Prof, Thomson on the Dynamical Theonj of Heat. 215 



laws of the dynamical theory of heat to this kind of agency was 

 made, and certain universal relations precisely analogous to the 

 thermo-elastic properties of fluids established in the previous 

 treatment of the first division of the subject, were established 

 between the thermo-electric properties of non-crystalline metals. 

 The object of the present communication is to extend the theory 

 to the phsenomena of thermo-electricity in crystalline metals; 

 but as recent experimental researches on air have pointed out an 

 absolute thermometric scale*, the use of which in expressing the 



* That is a scale defined without reference to effects experienced by any 

 particular kind of matter. Such a scale, founded on general thermo- 

 dynamic relations of heat and matter, and requiring reference to a particular 

 thermometric substance only for defining the unit or degree, was, so far as 

 I know, first proposed in a communication to the Cambridge Philosophical 

 Society (Proceedings, May 1848, or Philosophical Magazine, October 

 1848). The particular thermometric assumption there suggested was, that 

 a thermo-dynamic engine working to perfection, according to Carnot's 

 criterion, would give the same work from the same quantity of heat, with 

 its source and refrigerator differing by one degree of temperature in any 

 part of the scale ; the fixed points being taken the same as the 0° and 

 100° of the centigrade scale. A comparison of temperature, according 

 to this assumption, with temperatm-e by the air thermometer, effected 

 by the only data at that time afforded by experiment, namely Regnault's 

 observations on the pressure and latent heat of saturated steam at tempe- 

 ratures of from 0" to 230° of the air thermometer, showed, as the 

 nature of the assumption required, very wide discrepances, even inconve- 

 niently wide between the fixed points of agreement. A more convenient 

 assumption has since been pointed to by Mr. Joule's conjectm-e, that 

 Carnot's function is equal to the mechanical equivalent of the thermal unit 

 divided by the temperature by the air thermometer from its zero of expan- 

 sion ; an assumption which experiments on the thermal effects of air 

 escaping through a porous plug, undertaken by him in conjunction with 

 myself for the piu-pose of testing it (Philosophical Magazine, Oct. 1852), 

 have shown to be not rigorously but very approximatively true. More 

 extensive and accurate experiments have given us data for a closer test 

 (Phil. Trans., June 1853), and in a joint communication by Mr. Joule and 

 myself to the Royal Society of London, to be made during the present 

 session, we propose that the numerical measure of temperature shall be not 

 founded on the expansion of air at a particular pressure, but shall be 

 simply the mechanical equivalent of the thermal unit (hvided by Carnot's 

 function. We deduce from our exj^erimental resvdts, a comparison between 

 differences on the new scale from the temperature of freezing water, and 

 temperatures centigrade of Regnault's standard air thermometer, which 

 shows no greater discrepance than a few hundredths of a degree, at tem- 

 peratures between the freezing- and boiling-points, and, through a range of 

 300 above the freezing-point, so close an agreement that it may be con- 

 sidered as i)erfect for most practical purposes. The form of assumption 

 given below in the text as the foundation of the new thermometric system, 

 without explicit reference to Carnot's function, is equivalent to that just 

 stated, inasmuch as the formula for the action of a perfect thermo-dynamic 

 engine, investigated in § 25, expresses (§ 42) that the heat used is to the 

 heat rejected in the proportion of the temperature of the source to the 

 temperature of the refrigerator, if Carnot's function have the form there 

 given as a conjecture, and now adopted as the definition of temperature. 



