376 /. D. Dana on Cohesive Attraction. 



as there are planes. When therefore the principal axes lose their 

 concentration, this loss consists in a distribution of the force into 

 subordinate axes intermediate between the primary axes. For a 



axes 



have their poles just at the middle point between every two poles 

 of the primary axes ; for a truncation of the angles, the poles 

 would be at the middle point between every three poles. We 

 have remarked upon the symmetrical arrangement of secondary 

 planes in general, and this would follow from the necessary sym- 

 metrical arrangement of such axes. Moreover the length of time 

 /?, will be greater the farther the secondary pole is situated from 

 the primary poles. And this is true in fact. The pole for the 

 octahedron is the most distant, being at the central point between 

 three primary poles.* The number of combined secondary forms 

 may still seem mysterious. But a crystal, in its capacity as a 

 unit, would necessarily have a corresponding character in its dif- 

 ferent parts to the molecules of which it consists, and consequently 

 the attraction exerted by the molecules in these different parts 

 would correspond, occasioning thus the secondary planes. More- 

 over the relative extent of the several different kinds of planes 

 will depend primarily on the relative force of action in the differ- 

 ent sets of axes. 



? 



These considerations lead us to conclude, that 

 XII. The diminution of attracting force i\ 

 which the formation of a secondary depe\ 

 rtial action of this force along intermediate 



7 



situated with reference to the primary axes ; and the greater or 

 less amount of diminution, determines the kind of distribution .f 



13. The same crystalline forms, may have different cleavage 

 in the case of different species of matter. Thus, cubes of gale- 

 na have a cubical cleavage, while cubes of fluor spar have an oc- 

 tahedral cleavage or yield octahedrons when cleaved. In ordi- 

 nary crystallographic language, the cube is therefore said to De 

 the primary of galena, and the regular octahedron is the primary 

 of fluor spar. These different circumstances would result, pro- 

 vided that in one case (for galena) the three primary axes oi t 

 molecule were dominant, and in the other the eight intermedia 

 or octahedral axes. The arrangement of the molecules m ea 

 case would depend on the dominant axes, and so also would 

 direction of the cleavage. Hence, 



Here is evidentl 



iently basis for mathematical calculations of some inter c» j^ ^ . 

 t In the case of substances that very seldom crystallize or never, we diffused 

 dence that the polar forces are very weak. The attractive force may be so 

 as to approximate to the ordinary state in liquids. 



