in producing expansion of Fluids and Solids. 



21 



on the one hand, the elastic force of the caloric itself is greater 

 at the higher temperature, on the other hand, its exercise is 

 probably somewhat modified by the increased capacity of the 

 fluid for caloric, in consequence of the absolute space having 

 been increased by the previous expansion of the fluid. 



We have hitherto supposed the particles of the fluid to be 

 arranged one directly over the other. We are, however, by 

 no means certain that such is the case. Let us now suppose 

 them to be arranged triangularly, so that any four particles shall 

 form an equilateral triangular pyramid. It is evident that they 

 will be arranged in the containing vessel in alternate rows, 



presentmg m a section per: 



oooo 

 ooooo 



oooo 

 ooooo 



appearance. 



pendicular to the base either this 



ooooo 

 Ao-ooo 



ooooo 

 obooo 



or this. 



In 



both cases we perceive that the perpendicular distance between 

 each stratum is less than the distance between the atoms. The 

 distance between each stratum is, however, easily obtained, in 

 terms of the distance between the atoms and their diameter. 

 For let p be the diameter of the atom, t the distance between 

 the atoms, then the perpendicular distance between each stra- 

 tum =r + ( ^^(p + j, as is evident from the particles be- 



ing arranged so as to form in the section equilateral triangles. 



" y ) 



We may further observe, that, if the particles are arranged as 

 in the first case, and the vessel of an hexahedral form, then 

 the number of atoms expelled from the lowest stratum must 

 be a multiple of six, and the number expelled from the stratum 

 above it must be the same multiple of twelve, and so on through 

 the alternate strata, as this is necessary in order to maintain 

 the equidistance of the particles, and consequently the homo- 

 geneity of the fluid. Hence the number of atoms driven off 

 from the lowest stratum being m6, the entire number driven 



off will = '-ml8 = 9sm. It is obvious, however, that this 



