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SCIENCE 



[N. S. Vol. XXXIX. No. 993 



in terms of a certain number of variable 

 parameters, in terms of which two energy 

 functions may be formed, one involving 

 both the parameters and their velocities of 

 change, and called kinetic energy, the 

 other the parameters themselves only, and 

 called potential energy. Now since we can 

 not see the atoms or molecules, and do not 

 know how they move, we can not form 

 these energy functions, and hence can not 

 form the differential equations. But by 

 means of the principle of equivalence, we 

 may determine the sum of the energies, by 

 allowing them to be transformed into heat, 

 and measuring this in a calorimeter. For 

 this purpose we have the valuable thermo- 

 chemical material of Julius Thomsen and 

 others. But later other methods were de- 

 vised of holding chemical reactions in 

 equilibrium, and making them go in either 

 direction reversibly. For instance, a salt, 

 which would dissolve in water or an acid 

 with the emission of heat, could in an elec- 

 trolytic cell, to which a balancing electro- 

 motive force is applied, be dissolved or re- 

 moved from the solution. By distillation the 

 salt could also be removed from the solution, 

 while the use of the semipermeable dia- 

 phragm and the methods of osmotic pressure 

 introduced by van't Hoff furnished a va- 

 riety of methods for the calculation of the 

 energy involved, and the separation of it into 

 two factors, one analogous to a force and the 

 other to a displacement, leading to the defi- 

 nition of chemical affinities. This necessary 

 step being taken, and Rayleigh and Gibbs 

 having shown how the entropy could be 

 computed, the methods of thermodynamics 

 became applicable, and chemistry came un- 

 der the domain of mathematical treatment. 

 During all this time the question had 

 been many times asked whether the second 

 law of thermodynamics and the properties 

 of entropy could not be deduced from 

 purely dynamical principles, so that ther- 



modynamics should be brought under the 

 classification of dynamics. To this ques- 

 tion a negative answer had always been re- 

 turned, although Helmholtz had described 

 a certain sort of system for which the law 

 of entropy applied. It was not until the 

 development of a new method in physics, 

 which though using the principles of pure 

 dynamics, went much farther, that this end 

 seemed to be attained. This was the so- 

 called statistical method, which becomes 

 every day more important, and may sooner 

 or later supersede some of our classical 

 methods involving differential equations. 

 The first example of this was afforded by 

 the kinetic theory of gases, in which the 

 properties of a gas were explained by con- 

 sidering it to be instead of a continuous 

 body, an aggregation of a huge number of 

 small similar molecules, moving about with 

 great velocities in all directions, and by 

 their impacts on each other and the sides 

 of the containing vessel causing the pres- 

 sure. It was at first the custom to treat 

 them as if moving all with a common ve- 

 locity, the directions being distributed at 

 random, but to Maxwell occurred the happy 

 idea of applying the principles of proba- 

 bility or statistics, the method namely of 

 averaging up the actions of a great number 

 of individuals of which we know little or 

 nothing singly. For instance, we know 

 nothing of the direction or magnitude of 

 the velocity of any particular molecule, nor 

 of the direction joining the line of centers 

 of two colliding molecules, but we may as- 

 sume, since we know nothing to the con- 

 trary, that all velocities and directions are 

 represented, and that there are fewer indi- 

 viduals possessing very large or very small 

 velocities than those having some mean ve- 

 locity. The only laws of mechanics made 

 use of were that between impacts the veloc- 

 ity of a particle was constant, and that in 

 each impact the momentum and energy 



