358 On the Expansion of certain Substances by Cold. 



When this product is positive, it represents heat which disap- 

 pears ; when negative, heat which appears. 



Neither of those laws indicates any particular relation between 

 the pressure, volume, and temperature of a given mass of a given 

 substance as more probable than any other. The nature of such 

 relations must be determined for each substance by experiment, 

 before the two general laws above stated can be applied to it. 



Hence it appears that it is not the province of the theory of 

 thermo- dynamics to explain the fact of the expansion of certain 

 substances with cold, but simply to deduce the consequences of 

 that fact, so far as they relate to the quantities of heat which 

 are made to appear and disappear by effecting given changes in 

 the volume of those substances*. 



It is true that if we frame a hypothesis as to the molecular 

 structure of matter (such as the hypothesis of molecular vortices), 

 so as to deduce the two laws of thermo- dynamics from those of 

 ordinary mechanics, that hypothesis must lead to many conse- 

 quences besides those two laws ; and it is necessary that those 

 consequences should not be inconsistent with any of the phse- 

 nomena of the relations between the temperature, volume, and 

 elasticity of bodies. No such inconsistency has hitherto been 

 proved; but even were such inconsistencies to be proved, no 

 objection to a molecular hypothesis can affect the certainty of 

 the two laws of thermo-dynamics, which, though at first antici- 

 pated as the results of a hypothesis, have now been indepen- 

 dently established by experiment. 



With respect to the molecular mechanism that may be sup- 

 posed to give rise to the expansion of certain liquids in cooling, 

 near their freezing-points, it appears to me that, so far as our 

 present knowledge enables us to judge, the most probable view is 

 one concurred in by Professor Thomson, viz. that in a liquid 

 near its freezing-point, there is an incipient tendency of the par- 

 ticles to assume a definite arrangement with respect to certain 

 fixed axes ; and that in substances which expand in freezing, 

 that arrangement is such as to make the particles occupy more 

 space than they do in the perfectly liquid state. 



Glasgow, October 10, 1854: 



* One of those consequences was anticipated by Mr. James Thomson, 

 and proved experimentally by Professor WiUiam Thomson, at a time when 

 the theory of thermo-dynamics was in a very imperfect state, viz. that the 

 freezing-point of water is lowered by pressure. 



