1908] [on the Scientific Worlt of Lord Kelvin. 221 



Properties of Matter, Part I.,' which represents the contents of the 

 latter part of the paper to which the more general introductory 

 matter was probably added. This paper was reprinted in ' Phil. 

 Mag.,' January 1878, with some additional notes.* The principles 

 that we are now concerned with occupy the first few pages ; the 

 argument is expressed in terms of elastic strain, but that is obviously 

 only for convenience of exposition. The total intrinsic energy e of a 

 material system, measured from a standard initial configuration and 

 temperature, is defined as a function of its actual configuration and 

 temperature. It is established from Carnot's principle, as in the 

 quotation above, that for transformations conducted entirely at 

 the same definite temperature t, the mechanical forces applied to the 

 system must be derivable from a Avork function w which represents, 

 in fact, the potential energy acquired by the system in passing at that 

 temperature from the standard configuration to the actual one. If e 

 denote the simultaneous increment of e, then e — lu must be the heat 

 H taken in from outside during that change from the standard con- 

 figuration, when conducted at the actual temperature. 



It is to be observed that this simple consideration, which appa- 

 rently here appears in science for the first time, carries the principle 

 of potential energy in its mechanical application right back to Carnot's 

 principle of 1824. In the previous writings on general potential 

 energy, such as Helmholtz's ' Erhaltung der Kraft,' nothing of the 

 kind is hinted at ; while Clausius' treatment, being restricted to 

 transformation of heat, is nowhere connected up with the general 

 theory of energy. The first law of thermodynamics hencefortli drops 

 to more restricted scope, for it merely asserts that availa])le energy 

 when lost is changed into heat in equivalent amount. Yet it still 

 suffices to maintain the presumption that all energy-processes have 

 their source in — are consistent with — the ordinary Newtonian prin- 

 ciples of dynamics as applied to ultimate molecules ; considering the 

 difficulty experienced by Thomson in reconciling Joule's law with 

 his innate conviction of the validity of Carnot's principle, it is not 

 surprising that this inference appealed to him with special force. 

 Indeed, when the historical conflict between the two laws is kept in 

 mind, the value of the first will not be disparaged. From this point 

 of view the principle of Carnot appears in transformed aspect. Its 

 chief interest is now transferred to the two creative ideas which it 

 contains, the introduction into science (i) of the idea of a complete 

 cycle of transformations, and (ii) of the criterion of absence of waste 

 of power in any mechanical process, namely, that the process can 

 be reversed, which includes the condition of temperature uniform 

 throughout the system at each instant. The further development, 

 including Carnot's function and the quantitative determination of 

 the idea of temperature which it brings with it, is the thermal com- 



Math. and Phys. Papers, i. pp. 291-316. 



