So

experiments) they do not assume the temperature of the liquid during the reaction simultaneously, and since their heat capacity is in comparison with that of the liquid by no means a negligible quantity, this constitutes a source of error. also is it with the reading of time. It is very difficult to make accurately several readings during a time of 15 seconds, if no special arrangements are made for the purpose.

Now if the equation for the velocity of reaction is to claim that it represents a law of nature it must satisfy two very essential points: first, it must hold good for the whole curve, and, secondly, it must be general, and it must be based on a simple clearly conceivable rational basis. It must be further remarked that it is just the end of the curve which has great theoretical interest, since the physico-mathematical theory of freezing-points, vapour-pressures, solubility, &c. is very deeply connected with this part of the curve. It was, therefore, of importance to ascertain beyond any doubt whether the equations which I used in the theory of freezing-points (see "On Real and Apparent Freezing-points and the Freezing-point Methods," Phil. Mag. Dec. 1897 and Zeitschrift für physikalische Chemie, 1899, p. 577) are correct, and if so whether, in the case of all other kinds of perfect equilibrium, we also have to distinguish between "apparent" and "real" points of equilibrium.

The splendid arrangements of the Davy-Faraday Laboratory and the kind assistance given to me by Dr. Ludwig Mond in procuring for me all the expensive instruments necessary for this investigation, enabled me to resume the same research in January 1896, under very much more favourable experimental conditions of which a detailed account is now given.

The method employed is first described fully, as upon this the value of the whole research greatly depends.

III. The Method of investigating the Velocities of the Separation of Ice from Water and Solutions cooled below their freezing temperature, of the Separation of Salts from Supersaturated Solutions, and of the Melting of Ice in Water and Aqueous Solutions, &c.

All the above reactions take place with very great speed,. most of them lasting only a fraction of a minute, and as many observations have to be made during this time in order to get the curve for the velocity of reaction, the method described below is the only one which enables us to investigate the problem successfully. Advantage has been taken of the fact

that all the above reactions take place with evolution or absorption of heat.

To get a successful experiment the following arrangements proved to be necessary:

A. An instantaneous registration of temperature with an accuracy of one or two ten-thousandths of a degree, and of time to about 1/50 of a second has been made.

B. The point of the obtained apparent equilibrium has been so arranged that it differed from the real one only by 0°00001 to 0°-0001. This was absolutely necessary since the equations for the velocity of reaction proved to be dependent upon the points of equilibrium.

C. The equalization of temperature throughout the liquid, thermometer, beaker, and stirrer has been made instantaneous, so that the thermometer gave true indications of the temperature of the liquid at any moment.

D. The amount of heat given off or taken up by the liquid, &c., from the surrounding medium during the time of the experiment has been made so small that it could be safely neglected.

A. The Platinum-Thermometer for Measurement of Boilingand Freezing-points, Solubilities, and Velocity of Reactions. The object of this part was to adapt the platinum-thermometer for the special purpose of investigating freezing- and boiling-points, solubilities, and the velocity of reactions. in my investigations an accuracy in the registration of the thermometer of 0°-0001 or 0°-0002 had to be ensured, and instantaneous indications of temperature were required, the chief object was to arrange the method so as to avoid the necessity for the multitudinous corrections of other methods, i. e. to reduce these corrections to the smallest values possible, so that the aggregate error, when they are neglected, does not exceed the above value of 0°·0001-0°0002. We must always bear in mind that the application of a correction never completely removes the error, and that it depends upon the absolute values of these corrections how far we are able to ensure results of the desired degree of accuracy.

Fig. 1 (p. 70) gives the general arrangements of the apparatus I employ. R is the resistance-box, containing manganin coils 20 ohms (1st arm of the Wheatstone-bridge), 20 ohms (2nd arm), 20, 10, 5, 3, 1, 1, 0.5 ohms (3rd arm); A, B, C, D, d, a are terminals. A and a are connected with the Callendar-Griffiths compensating-leads; C and D'-e with the leads of the platinum-thermometer (4th arm of the bridge). D (or d when the 0.5 ohm is not used) and D'

are connected with the bridge and rheostat; A and C with the battery, b and B with the galvanometer, K is a reversingkey, Z is a contact-maker for battery and galvanometer. Plate I. gives the outlines of a photograph taken from the actual experimental arrangements of the method.

I pass now to the description of all essential parts:The Resistance-Box.-Prof. Callendar and Mr. Griffiths, who, as known, have considerably advanced the subject, use for their coils german-silver, which has a temperaturecoefficient of 0.00026 between 15° and 25° in terms of the resistance at 20°.

Mr. Harker (Proc. Royal Society, 1896) uses manganin coils suspended in air, the temperature of which is indicated by a mercury-thermometer. The Berlin Reichsanstalt found the temperature-coefficient of manganin to be about 000002. Messrs. Crompton and Fisher found that some samples of manganin can be brought by repeated annealing to a temperature-coefficient of a few in a million at about 20°, The temperature-coefficient of my manganin coils Messrs. Crompton and Fisher found to be 00000025 between 15° and 25°. I found it somewhat higher, about 0·0000035, i.e. the temperature-coefficient of my coils is about 100 times smaller than that of german-silver. I presume the temperature-coefficient of Mr. Harker's coils was also very

small*.

The error arising from the coils is thus arranged: the two arms A-B and B-C are practically equal (20 000 and 20-0004 ohms), and do not come into consideration, so that the third arm only has to be considered. Since the temperature-coefficient of the platinum coil is about 0·0036, that of my manganin coils 00000035, the variations of the registereď temperature due to the manganin coils is 0°.0001 if

The values of my coils were found with the potentiometer of Crompton to be, when again measured January 1896 :

On comparison of the above data with those obtained by myself by means of Wheatstone's bridge, using the standard of the Berlin Reichsanstalt, I found that the absolute values of the standard used by Mr. Crompton are all somewhat (but proportionately) smaller than those of the Reichsanstalt.

their temperature varies 0°1, and is 0° 00001 for a variation of 0°.01. As long as the coils are immersed in a homogeneous liquid-not in a heterogeneous system, where the warming of the liquid e. g. is prevented by the very rapid process of melting of the solid solvent, &c.-the coils cannot by simply stirring the liquid be kept constant more than to a few hundredths of a degree. In my paper (Phil. Mag. Dec. 1897) I have shown that in one of the most developed freezingpoint methods lately published even the equilibrium of ice and water is affected by errors which amount very nearly to 0°.01, so that we must not overrate the result we can obtain by bath-regulation only, unless quite extraordinary arrangements are made.

The Berlin Reichsanstalt conducted currents of different intensity from a thermopile through a coil, and measured the deflexion of the galvanometer, rapidly reversing the current. The results obtained were :—

Here Q is the transformed energy in watts in T—T1=d, T is the temperature of the wire, T of the surrounding medium (air or petroleum), E is the quantity of heat given up through 1 cm.2, when T-T,=1°. They also found that in petroleum the wire acquires a constant temperature within about a minute, whilst in air only after half an hour to an hour had elapsed. In some of my publications of 1896 I have already shown that a beaker with 1250 c.cm. water is cooled down in a liquid bath about twenty times more quickly than in the air.

To keep the coils at a constant temperature, and to avoid the heating effect of the current, the coils of the resistancebox have been immersed in 6 litres of petroleum, contained in a double-walled copper vessel with an air-space between them. The copper vessel could be heated by flame or kept in a thermostat if required. The coils have been covered with shellac, repeatedly annealed, and all placed by Mr. Fisher in the same plane so as to secure equality of their temperature. For the same reasons, my platinum coil, as will be shown. later, is always immersed in the liquid itself. Prof. Callendar and Mr. Griffiths have the coils of their resistance-box also immersed in petroleum, their platinum coil, however, still