132 The Rev. J. Bay ma on Molecular Mechanics, [Feb. 11, 



Secondly/. I divided these regular systems into different classes according 

 to their geometrical figure. Of these I have investigated the tetrahedric, 

 octahedric, hexahedric, octohexahedric, pentagonal-dodecahedric, and icosa- 

 hedric. 



I then divided these classes into different species, viz. j)ure centratcp, 

 centro-nucleatce, ceniro-hinucleatce^ centro-trinucleatm, &c., also into acen- 

 tratcB (without centre), truncates, &c. To enumerate the v^hole would take 

 too long ; indeed I only mention these to show how in such a multiplicity 

 of systems I endeavoured to introduce the order necessary for me to be able 

 to speak distinctly about them. 



Lastly, besides classes and species, it was requisite also to consider cer- 

 tain distinct varieties under the same species. And in this way I seemed 

 to myself to have embraced all the regular systems of elements possibly 

 conceivable. 



Thirdly. The several parts of which any system of elements can consist 

 are reduced by me to a centre, nuclei to any number, and an external enve- 

 lope. And thus I obtained not only a method of nomenclature for the dif- 

 ferent systems (a most important point), but also a method of exhibiting 

 each system under brief and intelligible symbols. Thus, e. g., the tetra- 

 hedric system pure centratum (i. e. without any nucleus), in which the 

 centre is an attractive element, and the four elements of the envelope repul- 

 sive, will be represented thus, 



m=A+4R, 



in which expression m signifies the absolute mass of the system (in this case 

 m=5), A represents the attractive centre, and 4R the four repulsive ele- 

 ments of the envelope. The letters A and R are not quantities, but only 

 indices denoting the nature of the action. 

 In a similar way, the following expression 

 m=R+6A + 8R' 



denotes a system whose centre R is repulsive, whose single nucleus 6A 

 is octahedric and attractive, and whose envelope 8R' is hexahedric 

 and repulsive : m, which, as before, indicates the absolute mass of the 

 system, here =15. 



This will sufiice to show how the different species and varieties of the 

 afore-mentioned systems may be named and expressed. 



Then I had to find mechanical formulas for the motion or equilibrium of 

 the several systems ; for it is only from such formulas that we can deter- 

 mine what systems are generally possible in the molecules of bodies. Speak- 

 ing generally, no system pure centratura, of whatever figure it be, can be 

 admitted in the molecules of natural bodies, whether gaseous, liquid, or 

 solid. 



Let V represent the action of the centre, and w that of one of the elements 

 of the envelope for a unit of distance ; and let r be the radius of the system, 

 i. e. the distance o 'any one of the elements of the envelope from the centre ; 



