380 MEMOIR OF HAUT. 



differently that they compose the crystals whose external shape deludes 

 us hy its variety. Setting out with this idea, he could readily imagine 

 that those particles, in accumulating and disposing themselves in lay- 

 ers, might form pyramids and polyhedrons of a new configuration ; 

 enveloping the primitive crystal as with another whose exterior faces 

 might differ much, both as to number and inclination, from those of 

 the first, according as the successive layers had diminished on one side 

 or another, and in such or such proportions. 



If this, then, was the true principle of the crystallization in question, 

 it could not but prevail in the crystals of other substances; each of 

 which ought, in like manner, to have its constituent particles the 

 same, a nucleus alike in each species, and superposed or accessory 

 layers producing all the varieties. Haiiy, who hesitates not to submit 

 to the hammer his own crystals, as well as those he could obtain from 

 his friends, finds everywhere a structure based upon the same laws. 

 In the garnet it is tetrahedral ; in fluor spar, octahedral ; pyrites pre- 

 sents a cube ; while gypsum and heavy spar offer straight four-sided 

 prisms, whose bases, however, have different angles. Invariably the 

 crystals break with faces parallel to those of the nucleus, the exterior 

 form being but the result of the more or less rapid decrease of the 

 superposed lamina?, a decrease which takes place sometimes at the 

 angles and sometimes on the sides. Thus, the new surfaces presented 

 are in reality a succession of minute points produced by the retreating 

 lamina), though they appear smooth to the eye from their extreme 

 tenuity. No crystal which Haiiy examines offers any exception to his 

 law, so that he exclaims, and this time with more assurance, all is clear. 



But, that this assurance should be complete, a third condition is to 

 be fulfilled. The nucleus or constituent molecule having in each case 

 a fixed form, geometrically determinable as to its angles and the cor- 

 respondence of its lines, every law of decrement must cause the second- 

 ary surfaces to be in like manner determinable; indeed, the nucleus or 

 molecule being given, it should be possible to calculate beforehand 

 what angles and lines the decrease in each instance would prescribe to 

 all the secondary surfaces. In a word, that the theory should be cer- 

 tain, it was necessary here, as in astronomy and every part of physics, 

 that it should not only explain with precision all known facts, but 

 that it should provide with equal precision for those which had not yet 

 come to light. 



This Haiiy perceived, but fifteen years passed chiefly in teaching 

 Latin had nearly effaced the small portion of geometry taught him at 

 college. Without being deterred by this, he tranquilly set himself to 

 regain it ; and as he had so quickly learned botany to please his friend, 

 he could not be long in acquiring enough geometry to complete his 

 discovery. Nor was his recompense delayed beyond the first trial of 

 this new auxiliary. The hexaheclral prism which he had broken by 

 accident was found, upon calculation, to yield a value closely approxi- 

 mate to that of the angles of the molecule of the spar ; other calcula- 

 tions gave him that of the retreating surfaces, the application of the 

 instrument to the measurement of the angles giving direct confirma- 

 tion to the previsions of theory. In other crystals the secondary were 

 found to be as easily deducible from the primitive planes, while in 



