226* Parallel of Rome de l'Isle*s and 



take place in a parallel with the diagonal of the faces of ther 

 primitive; they are then called decrements on the angles $ 

 because the diagonals are drawn from one angle to the op- 

 posite angle. This second species of decrement follows the" 

 same laws as the first. 



There is a third species, called by our author inter- 

 mediate decrements. In this case they are neither parallel 

 to the edges nor to the diagonals of the faces, but to inter- 

 mediate lines, which if prolonged would intersect both the 

 edges and diagonals, but otherwise they follow the same 

 laws as the two first. It is a general law, therefore, that hi 

 all cases the lamina? decrease in, arithmetical progression, 

 and its ratio or the number of ranges subtracted is always 

 commensurable. 



The particles of which the laminae are composed are to 

 be considered as parallelopipedons ; not that the integrant 

 particles always have this figure ; but if they have it not, 

 they must leave vacuities between them, and each vacuity 

 being added to its corresponding particle, will complete the 

 parallelopipedon. If this was not the case, the faces of the* 

 secondary crystals would not be planes, nor could they be 

 split smoothly in any direction. These little parallelopipe- 

 dons which compose the subtracted ranges are what I called 

 above, after our author, subtractive particles. 



I supposed the construction of the secondary form only 

 to take place on one of the faces of the rhomboid ; but what 

 was said relative to that face is applicable to all the others. 

 It is also to be remarked that different laws of decrement 

 may affect the different faces ; even further, different laws- 

 may successively affect the same face. Hence a diversity 

 of forms arise scarcely credible to a person unacquainted 

 with the doctrine of combinations. The Abbe Hauy has 

 calculated, " that confining oneself to decrements by 1, 2, 

 3, or 4 ranges, and not taking intermediate or mixt decre-< 

 ments into account, the rhomboid is capable of 8,324,604 

 varieties of crystalline forms. 



It is an important remark, that, whatever may be the va- 

 riety of form, the forms (in complete crystals) will always 

 be symmetrical. There are two sorts of symmetry, the 

 perfect and imperfect. In the perfect, the right is sym- 

 metrical with the left, and the top with the bottom ; but 

 in the imperfect, the top is not symmetrical with the bot- 

 tom. This latter species of symmetry appears, by general 

 observation, to be exclusively appropriated to crystals that 

 become electrical by heat 5 that is to say, which being ex- 

 posed to the heai of the fire, or plunged into hot water* 



acquire 



