11>3 DIRECT PROPERTIES OF MOLECULES 343 



clearly from a memoir by Gustav Liibeck, 1 who in- 

 vestigates the laws of the collision of massive particles 

 without introducing any further suppositions than the 

 above-named theorems. It follows that these assumptions 

 are sufficient to determine the velocities with which the 

 colliding particles separate from each other after an en- 

 counter when the velocities which the particles possessed 

 before the encounter are known. We easily see, for instance, 

 without calculation for direct impact, that from the two pro- 

 positions of the conservation of kinetic energy and of the 

 conservation of the motion of the centre of gravity we 

 obtain two equations, which must be sufficient to fully de- 

 termine the two unknown values of the velocities after the 

 impact. The same thing holds in the more general case of 

 oblique impact, in which only the number of unknown 

 magnitudes is greater since several components come into 

 account. 



We may from this conclude that the validity of the laws 

 which determine the change of the motions on the occur- 

 rence of an elastic impact is not confined to the case of 

 elastic bodies, but presupposes only that the above-named 

 theorems of mechanics hold good. We may therefore 

 assume that the laws of elastic impact are valid for the 

 encounters of molecules also without thereby ascribing elas- 

 ticity to the molecules themselves. 



If according to this the answer to the question, what 

 forces are developed at an encounter of two gaseous mole- 

 cules, does not touch the foundation of the kinetic theory, 

 that question still remains so important and interesting that 

 we cannot pass it over in silence. 



In memoirs upon this theory, and especially in the older 

 ones, we often meet with the assumption that two molecules 

 behave during an encounter like two elastic bodies, or even 

 like two elastic spheres. This hypothesis has much that is 

 tempting about it from the ease with which it can be 

 handled ; but the difficulty would only be transferred, and 

 not overcome, if we proposed to explain the elasticity of 

 gases by the elasticity of the molecules. 



1 Schlomilch's Zeitschr. f. Math. u. Physik, 1877, 22. Jahrg. p. 126. 



