494 heport— 1888. 



determined with sufBcient accuracy at such higher temperatures and 

 lower pressures that they conformed in regard to both compressibility 

 and dilatation as well as do hydrogen, nitrogen, and oxygen under normal 

 conditions, the specific heat of each of the three gaseous compounds men- 

 tioned would behave similarly. But in fact, as will be seen further on, 

 the nature of the molecule itself affects most powerfully the value of the 

 specific heat ; while the specific heat of a gas or vapour increases with 

 rise of temperature, and is independent of the pressure at temperatures 

 such that the gas nearly obeys Boyle's law. 



The 'Ratio of the two Specific Heats. 



The ratio {¥) of specific heat at constant pressure to that at constant 

 volume is greater than unity ; in the case of air and of another gas or 

 mixtures of gases whose dilatation is normal, the maximum value of this 

 ratio was calculated by Clausius to be If, or IQ. This number was by 

 A. Naumann ' supposed to represent the value for gases whose molecules 

 are single atoms and as an example for mercury-vapour. 



Relation of k to the Velocity of Sound, 



The value of the velocity of sound at any given temperature was 

 shown by Laplace to depend on the ratio /.• ; so that experiments on a 

 gas from which the velocity of sound can be deduced give the means of 

 detei-mining k. Now values of the velocity of sound in various media 

 have from time to time been found by a number of experimenters, and 

 from these values in the case of gases or vapours approximate values of 

 h have been calculated. Kundt, after determining the velocity of sound 

 by a new method devised by him in 1866 ^ in a number of solid bodies, 

 applied his method, in conjunction with Warburg,^ in 1868 to a comparison 

 of Jc' for mercury vapour with h for air ; a number of determinations 

 were made with different forms of apparatus, and the mean of the values 

 (1"1886) multiplied by the ratio Jc for air is the ratio k' for mercury 

 vapour. Now Rontgen * found the value 1'405 for air ; hence for mercury 

 vapour 7.;':=l-67^ which is almost exactly the same as the number 1^ 

 calculated by Clausius. 



Specific Meats of Gases and Vapotirs at High Temperatures. 



The results obtained for specific heats of bodies, simple and compound, 

 in the state of gas or vapour, although of great physical importance, 

 admit of no inference of a general nature as to the relations of specific 

 heats to known properties, physical or chemical, of the chemical elements 

 themselves in the free state or in combination. The specific heats of a 

 few elements and compounds which obey Boyle's and Gay-Lussac's laws 

 very nearly in the gaseous state are approximately, within the limits of tem- 

 perature 0° to 200°, independent of pressure and temperature, and are 

 such that the heat-capacities of equal volumes are nearly the same for 

 these gases ; but with all other gases and vapours this is not true, not 

 even approximately for ammonia or chlorine ; and we are far, apparently^ 

 from any very important generalisations with regard to specific heats 



' Avn. Ch. Pharm. 142, 1867, p. 267. = Pogg. Ann. 127, p. 497. 



=» Ibid. 135, pp. 337, 527. * Ibid. 148, p. 980. 



* Ber. 8, 1876, pp. 945-948. 



