PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 821 



indicated by pins stuck through the wax.* The tigure is a pro- 

 jection upon a plane -which makes an angle of 45° with each of 

 the three rectangular axes. Those portions of the orbits lying 

 above the phiue of the paper are represented with unbroken lines 

 and the atoms on them are made black, while below this plane the 

 lines are dotted and the atoms open. The circumscribing dotted 

 circle is the section of the imaginar}'' sphere of the molecule made 

 b}^ the paper. This circle will be called the dynamical equatov, for 

 reasons Avhich will presently appear. The two dynamical poles of 

 this equator are projected at G, and are the points where the 

 dynamical axis, a line passing through the centre of the molecule 

 at right angles to the plane of the dynamical equator, intersects the 

 surface of the molecular sphere. The six atoms A, B, C, D, E, 

 and F, are moving in the directions indicated by the arrows, and 

 each orbital pole is successively occupied, first by the atom of one 

 plane and then by that of the other, of the two whose intersoctiou 

 forms the axis of that pole. 



The question now naturally' arises, whether the atoms of a sys- 

 tem so constituted can continue to move in stable equilibrium. 

 While an analytical discussion of the question may prove exces- 

 sively intricate and difficult, the following simple geometrical 

 presentation is believed to demonstrate the stability of the molecule. 



We will first suppose that at the instant, represented in Fig. 5, 

 the six atoms are in a state of equilibrium, i. e., the centrifuo-al 

 and centripetal forces of each are balanced. Since in this posi- 

 tion the atoms are distributed at equal distances around their com- 

 mon centre of gravity, G, the resultant of gravitating force acting 

 upon each one is in the direction of that centre, and all these 

 resultants and the velocities of the atoms must be exactly equal. 



Let us now suppose that each atom has moved an iudefinitdy 

 small distance in the direction of the arrows to the positions rep- 

 resented in Fig. 6. Since the initial velocities were equal, the 

 small distances traversed will be equal, and they may be taken so 

 small that the paths will not differ materially from arcs of the cir- 

 cular orbits represented. 



The resultant forces acting upon each of the atoms, in its new 



position, is now to be considered. The atom H is acted upon by 



'its companion atom K, in the direction of the centre G, and with 



* A model of this kind was exhibited when this paper was read, and the demonstration 

 here given was illustrated by it. 



