PHILOSOPHICAL SOCIETY OF WASHINGTON. 139 



closures at the same temperature (i. e., the same energy) — for equal 

 pressures there must be the same number of impacts on any given 

 area, or in other words that the same volume must contain the same 

 number of molecules whether light or heavy : — the law of Avogadro 

 and of Ampere. 



And conversely, under the same conditions of pressure (or surface 

 impacts) and of temperature (or kinetic energy), the number of 

 molecules being the same, and the masses of the molecules being 

 the only variable, — the densities of different gases must be propor- 

 tional to their molecular weights or the masses of their individual 

 molecules : — the law of Gay-Lussac. 



Since the sum of the moving forces or the expanding power of 

 the molecular excursions is directly proportional to their kinetic 

 energy, it follows that the volume of a true gas under uniform pres- 

 sure must be proportional to this energy, that is to the absolute 

 temperature : — the law of Charles and of Dalton. 



Since the same kinetic energy of the molecules must exert the 

 same impulse, or the temperatures being constant, they must have 

 a definite mean momentum, and each molecule must execute on an 

 average the same number of impacts with the same energy, it fol- 

 lows that the pressure is directly proportional to the number of 

 molecules ; or in other words that the volume of a true gas at any 

 given temperature is inversely proportional to the pressure: — the 

 law of Boyle and Mariotte. Or combining the last two laws, the 

 volume of a gas multiplied by its pressure is directly proportional 

 to the square of the mean molecular velocity, or the absolute tem- 

 perature. The slight departure from the law of Boyle and Mariotte 

 observed in most gases when compressed (the internal pressure be- 

 ing somewhat in defect,) indicates a small range of attraction 

 between the molecules when brought close together.* 



In addition to the external kinetic energy of the molecule due to 

 its velocity of translation, it possesses an internal kinetic energy 

 due to oscillation or rotation of its parts (its constituent atoms) ; 

 and this internal energy<fcccording to Clausius — tends to a constant 

 ratio with the external energy. The amount of energy received or 



* " In the case of carbonic acid and other gases which are easily liquified, 

 this deviation is very great. In all cases, however, except that of hydrogen 

 the pressure is less than that given by Boyle's law, showing that the virial 

 is on the whole due to attractive forces between the molecules." James 

 Clerk Maxwell. (Encyclopced. Brit. 1875 : vol. in, p. 39.) 



