1820.] Mathematical Principles of Chemical Philosophy. 357 



curve, and multiply, as before, its ordiiiates into the correspond- 

 ing ordinates of the curve H I K, and the resulting curve is 

 « m I, whose area B « m / D B represents the whole of the latent 

 heat, and the difference, or the area D rZ L N n m I D, is propor- 

 tional to the quantity of caloric liberated by this reduction of 

 temperature, or to the capacity for heat. 



Cor. 1. — Hence the capacity for heat must be greater at high 

 than at low temperatures. 



Cor. 2. — Hence all bodies having the same density may not 

 have the same capacity for heat at the same temperature. 



Cor. 3. — Hence the true capacities of bodies for heat must be 

 those of weights which are proportional to those of their atoms. 



Cor. 4. — Hence the reason why the quantity of caloric which 

 is represented by the area B N L D cannot aftect the thermome- 

 ter, that instrument indicating the elastic force with which the 

 caloric endeavours to escape. 



Cor. 5. — The real capacities of bodies for heat must be in the 

 ratio of the evanescent increments of the area B N L D, belong- 

 ing to each. 



By help of these propositions, many curious phenomena admit 

 of an easy explanation. By considering caloric an elastic fluid, 

 which is attracted by every form of ponderable matter, we find 

 that in solid matter, the particles are always preserved in mutual 

 contact with each other by the cohesive force, by prop. 1 and 4 : 

 that variation of temperature, by causing a change to take place 

 in the order of their arrangement, prop. 10, produces expansion 

 and contraction, the utmost limits of which are small, compared 

 with the entire volume, and that the cohesive force of solids is 

 less at high than at low temperatures. From which facts it 

 follows, that the true ratio of the expansibility of the various 

 forms of solid matter is not that of equal lengths, but of lengths 

 which are proportional to the diameters of their atoms ; the ratio 

 of the diameters of the atoms of simple solids is easily ascertained 

 nearly by knowing the specific gravity and the atomic weights. 

 We may also see the reason why all solids do not expand equally 

 by the apphcation of equal increments of heat; for the particles 

 of different solids have various diameters and degrees of centri- 

 petal force, and consequently have calorific atmospheres of 

 different density. 



The whole quantity of caloric which is contained in any mass 

 of matter being the sum of all the calorific atmospheres ; and the 

 capacity for heat being the sum of all the increments of these 

 atmospheres by an increase of heat ; it is evident that the real 

 ratio of the capacities of bodies for heat is not that of equal 

 weights or volumes, but of weights which are proportional to 

 then- atomic weights. It is also manifest, prop. 11, that the 

 capacities will be somewhat greater at high than at low temper- 

 atures. 



By prop. 11, masses of matter will be surrounded by calorifio 



