216 Prof. Thomson on the Dynamical Theory of Heat. 



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 expressions brought forward in my 

 former communication, the elementary theory of thermo-electri- 

 city in metals will be included in the investigations now com- 

 municated. I shall take the opportunity of introducing deve- 

 lopments and illustrations, which, although communicated at 

 the meeting of the Royal Society along with the original treat- 

 ment of the subject, did not ajipear 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 convertible by means of any material system, sub- 

 jected either to a continuous uniform action, or to a cycle of ope- 

 rations 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, cither in heat or mechanical work. 



Law 11. — If every part of the action, and all its effects, be 

 perfectly reversible, and if all the localities of the system by 

 which heat is either emitted or taken in, be at one or other of 

 two temperatures, the aggregate amount of heat taken in or 

 emitted at the higher temperature, must exceed the amount 

 emitted or taken in at the lower temperature, always in the same 

 ratio when these tempei'atures are the same, whatever be the 

 particular substance or arrangement of the material system, 

 and whatever be the particular nature of the operations to which 

 it is subject. 



99. Definition of temperature and ffeneral thermometric assump- 

 tion. — If two bodies be put in contact, and neither gives heat to 

 the other, their temperatures are said to be the same; but if 

 one gives heat to the other, its temperature is said to be higher. 



The temperatures of two bodies are proportional to the quan- 

 tities of heat respectively taken in and given out in localities at 

 one temperature and at the other, respectively, by a material 

 system subjected to a complete cycle of perfectly reversible 

 thermo-dynamic operations, and not allowed to part with or take 

 in heat at any other temperature : or, the absolute values of two 

 temperatures are to one another in the proportion of the heat 

 taken in to the heat rejected in a perfect thermo-dynamic engine 



