In this reckoning the definition of any temperature, let us say 37° C., is the temperature of the vessel and its contents when the top of the mercury column stands at the mark 37 above 0, on the scale defined by the graduation of the instrument; but the numerical signification with relation to the volumes is given by equation (D). This shows that the numerical measure of any temperature involves both the expansion of the vessel and that of the glass vessel between the temperature of melting ice and the temperature in question. This result may be contrasted with the erroneous statement frequently made that equal increments of temperature correspond to equal increments of the volume of the thermometric substance. It also shows that different mercury-in-glass thermometers, however accurately made and graduated, need not agree when placed in a bath at any other temperature than 0° C. or 100° C. This fact, and the results of the comparison of thermometers made with different kinds of glass with the normal air thermometer, which was carried out by Regnault, were always insisted on by Thomson in his teaching when he dealt with the subject of heat. The scale of a mercury-in-glass thermometer is too often in text-books, and even in Acts of Parliament regarded as a perfectly definite thing, and the expansion of a gas is not infrequently defined by this indefinite scale, instead of being used as it ought to be, as the basis of definition of the scale of the gas thermometer. The whole treatment of the so-called gaseous laws is too often, from a logical point of view, a mass of confusion. In his article on Heat Thomson gave two definitions of the scale of absolute temperature. One is that stated on p. 126 above, namely, that the temperature of the source and refrigerator are in the ratio of the heat taken in from the source to the heat given to the refrigerator, when the engine describes a Carnot cycle consisting of two isothermal and two adiabatic changes. The other definition is better adapted for general use, as it applies to any cycle whatever which is reversible. Let the working substance expand under constant pressure by an amount dv (AB' in Fig. 12), and let heat H be given to the substance at the same time. The external work done is pdv. Thomson called pdv⧸H the work ratio. Now let the temperature be raised by dT without giving heat to the substance or taking heat from it, and let the corresponding pressure rise be dp; and call dp⧸p the pressure ratio. The temperature ratio dT⧸T is equal to the product of the work ratio and the pressure ratio, that is, dT⧸T = dvdp⧸H