Attraction of Mass, and some New Gas Equations. 73 



273 

 in which $ = : W- . i?, /3 and j3t are the co-volumes at the 



volumes v and <f> and 0°. In this expression consequently 

 v is the volume of cp reduced to 0° and r =l at n =l, 

 i. e. the experimental value of the volume. 



In other words, for the same relative change of the " free 



space " (jcjy — fft) or (v — ~=o & J for a gas at 0°, we obtain the 



same change of pressure II : we have reduced the actual gas 

 as regards pressure-changes to a perfect gas for which they 

 are only dependent on the changes of volume, whatever 

 the temperature T. The volume at the temperature T is 

 ■</}=: nbt, and atO°tJ = ?i. b , but the pressure II is the same ; 

 and the expression given by (16 c) applies to any temperature 

 between T c and 273, if T c >273, whatever the compression 

 at the temperature T from n o =l to II. 



If T c <273, then for any temperature between T c and 273 

 we have similarly : 



n = <Hk 1_ (n + l)6« 1 _(n+l)& 1 



d> ' <b n.b t ' n.bt n. b Q ' 273 , 



hjt n . b 



v + b Q 111 



v '273 273 (/>-&' 



~T' V T^-A) (16rf) 



in which <p is expressed in 6t = l, T, and 11 = 1? 



T T 



-6 =^yr, b t , r=Ty7T</). and v has the experimental value, 



reduced to <£* = 1, T°, and n o =l, and we have the gas 

 for temperatures below 0° in the same condition as above 

 that temperature. 



(We could of course just as well reverse the proceedings 

 and express the volume of a gas for temperatures >273 in <f> 

 in respect of <£*=1, at T c ° and 11 = 1, etc.) 



Making II of equations (16 a) and (16 b) equal to p-f 2p ls 

 we obtain for T>273, 



T 



9r 97* (* + *<) l 1 



for any temperature T (in which c is the constant of attraction 

 at t?o = l, 0° C, and 760 mm.), and always equal to 



2c v + b 1 1 /ia n 



j. v - v v v — p 



