Kinetic Theory of Solids. 539 



to see how an increase of only 2 per cent, in the distance 

 apart of the molecules can give them the freedom and mo- 

 bility of the liquid state. But if while heat is driving the 

 molecules apart from oue another it is also shrinking each, 

 the difficulty disappears, for if the shrinkage is six times the 

 expansion then at the melting-point the distance apart of the 

 molecules is nearly 16 per cent, greater than the diameter of 

 the molecule ; that is to say, the complete swing of the vibra- 

 tion is 16 per cent., and when two molecules have swung to 

 their greatest distance apart that distance will be 16 per cent. 

 greater than the diameter of the molecule. This is sufficient 

 to make melting quite comprehensible. Let us take a definite 

 instance : suppose four molecules at absolute zero in contact 

 so that their centres form a square of side E , and as the 

 temperature rises, suppose each to oscillate along a diagonal, 

 then the maximum distance apart of the opposite molecules 

 becomes 1*16 V 2 times the diameter of the molecule, that is 

 1*63 times, so that a molecule vibrating at right angles to the 

 plane of the square towards its centre, would, if it arrived at 

 the right moment, find an open space whose narrowest part 

 is "63 times its own diameter. This shows how, in the various 

 combinations possible in a large number of molecules, several 

 can occur favourable to the escape of a single molecule in a 

 neighbourhood, and a sufficient number of such escapes, even 

 though a small number, would upset the stability of the whole 

 system, which falls into the mobility of a liquid. This theory 

 of melting can be roughly tested by experiment; it is only 

 necessary to agitate a number of equal spheres in a closed 

 box and observe what ratio the free space bears to the volumes 

 of the spheres when each sphere acquires a noticeable amount 

 of mobility. I took a box which, when closed, just held 100 

 marbles, with five specially coloured ones placed near the 

 centre, and then noted how many had to be removed from 

 the box to allow the five coloured ones to scatter on agita- 

 tion ; a slight motion of the five as a body was not accepted 

 as a sign of mobility. It was necessary to remove 16 to get 

 slow and partial scattering of the central 5, and 20 or 25 to 

 get quick and decided scattering. Thus for mobility among 

 a set of marbles the free volume must be between 25 and 33 

 per cent, of the volume of the marbles. Of course the cir- 

 cumstances are in most ways vastly different from those of 

 perfectly rebounding swiftly moving molecules, but the com- 

 parison was worth making in passing. In the case of mole- 

 cules mobility is reached when the free volume is 1*16 3 — 1, 

 or 50 per cent, of the volume of the molecules. But the 

 melting volumes of the metals give more definite evidence. 



