There are several scales of temperature: in point of fact the scale of a mercury-in-glass thermometer is defined by the process of graduation, and therefore there are as many such scales as there are thermometers, since no two specimens of glass expand in precisely the same way. Equal differences of temperature do not correspond to equal increments of volume of the mercury: for the glass envelope expands also and in its own way. On the scale of a constant pressure gas thermometer changes of temperature are measured by variations of volume of the gas, while the pressure is maintained constant; on a constant volume gas thermometer changes of temperature are measured by alterations of pressure while the volume of the gas is kept constant. Each scale has its own independent definition, thus if the pressure of the gas be kept constant, and the volume at temperature 0° C. be v₀ and that at any other temperature be v₁ we define the numerical value t, this latter temperature, by the equation v = v₀(1 + Et), where E is 1⧸100 of the increase of volume sustained by the gas in being raised from 0° C. to 100° C. These are the temperatures of reference on an ordinary centigrade thermometer, that is, the temperature of melting ice and of saturated steam under standard atmospheric pressure, respectively. Thus t has the value (v⧸v₀ － 1)⧸E, and is the temperature (on the constant pressure scale of the gas thermometer) corresponding to the volume v. Equal differences of temperature are such as correspond to equal increments of the volume at 0° C. Similarly, on the constant volume scale we obtain a definition of temperature from the pressure p, by the equation t = (p⧸p₀ － 1)⧸E', where p₀ is the pressure at 0° C., and E' is 1⧸100 of the change of pressure produced by raising the temperature from 0° C. to 100° C. For air E is approximately 1⧸273, and thus t = 273(v － v₀)⧸v₀. If we take the case of v = 0, we get t = －273. Now, although this temperature may be inaccessible, we may take it as zero, and the temperature denoted by t is, when reckoned from this zero, 273 + t. This zero is called the absolute zero on the constant pressure air thermometer. The value of E' is very nearly the same as that of E; and we get in a similar manner an absolute zero for the constant volume scale. If the gas obeyed Boyle's law exactly at all temperatures, E would not differ from E'. It was suggested to Thomson by Joule, in a letter dated December 9, 1848, that the value of μ might be given by the equation μ = JE⧸(1 + Et). Here we take heat in dynamical units, and therefore the factor J is not required. With these units Joule's suggestion is that μ = E⧸(1 + Et), or with E = 1⧸273 μ = 1⧸(273 + t), that is, μ = 1⧸T where T is the temperature reckoned in centigrade degrees from the absolute zero of the constant pressure air thermometer.