Properties of a Molecule in a Substance, 103 



m a the absolute molecular weight of the liquid. We may 

 assume, without any serious error, that on the average the 

 expenditure of energy of a molecule against the attraction 

 of the surrounding molecules during its motion of trans- 

 lation is proportional to the distance traversed, and per unit 

 distance is equal to the above value. Therefore, when a 

 molecule traverses a distance equal to half the distance of 

 separation of the molecules in the liquid (which permits the 

 molecules to have a diameter equal to half their distance of 

 separation), it may on the average lose or gain in energy 



an amount equal to , ? u/ -j • ~^~ a " or undergo a change in 



{dp) •• z 



velocity equal to (_- p */»j 



In the case of ether at 



273° abs. this change in velocity amounts to 1*39 X 10 5 cm./sec., 

 using the internal heat determination of Mills *. The 

 minimum velocity of a molecule, which corresponds to that 

 of a molecule in the gaseous state at the same temperature, 

 is equal to 3'03 x 10 4 cm./sec. We see, therefore, that the 

 average velocity of a molecule in a liquid may be several 

 times that corresponding to its temperature. The same result 

 will be obtained in a different way in a subsequent paper. 



The Pressure exerted by the Molecules. 



According to the kinetic theory of gases, the pressure 

 exerted by a gas in a closed vessel upon its walls is due to the 

 change in momentum the molecules, which are supposed to be 

 in rapid motion, undergo during collision with the walls of the 

 vessel. Now it will be easily seen that the attraction the walls 

 of the vessel exert on a molecule will not affect the magnitude 

 of the change of momentum during collision. The pressure 

 exerted by a molecule will therefore depend only on its 

 minimum velocity — that is, the velocity it possesses when 

 not under the action of any external force — and the number 

 of times it collides per second with the wall of the vessel. 

 Suppose a molecule collides with the wall of the vessel 

 n a times per second. The pressure it exerts is then equal to 

 n a A dynes, where A is a constant which depends only on the 

 nature of the molecule and its temperature. 



The constant A can easily be deduced from the kinetic 

 theory of gases. Consider a perfect gas in which there are 

 N molecules per c.c, each of which has a velocity v. Since 

 the direction of motion of a molecule may lie in an}' direction. 



* Journ. Phy?, Chera. vol. viii. p. 405 (1904). 



