140 BULLETIN OF THE 



expended by a gas in gaining or losing one degree of temperature 

 (which is known as its " specific heat ") is proportional to this con- 

 stant ratio ; and hence the specific heat of a gas is inversely pro- 

 portional to the molecular mass; — that is to say, to the specific 

 gravity of the gas : — the law of Dulong and Petit. 



As the entire kinetic energy — molecular and atomic, is necessarily 

 tending constantly to a dynamic equilibrium both with regard to 

 any connected volume constituting a system, and with regard to 

 any kinetic energy of the circumambient aether as well, there is a 

 continual and mutual transfer of such energy : — the theory of ex- 

 changes announced by Prevost. 



Mean Length of Molecular Excursions. — By a neat application of 

 the calculus of probabilities, Clausius has determined that of the 

 whole number of free molecular excursions in a given time, (in any 

 large inclosure,) those having less than the mean length will be 

 0.6321 ; or nearly double the number of those having the mean 

 length or exceeding it. He supposes that under ordinary condi- 

 tions, the mean length of a free excursion of our air molecules is 

 about sixty times the mean distance between them. 



Maxwell has pointed out that three phenomena dependent on the 

 length of the free excursions of gaseous molecules, furnish functions 

 from which the mean length of such paths may be estimated ; first, 

 the rate of gaseous diffusion (or the bodily transfer of matter) ; 

 second, the rate of diffusion of their momentum, or the degree of 

 gaseous " viscosity " (dependent on the transfer and equalization of 

 motion); and third, the diffusion of their kinetic energy or temper- 

 ature, (the conduction of heat). In our atmosphere, under ordinary 

 conditions (30 inches and 60° F.) the mean length of the molecular 

 path is thus estimated at about the 1-^-300,000 of an inch, or about 

 one-sixth of a wave-length of yellow light. 



The average molecular velocity of oxygen has been estimated at 

 1640 feet per second;* and of nitrogen (which constitutes about 

 three-fourths of our atmosphere) at 1754lfeet per second ; while 

 hydrogen molecules having but one-sixteenth the weight or mass of 

 those of oxygen, would have under the same conditions, four times 

 their average velocity, or 6560 feet per second. And thus while a 



*A velocity sufficient to carry the molecule vertically about eight miles 

 high, if subjected to no resistance excepting gravitation. 



