the Ahlfe Hauifs Theories of Crystallography. Q2t 



acquire the electric power. These crystals, the tourmaenji 

 for example, acquire a positive electricity on one side, while 

 on the side diametrically opposite their electricity becomes 

 negative ; and all observations hitherto made give ns reason 

 to conclude that these sides are never symmetrical, and are 

 always produced by different or fewer laws of decrement. 

 " Hence," says the Abbe, " by mere inspection it is easy 

 to point out which is the side that will give the positive ancl 

 which the negative electricity." (Vol. i. p. 23J.) 



The astonishing variety in the crstalline forms leads U9 

 naturally to ask, What can be the cause of this variety ? 

 This question has not been treated by the Abbe : allow me, 

 jMTj to submit a few ideas on the subject for the opinion of 

 mathematicians. 



First causes, I repeat, are not the object of this discus- 

 sion. I state the question thus : Why does the same sub- 

 stance crystallize in such a variety of forms, always sym- 

 metrical and always terminated by planes ? 



The solution of this question seems to require three con- 

 ditions : 1st, That the particles of the substance dissolved 

 in the fluid all leave the state of rest at the same instant, to 

 form the crystal by their aggregation : 2dly, That, while 

 these particles are in the act of drawing near to each other, 

 no foreign power shall imprint on them any other motion 

 than a common motion, whether it be in a straight line, 

 or rotary round their common centre.pf gravity : 3dly, That 

 the particles all arrive at the state of rest at the same instant, 

 which takes place when the act of crystallization is finished. 

 The second condition is necessary, and infers the first and 

 third. The natural consequence of these conditions will be, 

 that the aggregation of the particles will only take place 

 conformably to a law acting equally on all of them, what- 

 ever may be the law. 



Since they all leave the state of rest at the same instant, 

 they are in equilibrio previous to that instant. Since they 

 all arrive at the state of rest at the same instant, they are in 

 equilibrio after that instant : but when particles that, are 

 acted upon by no other force than that which they exercise 

 on each other, are in equilibrio, they are in the closest pos- 

 sible union that concomitant circumstances will permit. If 

 the pai tides were in equilibrio previous to their leaving the 

 6tate of rest, something must have obstructed their approach. 

 Let us suppose that something to be the interposition of an- 

 other substance, and that so long as the interposition re- 

 mains equilibrium is maintained. But this can only be 

 the case, in as much as the whole of the particles of the iri7 

 1 terposcd 



