129 



expansion and compression determined by Regnault, are applied to 

 give a more precise evaluation. 



IV. An absolute scale of temperature, that is, a scale not founded 

 on reference to any particular thermometric substance or to any 

 special qualities of any class of bodies, is founded on the following 

 definition : 



If a physical system be subjected to cycles of perfectly reversible 

 operations and be not allowed to take in or to emit heat except in loca- 

 lities, at two fixed temperatures, these temperatures are proportional to 

 the whole quantities of heat taken in or emitted at them respectively 

 during a complete cycle of the operations. 



The principles upon which the unit or degree of temperature is to 

 be chosen, so as to make the difference of temperatures on the abso- 

 lute scale, agree with that on any other scale for a particular range 

 of temperatures. If the difference of temperatures between the 

 freezing and the boiling-points of water be made 100 on the new 

 scale, the absolute temperature of the freezing-point is shown to be 

 about 2 73 '7 ; and it is demonstrated that the temperatures from the 

 freezing-point on the new scale will agree very closely with Centi- 

 grade temperature by the standard air-thermometer; quite within 

 the limits of the most accurate practical thermometry when the tem- 

 perature is between and 100 Cent., and very nearly if not quite 

 within these limits for temperatures up to 300 Cent. 



V. An empirical formula for the pressure of air in terms of its 

 density, and its temperature on the absolute scale, is investigated, by 

 using forms such as those first proposed and used by Mr. Rankine, 

 and determining the constants so as to fulfil the conditions (1) of 

 giving the observed cooling effects, (2) of agreeing with Regnault's 

 observations on expansion by heat, and (3) of agreeing with Reg- 

 nault's experimental results on compressibility at a particular tem- 

 perature. 



A table of comparison of temperature by the air-thermometer 

 under varied conditions of temperature and pressure with the abso- 

 lute scale, is deduced from this formula. 



Expressions for the specific heats of any fluid in terms of the ab- 

 solute temperature, the density, and the pressure, derived from the 

 general dynamical theory, are worked out for the case of air accord- 

 ing to the empirical formula ; and tables of numerical results derived 



