In addition to the above, there are mixed methods in which both p and V or M are variable, such as those employed by Rud berg or Becquerel; but these are unsatisfactory for precision, as not leading to a sufficiently definite thermometric scale. There is also a variation' of the constant-volume method (ii.), in which the pressure is measured by the volumetric compression of an equal mass of gas kept at a constant temperature, instead of by a manometer.
Construction of Apparatus.—The manometric or constant volume method was selected by Regnault as the standard, and has been most generally adopted since his time. His apparatus has not been modified except in points of detail. A description of his instrument will be found in most text-books on heat.
A simple and convenient form of the instrument for general use is Jolly's (described in Poggendorff's Jubelband, p. 82, 1874), and represented in fig. 3. The two vertical tubes of the manometer are connected by an india-rubber tube properly strengthened by a cotton covering, and they can be made to slide vertically up and down a wooden pillar which supports them ; they are provided with clamps for fixing them in any position and a tangent screw for fine adjustment. The connection between the bulb and the manometer is made by means of a three-way tap. The scale of the instrument is engraved on the back of a strip of plane mirror before silvering, and the divisions are carried sufficiently far across the scale for the reflections of the two surfaces of the mercury to be visible behind the scale. Par allax can thus be avoided and an accurate reading obtained without the necessity of using a cathetometer. In order to allow for the expansion of the glass of the reservoir a weight-ther mometer bulb is supplied with the instrument, made from an other specimen of the same kind of glass, and the relative expan sion of the mercury and the glass can thus be determined by the observer himself. The volume of the air-bulb and that of the capillary tube and the small por tion of the manometer tube above the small beak of glass, the point of which serves as the fidu cial mark, are determined by the instrument-makers. The improve ments introduced by Chappuis, of the International Bureau at Sevres, in the construction of the con stant-volume hydrogen thermometer selected by the committee for the determination of the normal scale, are described in the text-books (e.g., Watson's Physics).
The volume of the bulb is not accurately constant, but varies with change of pressure and temperature. The thermal expan sion of the bulb is common to all methods, and will be considered in detail later. The pressure correction is small, and is determined in the same manner as for a mercury thermometer. The value so
determined, however, does not apply strictly except at the tem perature to which it refers. If the pressure-coefficient were con stant at all temperatures and equal to e, the pressure correction, dt, at any point t of the scale would be obtainable from the simple formula where po is the initial pressure at the temperature T2. But as the coefficient probably varies in an unknown manner, the correc tion is somewhat uncertain, especially at high temperatures. An other very necessary but somewhat troublesome correction is the reduction of the manometer readings to allow for the varying temperatures of the mercury and scale. Since it is generally impracticable to immerse the manometer in a liquid bath to secure certainty and uniformity of temperature, the temperature must be estimated from the readings of mercury thermometers sus pended in mercury tubes or in the air near the manometer. It is therefore necessary to work in a room specially designed to secure great constancy of temperature, and to screen the man ometer with the utmost care from the source of heat in measure ments of high temperature.