1864.] The Rev. J. Bayma on Molecular Mechanics. 



133 



the general formula of motion for any system pure centratim (expressed as 

 above by m=A+wR) will be 



_ = -_(.-M»). 



where M signifies a constant, and the actions which tend to increase r are 

 taken as positive. 



If the system is tetrahedric, M = • 9 1 8 5 6 

 octahedric, M= 1-66430 

 „ hexahedric, M= 2*4 6 75 9 



„ octohexahedric, M =4-111/0 



„ icosahedric, M=4- 19000 



pentagonal dodecahedric, M= 7*824 19. 

 Now none of these varieties satisfies the conditions either of solid, liquid, 

 or gaseous bodies ; because they either will not resist compression, or they 

 form masses which are repulsive at all great distances ; or if they could 

 constitute gaseous bodies, they do not allow the law of compression to be 

 verified, which we know to hold for all gases. 



Passing on to the systems centro-nucleata, the formulas will differ according 

 to the several figures of the nuclei and envelope. Taking, e. g.^ the system 

 m=R4-6A + 8R', 



which is hexahedric with an octahedric nucleus, and taking v, v'y w to 

 represent respectively the actions of the centre, one element of the nucleus, 

 and one element of the envelope ; taking also r and p for the radii of the 

 nucleus and envelope, the equations of motion for such a system will be 



where M=2-46759, and M'= 1*66430. The conditions of equilibrium * 

 will be obtained by making the two first members equal to zero. 



What systems of this class {centro-nucleata) can satisfy the conditions 

 of solid, liquid, or gaseous bodies, is exceedingly difficult to determine, for 

 reasons which I have above touched on, viz. that the formulae of these 

 systems are not integrable, and we have consequently to proceed indirectly 

 with great expenditure of time and trouble. It seems to me, however, as 

 far as I can judge, that some of these systems may be found in rerum 

 natura. 



Passing to another class of systems {centro-hinucleatd)y we shall have 

 three equations to express its laws of motion. Taking, e, g., the system 



7«=A + 4R + 4A'4-4R', 



