By Professor Pell. 5 



remain. "Witli a greater velocity it will pass beyond B, and the 

 solid connection between the atoms will be destroyed. It may 

 be seen without any mathematical investigation that the vibratory 

 motion about A produces two eifects. 



(1) It increases the mean distance between the atoms ; that is, 

 it produces expansion. 



(2.) It diminishes the cohesive force between the atoms ; that 

 is, it produces softening. 



If the initial velocity be sufficient to carry the atom to B, the 

 cohesive force is entirely destroyed, and the condition is that of 

 perfect liquidity ; the mean distance between the atoms being 

 then OB. It may be observed that the greater the initial velocity, 

 and the more nearly in consequence the atom approaches B, the 

 position of unstable equilibrium, the greater is the proportion of 

 energy in the potential or latent state. If the atom just reaches 

 B, the whole energy becomes latent. 



With reference to the obvious objections that the liquid state, 

 as thus represented, is one of absolute instability, and that the 

 whole of the heat appears to become latent, I must remark in the 

 first place, that probably the liquid condition cannot exist with 

 any permanence except under the combined effects of tempera- 

 ture and pressure ; and in the second place, I must anticipate so 

 much as to say, that I hope to succeed in shewing that it is pro- 

 bable that the atoms of a solid, under the action of heat, aggre- 

 gate themselves into molecules, and assume the liquid and 

 gaseous condition, at a far lower temperature than what could 

 correspond to the velocity necessary to the carry the atom from 

 A to B. That velocity corresponds, not to the melting point of 

 the substance, but to the far higher temperature, higher perhaps 

 than any at present existing in the solar system, under which a 

 molecule would be resolved into atoms. 



If X be the distance between the atoms, and/" (x) the dynami- 

 cal measure of the attraction between them, the conditions which 

 have been stated mav be approximately expressed by supposing 



f{x) = ix-a) i^-xY^i:.) 

 where OA = «, OB = /S, and p (^x) is a function which does not 

 change sensibly within the small limits a; = a, a? = /3. Let 

 fi — a = h, X = u -\- z, h and z being supposed small compared 

 with u, then 



f{x)=Z [h - zY ^{a + z) 



= z {h — zY <^ (a) nearly 

 Put/ (a) == h^ <p («) = W-, then 



/ (a?) = m- ^ ( 1 — -^- ) 



