By Professor Pell. 17 



points at once, for the weakening of the connection between tlie 

 groups would impede tlie propagation of the disturbance. The 

 first group would first melt off; or if the temperature were 

 higher, would fly off" as a molecule of vapour ; and the next group 

 would then be directly exposed to the disturbance, and be melted 

 or evaporated in its turn. It should be observed that the energy 

 employed in severing the cormection between the groups, does 

 not increase the temperature, but becomes latent. I must remark 

 here that the liquid condition would be better accounted for, and 

 some other phenomena perhaps explained, by supposing the 

 three roots equal to j3 of the equation _/ (a;) = 0, to be replaced 

 by three roots nearly equal to each other ; that is roots whose 

 differences are generally small compared with h. If it be objected 

 that I am assuming an unnaturally complicated and fantastic 

 law, I can only repeat that it is not assumed arbitrarily, but is 

 little more than a reflex of plain facts. If all the various phe- 

 nomena relating to inorganic matter, are to be accounted for by 

 the motions of atoms acting upon one another according to some 

 one law ; and this assumption must be the foundation of every 

 such attempt as the present ; it is hardly reasonable to suppose 

 that the law of action which is to be the cause of such a vast 

 variety of complex relations, should be of a very simple kind. 



Having considered the motion of the system whilst being 

 heated as it were, let us now consider what would occur, if the 

 disturbance were to cease, and the system be left to vibrate of 

 itself When |U, ^ is any multiple of 2 tt 



cos (2 » — 2 r + 1) \^ d X ^ 



cos (2 ?i + 1) 4/ ' dt 



At any such instant let the disturbing atom be removed, and 

 we have for the subsequent motion, the initial conditions 



P « = '• ""^(^"-a-' + iH (,,) ^ 



cos (2 « + 1) v|/ ^ 



"We suppose that the system is an aggregation of molecules, 

 formed as above described, under the action of the prevailing 

 heat ; so that « is a multiple p v oi p, and if 2 ^ i|; = tt exactly, 

 we have 



o , .^ C0s(2r-1)^ cto^{2r~-l)vy 

 2n^ = V7:,<p (r) = a ±1 = a ^ 1 L 



cos 



COS V 



Eeferring to equation (6), S (p (?•) = 



2 <p (r) COS (2 r — 1 s y 

 a 



-2 COS (2 r — 1) ^"/ COS (2 r — 1) ^ y 



