§ l6 OF ARTS AND SCIENCES. 419 



is the ratio of the probable to the mean velocity, and B 

 may be taken as 1.974; W'l?, the total energy contained in 

 the substance; and n is nearly equal to unity. The for- 

 mula indicates, in a general way, the variation of vapor ten- 

 sion with the temperature and in different substances. 

 Solved by the ordinary tables of probability, its results 

 may vary widely from the truth (though seldom by more 

 than one decimal place), which is in part owing to the 

 uncertainty of the true value of W. Were there a table 

 constructed to represent the actual probability of a velocity 

 bearing various ratios to the probable velocity, one might 

 reasonably expect to obtain more accurate results. 



The theory of probability throws much light on the sub- 

 ject of the expansion of liquids near their melting point. 



In the solid or crystalline state, bodies may occupy 

 more or less space than in a state of fusion, according to 

 circumstances; and we conclude that there must exist cer- 

 tain molecular arrangements which are more compact, and 

 others less compact, than a simple chance distribution.'^ 



Whenever a particle contains two or more molecules 

 having, as a system, sufficient velocity to overcome their 

 mutual cohesion, the particle ma}' be said to be in a state 

 of fusion; if, on the other hand, their velocity is so slight 

 that the molecules must return to the same relative posi- 

 tions, the particle may be considered to be solid. 



The principle of the distribution of velocities asserts that 

 in any substance in which the mean velocity is given, 

 there are always a certain number of molecules which 

 have, for the moment, more than twice that velocity, for 

 instance; that no matter how high the temperature may 

 be raised, through the inequalities of chance, there will 

 alwavs be some molecules whose relative velocities are 



* A homely illustration might be derived from architecture, in which the general structure 

 is less aggregated, and the solid portions more so, than the materials would be if completely 

 disarranged. 



