404 Dr. H. Hervyig on the Expansion 



(5) The weight of the mercury which occupies the length 

 of a millimetre in the cylindrical part of the tube at the 

 temperature 6 3 ; let this be u. 

 With these data the entire calculation can be effected. 



§2. 

 Two formulas especially present themselves from which we may 

 endeavour to judge of the behaviour of superheated vapour. Let 

 p, v, and t be the values of pressure, volume, and temperature 

 (Celsius) of a determined weight of superheated vapour; we 

 can either put 



pv = 4> (273 + /), 

 where <f> is then a variable whose law of variation must be sought, 

 or we can put 



pv=C(E + t), 



where E is such a variable, but C is a constant dependent on 

 the quantity by weight of the vapour. 



The latter formula was applied by Fairbairn and Tate* to 

 their observations on steam (to be considered further on). I 

 have not chosen it, because, with the proportions of my experi- 

 ments, the results calculated after this formula must have given 

 less striking numbers than those calculated according to the 

 first. We shall easily be convinced of this from the following. 



Thus, if we take the formula 



pv=<f>(273 + t), 



it is only when the vapour exhibits the behaviour of a perfect 

 gas that <£ becomes a constant depending on the weight of the 

 vapour. At the same temperature t } for dry air, we have 



PV=R(273 + Z), 



where P and V denote pressure and volume, and R is a constant 

 depending on the quantity of air employed. This equation pre- 

 supposes, of course, the full validity of Mariotte and Gay-Lus- 

 sac's law. 



From the two equations we get 



i) -P=(273 + 0(t-?> 

 Putting p-?=U, 



according to which I have calculated my observations. 

 * Phil. Trans. 1862, p. 591. 



