342 DIRECT PROPERTIES OF MOLECULES 123 



these hypotheses. The kinetic theory of gases is based on 

 firmer ground than that it should stand or fall with one 

 of these hypotheses. 



Even though a decision respecting these hypotheses is 

 therefore not necessary for our theory, the question still 

 arises, whether absolutely no hypothesis at all as to the 

 process of an encounter has been introduced into our de- 

 monstration or general assumptions have tacitly been made. 

 The answer lies in the remarks which I have made in 25 

 with respect to the basis of Maxwell's law, as to the dis- 

 tribution of the different values of the speed among the 

 individual molecules. 



Some general theorems of analytical mechanics have in 

 fact been introduced into our reasoning as the conditioning 

 assumptions upon which that important law rests ; first and 

 ^/foremost the proposition of the conservation of energy, then 

 some less important theorems which are generally looked 

 upon as conditions of that proposition, viz. the theorem of 

 the equality of action and reaction, and, lastly, the theorem 

 of the conservation of the motion of the centre of gravity of 

 two molecules both before and after an encounter. In addi- 

 tion to these, the hypothesis has also been made that the 

 duration of an encounter is very small in comparison with 

 the interval between two encounters. Other assumptions 

 were not necessary. 



The assumptions enumerated are all satisfied, both if 

 the molecules are perfectly elastic and if they act on each 

 other with forces which fall off very rapidly as the distance 

 increases and which are therefore only sensible at exceedingly 

 small distances. They can also be fulfilled with other laws 

 of impact, as, for instance, when two absolutely hard bodies 

 collide, the hardness of which, together with the impossi- 

 bility of compressing them, causes a repulsive force to come 

 suddenly into play at the moment of the collision. 



This follows from Poinsot's 1 investigations on impact, 

 so far as his results relate to perfectly elastic and absolutely 

 hard bodies. The correctness of this view is seen more 



1 Liouville's Journ. de Math. [2] 1857, ii. p. 281; 1859, iv. p. 421; 

 Schlomilch's Zeitschr.f. Math. u. Physik, 1858, 3. Jahrg. pp. 143, 274. 



