September 22, 1905.] 



SCIENCE. 



363 



defined and computed the mechanical 

 equivalent of heat, and when Joule (1843, 

 1845, et seq.) made that series of pre- 

 cise and judiciously varied measurements 

 which mark an epoch. Shortly after Helm- 

 holtz (1847), transcending the mere bounds 

 of heat, carried the doctrine of the con- 

 servation of energy throughout the whole 

 of physics. 



Earlier in the century Carnot (1824), 

 stimulated by the growing importance of 

 the steam engine of Watt (1763, et seq.), 

 which Fulton (1806) had already applied 

 to transportation by water and which 

 Stephenson (1829) soon after applied to 

 transportation by land, invented the re- 

 versible thermodynamic cycle. This cycle 

 or sequence of states of equilibrium of two 

 bodies in mutual action is, perhaps, without 

 a parallel in the prolifie fruitfulness of its 

 contributions to modern physics. Its con- 

 tinued use in fifty years of research has 

 but sharpened its logical edge. Carnot de- 

 duced the startling doctrine of a tempera- 

 ture criterion for the efficiency of engines. 

 Clapeyron (1834) then gave the geomet- 

 rical method of representation universally 

 used in thermodynamic discussions to-day, 

 though often made more flexible by new 

 coordinates as suggested by Gibbs (1873). 



To bring the ideas of Carnot into har- 

 mony with the first law of thermodynamics 

 it is necessary to define the value of a 

 transformation, and this was the great 

 work of Clausius (1850), followed very 

 closely by Kelvin (1851) and more hypo- 

 thetically by Rankine (1851). The latter 's 

 broad treatment of energetics (1855) ante- 

 dates many recent discussions. As early 

 as 1858 Kirchhoif investigated the solution 

 of solids and of gases thermodynamically, 

 introducing at the same time an original 

 method of treatment. 



The second law was not generally ac- 

 cepted without grave misgiving. Clausius, 



indeed, succeeded in surmounting most of 

 the objections, even those contained in 

 theoretically delicate problems associated 

 with radiation. Nevertheless, the confu- 

 sion raised by the invocation of Maxwell's 

 'demon' has never quite been calmed; and 

 while Boltzmann (1877, 1878) refers to 

 the second law as a case of probability, 

 Helmholtz (1882) admits that the law is 

 an expression of our inability to deal with 

 the individual atom. Irreversible proc- 

 esses as yet lie quite beyond the pale of 

 thermodynamics. For these the famous 

 inequality of Clausius is the only refuge. 

 The value of an uncompensated transfor- 

 mation is always positive. 



The invention of mechanical systems 

 which more or less fully conform to the 

 second law has not been infrequent. Ideas 

 of this nature have been put forward by 

 Boltzmann (1866, 1872), by Clausius 

 (1870, 1871) and more powerfully by 

 Helmholtz (1884) in his theory of cyclic 

 systems, which in a measure suggested the 

 hidden mechanism at the root of Hertz's 

 dynamics. Gibbs 's (1902) elementary 

 principles of statistical mechanics seem, 

 however, to contain the nearest approach 

 to a logical justification of the second law 

 — an approach which is more than a dy- 

 namical illustration. 



The applications of the first and second 

 laws of thermodynamics are ubiquitous. 

 As interesting instances we may mention 

 the conception of an ideal gas and its prop- 

 erties ; the departure of physical gases from 

 ideality as shown in Kelvin and Joule's 

 plug experiment (1854, 1862) ; the cor- 

 rected temperature scale resulting on the 

 one hand, and the possibility of the modern 

 liquid air refrigerator of Linde and Hamp- 

 son (1895) on the other. Difficulties en- 

 countered in the liquefaction of incoercible 

 gases by Cailletet and Pictet (1877) have 

 vanished even from the hydrogen coercions 



