Steam of Maximum Density . 1 79 



It has already been shown that d . log P = a -. On di- 



( i+ ;) r 



viding the latter equation by the former, we have 



rf.logP /: t\~ n 



7 . p =aa(l + -) =uap- n = < 

 d.logp \ a} 



on putting jo = l+ -=e'i so that ^=hyplogjo, then 



«ae' 



■nt x 



a 



' ° g =aae~ nt i and d . log P = a«e~ n ^ <# ; 

 integrating, we get 



log P = constant — —e~ nt ^ = — I 1 — e-^i \ . 

 n n L J 



which agrees with the general equation first obtained. 



It has been shown that d . log P varies as (1 + -) k , and 



d.logp as ( 1 + ~) . The quantity a, which is common to 



both expressions, is the most important constant in the laws 

 of steam and other vapours, and probably in the laws of liquids 

 and solids also. At the zero of the Centigrade thermometer 

 (the temperature of melting ice) a is equal to 276 Centigrade 

 degrees. This number represents the absolute temperature of 

 melting ice, measured from an ideal fixed point at which all heat 

 disappears. This number approaches very near to the recipro- 

 cal of the coefficient of expansion of gases whose elasticity is 

 nearly perfect, and probably would be found exactly equal to 

 such reciprocal if a gas of perfect elasticity could be found. 

 At the zero of the Centigrade thermometer, in atmospheric air 

 of the ordinary density for that temperature, the coefficient of 



expansion per degree is -003665= , nearly as determined 



by M. Regnault (page 73). According to the same authority 

 (page 120), the coefficients of expansion of different gases ap- 

 proach nearer to equality with one another according as their 

 densities diminish ; and he believes that it is not improbable 

 that the supposed law, that all gases have the same coefficient 

 of expansion, may be true when their densities are indefinitely 

 diminished. In air of the temperature of melting ice and of 

 density 4*810, he found (page 110) the coefficient of expansion 



to be k^qt^; and in air of density 0*144 to be 9 . Accord- 

 ing to these two experiments, there is a difference of 4°*8 C. in 



