820 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



"Why does the polar force remain dormant in the liquid, and sud- 

 denly start into existence at the instant of solidification ? Why is 

 it confined to six mere points on the surface of the ellipsoid ? To 

 these inquiries, the most diligent questioners of nature seem as yet 

 to have received no satisfactory answer. 



What will now be offered, is barely more than a suggestion, 

 which is thrown out with the hope that the new field of inquiry 

 thus indicated, will, in skillful hands, prove prolific of fruitful 

 results. 



Upon the surface of the primary ellipsoid of Wollaston and 

 Dana suppose three ellipses to be described by the intersection of 

 bisecting planes parallel with the sides of the circumscribing prism 

 and to the planes of crystallization. These three ellipses Avill 

 intersect each other at the six poles of crystalline attraction. Ee- 

 moving the ellipsoid, we will retain only the imaginary ellipses, to 

 represent the orbits of the three pairs of atoms, which we have 

 already considered as forming the molecule in the liquid and gase- 

 ous states, one pair of atoms revolving in each orbit. 



To account for the ellipsoidal forms of the molecules, we have 

 only to bear in mind that in a body of uniform temperature the 

 mean momenta of the atoms are equal. If therefore the pairs 

 forming a molecule are unequal in inertia, it follows that the 

 heavier pairs will move in shorter orbits. 



The analytical investigation of the motion of six or more atoms, 

 subject to mutual gravitatious, seems, at the first glance, to be too 

 complicated a problem for the human intellect. It will be found, 

 however, to possess ceft'tain features of symmetry, which will per- 

 haps l)ring it practically within the grasp of the mathematician. 

 To illustrate this symmetry, we will bestow a passing glance upon 

 the most simple case of the ellipsoidal molecule, viz., that with 

 equal axes, or the true sphere, in which the three orbits are circles, 

 intersectino; each other at right auijles. 



By the diminution of heat or momentum, the long elliptical 

 orbits of the liquid have been rounded into circles which intersect 

 each other at the six poles. A system of this kind is shown in 

 figure 5, which represents the molecule at the instant when each 

 pole is occupied by an atom. A more convenient way, however, 

 to study the relative motions of the atoms, is by constructing a 

 wire model of the intersecting orbits, upon which bits of wax may 

 be placed to represent atoms. The directions of motion may be 



