On the Expansion of certain Substances by Cold, - 357 



\, P must vary as X; this furnishes a ready means of deter- 

 mining the lengths of the undulations, and of deciding whether 

 a given light is homogeneous, or what are the different rays 

 which compose it. 



14. The phsenomena of magnetic rotation disappear in sub- 

 stances according as they cease to be mechanically homogeneous 

 and optically isotropic ; it is to be remarked, that among natu- 

 rally birefractive bodies, or bodies rendered so by the application 

 of a mechanical force, those which possess the most energetic 

 powers of rotation are at the same time endowed with the fee- 

 blest powers of double refraction. 



XLV. On the Expansion of certain Substances by Cold. By 

 W. J. Macquorn Rankine, Civil Engineer j F.R.SS. Lond. 

 and Edinb. ^c* 



DURING the discussion which followed the reading of the 

 Rev. Prof. PowelFs Report on Radiant Heat, at the late 

 meeting of the British Association, it appears, from the report 

 in the Athenaum, that a question was proposed by Dr. Stevelly 

 as to the means of reconciling the dynamical theory of heat with 

 the fact of the expansion of water, antimony, cast iron, and bis- 

 muth, by cold, at and near their freezing-points ; and that some 

 observations were made in reply by Professor Powell and Prof. 

 William Thomson. 



The question is one of much importance, and calls for the 

 attention of every one who has been instrumental in maintaining 

 the dynamical theory of heat. Having been prevented by illness 

 from attending the meeting of the Association, I beg leave to 

 offer the following remarks for publication in the Philosophical 

 Magazine. 



The theory of thermo-dynamics, strictly speaking, is a system 

 of propositions, all of which are deducible from the following 

 two laws : — 



I. Heat is convertible with mechanical power. 



II. The mechanical equivalent of the quantity of heat which 

 disappears or appears during any indefinitely small change {dY) 

 of the volume of a given mass of a given substance, at a constant 

 absolute temperature (t), is the product of the following three 

 quantities : the variation of volume, the absolute temperature, 

 and the rate of variation of the expansive pressure (P) with tem- 

 perature at constant volume ; that is to say, 



T-j-dV, 

 dr 



* Communicated by the Author. 



