512 Mr. Rankine on the Centrifugal TJieory of Elasticity, 



are supposed to be those of the atomic nuclei, on whose mutual 

 forces and positions the form of crystallization must depend. 



[Note. — The consequences of this supposition, in the theory 

 of double refraction and polarization, are pointed out and shown 

 to be corroborated by Professor Stokes's experiments on diffrac- 

 tion, in a paper read to the Royal Society of Edinburgh on the 

 2nd of December 1850, and published in the Philosophical Ma- 

 gazine for June 1851.] 



Section II. Investigation of the General Equations between the 

 Heat and the Elasticity of a Gas. 



(5.) I now proceed to investigate the statical relations between 

 the heat and the elasticity of a gaseous body ; that is to say, 

 their relations when both are invariable. The dynamical rela- 

 tions between those phaenomena which involve the principles of 

 the mutual conversion of heat and mechanical power by means 

 of elastic fluids, and of the latent heat of expansion and evapo- 

 ration, form the subject of another paper. 



(6.) It is obvious that, in the condition of perfect fluidity, the 

 forces resulting from attractions and repulsions of the atomic 

 centres or nuclei upon their atmospheres and upon each other, 

 must be considered as being sensibly functions merely of the 

 general density of the body, and as being either wholly inde- 

 pendent of the relative positions of the particles, or equal for so 

 many different positions as to be sensibly independent of them ; 

 for othei-wise a certain degree of viscosity would arise,, and con- 

 stitute an approach to the solid state. For the same reason, in 

 the state of perfect fluidity, each atomic atmosphere must be 

 considered as being sensibly of uniform density in each spherical 

 layer described round the nucleus with a given radius, and the 

 total attractive or repulsive -force on each indefinitely small por- 

 tion of an atmosphere must be considered as acting in a line 

 passing through its nucleus ;• that force, as well as the density, 

 being either independent of the direction of that line, or equal 

 for so many different and symmetrical directions as to be sen- 

 sibly independent of the direction. 



(7.) An indefinite number of equal and similar atoms, under 

 such conditions, will arrange themselves so that the form of their 

 bounding surfaces will be the rhombic dodecahedron, that being 

 the nearest to a sphere of all figures which can be built together 

 in indefinite numbers. 



(8.) I may here explain, that by the term bounding surfaces of 

 the atoms, I understand a series of imaginary surfaces lying be- 

 tween and enveloping the atomic centres, and so placed that at 

 every point in these sui-faces the resultant of the joint actions of 

 all the atomic centres is mUl. To secure the permanent existence 



