66 Royal Society: — 



If we put p=ep, and calculate the values of p for each of the 

 above experiments, it will be found that these, values diminish 

 regularly as the pressure increases at each temperature, with the 

 exception of the last observation at 64°, where the value of p is 

 greater than at the preceding observation. This change of direc- 

 tion in the value of p is explained by the circumstance already 

 mentioned, that the carbonic acid at the higher pressure has been 

 reduced to the liquid volume (although no liquefaction has taken 

 place) in passing through the conditions of matter intermediate be- 

 tween the gaseous and liquid states. 



The relations between the volumetric curves in the ordinary 

 gaseous state for different temperatures are determined by means 

 of what the author calls the homologues or homologous points of 

 those curves — that is, the points in any two isothermals where the 

 values of p are equal, or 



pv=2 :) ' v ' 0^-) 



From a careful analysis of the experiments described in this com- 

 munication and in his former Bakerian Lecture, the author shows 

 that the ordinary gaseous state is characterized by the ratio of the 

 external pressures for all the homologues of any two given tempe- 

 ratures being constant, or 



|=1l' '•••(B) 



where H\ is a constant. It must be carefully observed that v and 

 v in equation (A) are the volumes of the gas on different iso- 

 thermals. 



It follows from these results that, in the case of a body in the 

 ordinary gaseous state, if the relations of pressure and volume are 

 known at any one temperature, the corresponding relations at any 

 other temperature can be calculated from the observation of a single 

 homologue at the second temperature. Thus the whole relations of 

 volume and pressure will be known from a set of primary obser- 

 vations at a fixed temperature and the determination of one 

 homologue for each of the other temperatures. 



The general form of the primary curve itself, or curve exhibiting 

 the relations of pressure and volume at a given temperature, is next 

 investigated ; and the author finds, as the result of, all his experi- 

 ments under very varied conditions of temperature and pressure, 

 that the value of e(l— p) is constant for the same temperature. 

 Hence we have for the third equation of the ordinary gaseous state 



v(l- 2 w) = c ..(C) 



From this last equation the relations of homologous points, as 

 defined by equations (A) and (B), may be deduced. 



The author concludes with some general observations on the 

 action of the internal attractive forces in the ordinary gaseous state, 

 and also on the resistance to diminution of volume, which, under 

 certain conditions, modifies largely the effects both of external 

 pressure and of internal attraction. 



