Methods based upon the changes of volume under a constant pressure, and upon the changes of pressure for a constant volume. The disagreement of these two methods is due to deviations from the law of Mariotte. The constancy of the co-efficients of dilatation previously defined is only approximately true. Necessity of employing two different co-efficients of dilatation according as consideration is being had to the variations of volume to a given pressure, or of pressure to a given volume. Empirical formulæ for the dilatation of liquids. Graphical constructions. LESSON 10. _Thermometers._ Construction of thermometers. Mercurial thermometer. Details of construction. Fixed points. Different scales; their relation. Arbitrary scales. Change which takes place in the zero point. Different precautions to be observed in using the mercurial thermometer. General want of comparability of mercurial thermometers with tubes of different material. Air thermometers. They are comparable with one another within the limits of the errors of experiment, whatever the nature of the tube employed. This property entitles the air thermometer to a preference for all accurate measures. Comparison of the air and mercurial thermometers. THERMOSCOPE, DIFFERENTIAL THERMOMETER, PYROMETERS, BREGUET’S THERMOMETER. LESSONS 11-13. _Changes of State produced by Heat._ Exposition of the phenomena which accompany the liquefaction of solids and the solidification of liquids. Constancy of the temperature whilst the phenomenon is going on. Sudden melting and freezing. Persistance of the liquid state beneath the melting point. Influence of pressure. Exposition of the phenomena which accompany the conversion of liquids or solids into vapor, and the inverse passage from the gaseous to the liquid or solid state. Constancy of the temperatures whilst the phenomenon is going on. Influence of pressure. Phenomena of ebullition in free space. Augmentation of the temperature and pressure in a confined space. Papin’s digester. Properties of vapors in spaces and in gases. Saturated vapors. Their tension does not depend upon the space which they occupy, but only upon their temperature. Effects of a diminution or increase of pressure without change of temperature; the same without change of pressure. Effects of lowering the temperature in a limited region of space occupied by vapor. Tension of a saturated vapor at the boiling point of its liquid. Measure of the tensions of the vapor of water. Experiments of Dalton, Gay-Lussac, Dulong, and Arago, and of M. Regnault. Tables of the tensions of steam. Empirical formulæ. Graphical constructions. It is assumed that non-saturated vapors are subject to the same laws as gases. APPLICATIONS. CORRECTION OF THE BOILING-POINT IN THE CONSTRUCTION OF THERMOMETERS. BAROMETRICAL THERMOMETERS. LESSONS 14-16. _Various Applications of the Laws previously established._