y. D. Dana on Cohesive Attraction. 375 



To understand the origin of planes on an Fi>. 20. 



angle, we must again consider the actual cir- 

 cumstances. Fig. 20 (the same secondary as 

 in fig. 13) will aid the mind in conceiving of 

 it. Here, when the summit particle unites it- 

 self, it adds nothing laterally, as was the case 

 also in fig. 17 ; when another unites beyond, 

 then four particles are united, one by each lateral pole ; but these 

 four add nothing, until still another particle is added to the sum- 

 mit In this case there is an interval of time p, between the ac- 

 tion of the terminal and lateral axes, and another interval p\ be- 

 tween the adding of the four molecules and the action by their 

 lateral axes. And this is the difference between the plane trunca- 

 ting an angle (figs. 9 and 13), and another truncating an edge of a 

 cube, (figs. 7 and 11.) This plane truncating an angle has the 

 ratio 1:1:1. For a plane 1:2:2, the times will be each Jp, 

 and for any plane 1 : m : rc, the times will be ±p and \p. 



It appears that the lateral axes act less speedily therefore for the 

 truncating plane of an angle, than for that of an edge ; the centre 

 of the former in a cube is 54° 44' from the centre of a face of 

 the cube, .and the centre of the latter from the same is 45°. 



We have before observed, that the production of secondary 

 forms depends on the fact, that the force of attraction in the axes 

 of the molecules when secondaries are produced, is less than that 

 which is exerted when the primary prism or cube is formed. But 

 we cannot suppose the whole force of attraction in a molecule to 

 be different in different circumstances. No facts nor reasoning 

 would sustain this conclusion. We may admit that the attraction 

 fray be more concentrated in the primary axes, in some cases than 

 in others. It is well known that the polar condition in bodies 

 does not imply an addition of force, but simply an axial action or 

 concentration of the force. This concentration or excited action 

 m ay be induced by the condition of neighboring bodies or influ- 

 xes : and different bodies should differ widely in their suscepti- 

 bly to it, as is evidently the fact. Now if the attraction is less 

 concentrated in the primary axes, when a secondary plane forms, 

 the interval of time above alluded to as characterizing the forma- 

 tion of different secondaries, will be longer or shorter according 

 t0 the state of concentration in the primary axes. The mere or 

 ,e ss diffused state of the attraction is connected with the kind of 



secondary produced. 



But when we observe in a complex crystal, the evenness ol the 

 feces, the neat regularity of the edges, and the perfection through- 

 °ut, even when many secondary planes are combined, it appears 

 cl ear that such forms could not result from simply a generally dif- 

 fused state of the attraction, any more than a primary could be 

 so produced. In each case there must be as many distinct axes 



