since at the freezing point of the solvent the vapour pressure P of ice and that p of the liquid must be the same, and for this we may, without appreciable error, use pg.
If we introduce the values—
Pa ~ P'» _ "_ i'«_~ Pi — '*i-^ p„ 100 ' p,i 1000(Z'
and i? = 2, we find for dT—
��~ loborfit'
that is, the same formulae as were found for the rise of boil- ing point with the heat of vaporisation A replaced by the heat of fusion u.
Experimental Determination of the Freezing Point. — The depression of the freezing point and the rise of the boiling point can now be determined with a very high degree of accuracy by the methods worked out by E. Beckmann (^). The apparatus devised by him for the determination of freezing points is shown in Fig. 17. A known weight of the solvent whose freezing point is to be determined is introduced into the tube A, which is about the size of an ordinary test-tube, and is provided with a side tube B. Through a rubber stopper in A there passes a platinum ■wire, G, which serves as a stin-er, and a thermometer, C, graduated into hun- dredths of a degree. The tube A is sur- roimded by an air-mantle by inserting it into a wider tube, B. The whole appa- ratus is placed in a freezing mixture con- tained in the vessel E, which is provided Fk. 17,
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