124 PROFESSOR W. THOMSON ON THE 
ing the general laws of the dynamical theory of heat, both leads to a very concise 
mode of stating the principles, and shows the most convenient forms of the expres- 
sions brought forward in my former communication, the whole subject of thermo- 
electricity in metals will be included in the theoretical investigations now com- 
municated. I shall take the opportunity of introducing developments and illus- 
trations, which, although communicated at the meeting of the Royal Society 
along with the original treatment of the subject, did not appear in the printed 
abstract; and I shall add some experimental conclusions which have since been 
arrived at, in answer to questions proposed in the former theoretical investigation. 
98. Before entering on the treatment of the special subject, it is convenient to 
recal the fundamental Laws of the Dynamical Theory of Heat, and necessary to 
explain the thermometric assumption by which temperature is now to be measured. 
The conditions under which heat and mechanical work are mutually convert- 
ible by means of any material system, subjected to either a continuous uniform 
action, or a cycle of operations at the end of which the physical conditions of all 
its parts are the same as at the beginning, are subject to the following laws :— 
Law I. The material system must give out exactly as much energy as it takes 
in, either in heat or mechanical work. 
Law II. If every part of the action, and all its effects, be perfectly reversible, 
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 Carnov’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 temperature by 
the air thermometer, effected by the only data at that time afforded by experiment, namely, Recnautr’s 
observations on the pressure and latent heat of saturated steam at temperatures of from 0° to 230° of 
the air thermometer, showed, as the nature of the assumption required, very wide discrepance, even incon- 
veniently wide between the fixed points of agreement. A more convenient assumption has since been 
pointed to by Mr Jourx’s conjecture, that Carnor's function is equal to the mechanical equivalent of 
the thermal unit divided by the temperature by the air thermometer from its zero of expansion; an 
assumption which experiments on the thermal effects of air escaping through a porous plug, undertaken 
by him in conjunction with myself, for the purpose of testing it, (Philosophical Magazine, Oct. 1852,) 
have shown to be not rigorously but very approximately true. More extensive and accurate experi- 
ments have given us data for a closer test (Phil. Trans., June 1853), and in a joint communication 
by Mr Jourz 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 divided by 
Carnor’s function, We deduce from our experimental results, 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 
temperatures between the freezing and boiling points, and, through a range of 300° above the freezing 
point, so close an agreement that it may be considered as perfect for most practical purposes. The 
form of assumption given below in the text as the foundation of the new thermometric system, with- 
out 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 Carnor’s function have the form there given as a conjecture, and now adopted as 
the definition of temperature. 
