may be neglected; and the volume of the cube after a rise in temperature of one degree is is, therefore, the coefficient of voluminal expansion.
186. Measurement of Coefficients of Linear Expansion.—Coefficients of linear expansion are measured by comparing the lengths, at different temperatures, of a bar of the substance the coefficient of which is required, with the length, at constant temperature, of another bar. The constant temperature of the latter bar is secured by immersing it in melting ice. The bar the coefficient of which is sought may be brought to different temperatures by immersing it in a liquid bath; but it is found better to place the bar upon the instrument by means of which the comparisons are to be made, and leave it for several hours exposed to the air of the room, which is kept at a constant temperature by artificial means. Of course several hours must elapse between any two comparisons by this method, and its application is restricted to such ranges of temperature as may be obtained in occupied rooms; but within this range the observations can be made much more accurately than would be the case when the bar is immersed in a bath, and it is within this range that an accurate knowledge of coefficients of expansion is of most importance.
187. Expansion of Liquids.— In studying the expansion of a liquid, it is important to distinguish its absolute expansion, or the real increase in volume, and its apparent expansion, or its increase in volume in comparison with that of the containing vessel.
To determine the absolute expansion, some method must be used which does not require a knowledge of the expansion of the vessel containing the liquid. The method used by Regnault in determining the absolute expansion of mercury consisted in comparing the heights of two columns of mercury at different temperatures when they were so adjusted as to give the same pressure.
The apparent expansion is determined by filling a vessel of known volume with the liquid at one temperature, and by measuring the amount of the liquid which runs out when the temperature is raised. This method was also used by Regnault in his study of
