Formation of Compound or Twin Crystals. 283 



object of the memoir, the explanation of twin crystals according to 

 the principles of the theory, will be attempted. 



Similar secondary planes are invariably situated at equal distan- 

 ces from similar crystallogenic axes, and when a point in a molecule 

 has a secondary plane tangent to it, or rather parallel to a tangent 

 to this point, all similarly situated points will also have their tangent 

 planes. This is but another statement of the fundamental principle 

 in Crystallography, that similar parts of a crystal are similarly mod- 

 ified. For instance, in Fig. 3 of the Right Square Prism, if the 

 central point between two of the lateral poles is opposite a seconda- 

 ry plane, a similar secondary plane will be opposite to each one of 

 the other three similarly situated points, or in the ordinary language 

 of Crystallography, if one of the lateral edges is replaced by a tan- 

 gent plane, the others will be similarly replaced. Again, if the 

 point opposite the secondary plane be between the same poles, but 

 is not central, there are two similarly situated between these two 

 poles. Consequently both of these points will be opposite to a 

 plane, and more than this the similar points between the three other 

 pairs of poles will also have their tangent planes ; or using Crystal- 

 lographic instead of Crystallogenic language, if, one of the lateral 

 edges of a Right Square Prism be beveled, the others will be simi- 

 larly beveled. 



These facts are a necessary consequence of the existence of axes 

 of attraction. Any cause which may effect a variation in the force 

 of attraction (the cause of secondary planes,) in the direction of one 

 axis will naturally and necessarily produce the same result in all 

 similar axes, and therefore all points similarly situated will be equal- 

 ly affected by the poles of these axes. Dissimilar parts of a crystal 

 are not of necessity modified at the same time, because of the gen- 

 erally admitted principle, the same cause cannot produce the same 

 effect in dissimilar circumstances, or as here, on unlike axes. The 

 cause which might produce a variation in the attraction along the 

 lateral axes of the Right Square Prism, and thus give rise to a re- 

 placement of the lateral edges, would not necessarily so alter the at- 

 traction in the vertical axis as to effect a modification of the basal 

 edges. 



This affords a strong argument, — if any in addition to the cleavage 

 is necessary — that the Rhombohedron does not contain four Crys- 

 tallogenic axes, (the four axes of a Hexahedral Prism,) since if the 



