplied by
or 3.764. (No correction is made here for the time indicated by the chronograph, i. e. (K') and K' is
1000×0.3670'
times greater than those given in this table, because 1 cm.=5925 seconds.)

60

59.25

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=

20th May, 1898. IABLE 11.—The Velocity of Separation of Solid NOK from Oversaturated Solutions of NOK. to-to-64 cm. on the photographic curve the data concerning the Pt-thermometer). =17·06 cm. of the bridge (derived from the calibration of the curve) =0·4473 (derived from ice-bath about -3°, of the air-bath = about -0°.7. Point of equilibrium is at +06475 (on the Pt-thermometer). Temperature of the The curve calibrated in 7 points. Before KNO, was made to separate, the velocity of cooling was only 00:01 to 09:02 in 30 minutes (movements of the stirrer were 36 per minute), so that for was only about 0°-1 removed from the convergence-temperature tg (for this reason it was no longer necessary to control the constancy of for by getting the parallel on the curve). It should be remembered that in case of supersaturated solutions we cannot stir the solution without salt beginning to separate, so that we make the complete equalization of temperature throughout the liquid just when we start the experiment of separation of the salt. The point top is here that which is most removed from the point of equilibrium; it gives on the curve a line which is quite parallel to the edge of the paper, the reaction at the beginning being very slow. To get (K') and K' for to-toy-1° rise of temperature during the reaction, and T-71 minute, the values of (K'). 1000 and K'. 1000 must be multiplied by or 0.3088. (No correction for the time indicated by the chronograph is made.)

60 × 2·3026
1000 × 0.4473

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