123 DIRECT PROPERTIES OF MOLECULES 345 



attractive forces act only at quite small distances, he obtains 

 the very same laws for an encounter which Maxwell ob- 

 tained with his repulsive forces. This result is in excellent 

 agreement with Liibeck's proposition, of which we have 

 made mention. We may therefore consider all the forces 

 as attractive which gaseous molecules exert upon each 

 other, whether at large or small distances apart. This 

 corresponds to the experimental results of Joule and Lord 

 Kelvin as to the heat-effects of flowing gases, and also 

 no less to the ideas employed by Sutherland to explain 

 the large variation of the coefficient of viscosity with the 

 temperature. 



The law of variation of the strength of these attractive^ 

 forces with the distance between the particles cannot yet be 

 decided from our present knowledge. It j^jioweyer, guite 

 possible to calculate, or at least to estimate, the amount of 

 the energy that comes into play during the action of these 

 unEown" forces. This is just as possible ~as it was possible 

 to estimate the energy of the heat contained in a body 

 without its being necessary to know the law of the molecular 

 movement in which heat consists. 



Boltzmann 1 has made a first essay in this direction, 

 and has thereby proved that we have to do with forces 

 of extraordinarily great intensity. In this calculation 

 Boltzmann introduces manifold hypothetical suppositions 

 which are approximately admissible for every case ; we may 

 especially mention that, just as we did in former para- 

 graphs, he looks upon the molecules themselves as the same 

 in the liquid and gaseous states, and upon their motions only 

 as different. 



With Boltzmann we will first of all calculate the 

 amount of energy needed for two molecules of water, whose 

 mean distance apart is p, to approach each other by the 

 length xp, so that their distance apart is reduced to (1 x)p. 

 For this we make use of a result of Gr as si's experiments 

 on the compressibility of liquids, viz. that water is com- 

 pressed by 0*000048 of its volume by the pressure of one 

 atmosphere, so that by the addition of an atmosphere to 



1 Wien. Sitzungsber. 1872, Ixvi. Abth. 2, p. 213. 



