356 Mr. Emmet t on the [Not. 



by the two nearest particles, B and D, will be more diminished 

 than that of the more remote, A and C ; consequently the former 

 will recede from, and the latter approach nearer to, each other, 

 and they will become quiescent when, by this change of dist- 

 ance, the forces again attain a mutual equilibrium ; therefore, 

 Euclid, book 1, prop. 36, an augmentation of volume is produced. 

 In the same manner, diminution of temperature is the cause of 

 contraction. 



Cor. 1. — Hence a solid will continue to expand, by reason of 

 this change which takes place in the arrangement of its particles, 

 so long as the centripetal force upon the surface is greater than 

 the force of repulsion. 



Cor. 2. — The greatest possible expansion of a solid has taken 

 place when B D is perpendicular to A C, first demonstration, or 

 when AC = B D in the second: in many forms of matter, the 

 cohesive force may be overcome before this is attained ; in 

 others, after this arrangement has taken place, a considerable 

 increase of heat may be required to cause a separation of the 

 particles, in which state such a mass will retain a considerable 

 cohesive force, and at the same time may be in a semifluid state^: 

 such is melted glass. 



Cor. 3. — Hence no form of matter with which we are 

 acquainted can at any time have been exposed to the true zero 

 of temperature ; for then, by prop. 9, their arrangement must 

 have been such that straight hues which join their centres form 

 equilateral triangles : there could, therefore, be no expansion by 

 the operation of heat, until its repulsive force upon the surface 

 exceeds the force of cohesion. In such substances, the first 

 sensible effect of heat must be a total separation of the atoms. 



Prop. 11. — To find the specific heat and capacity for heat, of 

 a particle of matter. 



Let A, fig. 8, represent a particle of matter, which is 

 immersed in a medium of uniformly diffused caloric ; it is 

 surrounded by a calorific atmosphere, by prop. 6, of which 

 the altitude is half the greatest distance between two par- 

 ticles, i. e. is D E, prop. 7. Let this altitude be B d, and let 

 the curve G F e be the curve K I L of prop. 6, cor. 1, or such 

 that its ordinate F C is always proportional to the density of the 

 caloric, at the distance to which its abscissa B C is proportional. 

 Let the curve H I K be such that its ordinate C I is proportional 

 to the square of the abscissa, i. e. to the concentric spherical 

 superficies. As C moves from B to d, multiply together the 

 ordinates C I and F C, and let the ordinate C M be proportional 

 to this product, and there results a new curve N M L, whose area 

 B N M L <i B represents the whole quantity of caloric contained 

 in a spherical atmosphere surrounding A, and having the altitude 

 B d ; this area, therefore, represents the specific or latent 

 he?it. 



If the temperature be diminished, the altitude and density of 

 the atmosphere will be diminished. Let gf E represent the new 



