502 EEroRT— 1888. 



to chlorine and iodine, and prefers interpreting the diminishing density 

 of both at very high temperatures by admitting these to be among 

 namerous exceptions to Boyle's and Gay-Liissac's laws ; 'there exists,' he 

 says, p. 88, ' no valid reason for preferring, in the definition of tempera- 

 tures, the indications of an air-thermometer to those of a chlorine-ther- 

 mometer.' Now Sir W. Thomson 1 had shown that Carnot's function 

 affords a foundation for a system of thermometry not dependent on 

 special properties of some individual substance, but derivable from the 

 properties of any substance whatever ; and in conjunction with Joule 

 published a series of investigations ' On the Thermal Effects of Fluids in 

 Motion ' ^ in which the authors arrived at a means of estimating tempera- 

 tures on an absolute scale. 



The definition given ^ shows the principle on which the absolute 

 system of thermometry is founded, by which temperatures are measured 

 on ' the thermodynamic scale ' ; ' if any substance whatever, subjected to 

 a perfectly reversible cycle of operations, takes in heat only in a locality 

 kept at a uniform temperature, and emits heat only in another locality 

 kept at a uniform temperature, the temperatures of these localities are 

 proportional to the quantities of heat taken in or emitted at them in a 

 complete cycle of the operations.' 



From the experiments of Joule and Thomson, in ■which gases, e.g., air 

 (hydrogen ; and carbon dioxide) was made to pass through a porous plug 

 at various pressures, the change of temperature being observed, results 

 ■were obtained by means of which a formula was deduced, giving the 

 absolute temperature in terms of the temperature by the air-thermometer, 

 and a table of corrections for temperatures from 0° C. up to 300" C. by 

 which these air-thermometer temperatures might be converted into tem- 

 peratures on the thermodynamic scale ; the correction not exceeding, 

 within this range of temperatures, half a degree on either scale whether 

 for air at constant pressure or for air at constant volume. 



Relation of Volume to Temper atti,re — Solids and Liquids. 



The rates of expansion of bodies in the solid and Uquid states are very 

 much smaller in general than in the gaseous state ; this rule does not 

 always hold, however, for liquids under the critical point when subjected 

 to great pressures, as shown first by Thilorier for CO^, the expansion of 

 "which in the liquid state under the conditions specified exceeds that of 

 gaseous CO2. 



Solids. 



For solids a very large number of results, sufficiently accurate for the 

 purpose at least of drawing an inference of a general kind, were obtained 

 by a number of experimenters about the end of last century and the 

 beginning of this, showing that the coefficients of linear expansion of a 

 large number of metals and alloys, and of glass, between 0° and 100° lie 

 in general between 10"^ and 3 x 10"^ ; to these have been added results 

 got by Dulong, Regnault, Kopp, for metals and other elements, for 

 varieties of glass, and for a number of minerals for this temperature- 

 range, and for higher temperatures in some cases ; by Playfair and Joule 

 for a number of crystalline compounds ; * by PfafF,-' and by others. 



' Cavih. Phil. Soc. Proc. June 5, 18-18 ; and Phil. 3Iag. Oct. 1848. 

 = Phil Trans. 1853, 1854. ^ 7j,-^_ i8o4, p. 351. 



* C. S. J. 1, 1849, p. 121. " Jahresb. 1858, p. 7. 



