THE DYNAMICAL EVIDENCE OF THE 



At higher temperatures the curve slopes upwards throughout, and there is 

 nothing corresponding to liquefaction in passing from the rarest to the densest 



fete. 



The molecular theory of the continuity of the liquid and gaseous states 

 forma the subject of an exceedingly ingenious thesis by Mr Johannes Diderick 

 ran der Waals*, a graduate of Leyden. There are certain points in which I 

 think he has fallen into mathematical errors, and his final result is certainly 

 not a complete expression for the interaction of real molecules, but his attack 

 on this difficult question is so able and so brave, that it cannot fail to give 

 a notable impulse to molecular science. It has certainly directed the attention 

 of more than one inquirer to the study of the Low-Dutch language in which 

 it is written. 



The purely thermodynamical relations of the different states of matter do 

 not belong to our subject, as they are independent of particular theories about 

 molecules. I must not, however, omit to mention a most important American 

 contribution to this part of thermodynamics by Prof. Willard Gibbsf, of Yale 

 College, U.S., who has given us a remarkably simple and thoroughly satisfactory 

 method of representing the relations of the different states of matter by means 

 of a model. By means of this model, problems which had long resisted the 

 efforts of myself and others may be solved at once. 



Let us now return to the case of a highly rarefied gas in which the 

 pressure is due entirely to the motion of its particles. It is easy to calculate 

 the mean square of the velocity of the particles from the equation of Clausius, 

 since the volume, the pressure, and the mass are all measurable quantities. 

 Supposing the velocity of every particle the same, the velocity of a molecule 

 of oxygen would be 461 metres per second, of nitrogen 492, and of hydrogen 

 1844, at the temperature of 0C. 



The explanation of the pressure of a gas on the vessel which contains it 

 by the impact of its particles on the surface of the vessel has been suggested 

 at various times by various writers. The fact, however, that gases are not ob- 

 served to disseminate themselves through the atmosphere with velocities at all 

 approaching those just mentioned, remained unexplained, till Clausius, by a 



Ovtr de continuitfit van den gat en vloeistoftoestand. (Leiden : A. W. Sijthoff, 1873.) 

 t " A method of geometrical representation of the thermodynamic properties of substances by means 

 of Burfacea." Trantactions of the Connecticut Academy of Arts and Sciences, Vol. n. Part 2. 



