the Abbe Haley's Theories of Crystallograhy. 233 



tfrons had been nearly neglected by geometers, both on 

 account of the difficulty to represent a polyedron on a plane, 

 aind because they did not feel the utility of the pursuit. 

 Nevertheless, strange to say, all the regular figures that are 

 to be found in one of the three kingdoms of nature are po-» 

 Ivedrons. In this point of view, the branch of mathematics 

 illustrated by the Abbe becomes very interesting; and it is 

 not a little so, to see with what ingenuity he extricates him- 

 self from the difficulties he meets with in his researches. 

 He forms all the poly edrons, however complicated, of little 

 equal rhomboids or parallelopipedons, and by that means 

 he reduces the theories of every possible polyedron to that 

 of the rhomboid, which is extremely simplified by two very 

 simple remarks: 1st, That in all equilateral rhomboids, 

 whatever may be the species, their projection on a plane 

 perpendicular to their axes will always be a regular hexagon: 

 2dly, That the axes will always be trisected by perpendicu- 

 lars drawn from all the lateral solid angles. His theory has 

 also led him to discover in a variety of crystals geometrical 

 properties, which must be highly gratifying to geometers. 

 But the ejeat advantage to be derived from it is, that it ena- 

 bles us with the fewest possible data to calculate the crys- 

 talline forms just as astronomers do the motions of the hea- 

 vens. By the very means by which the latter determine the 

 future motions of the heavens, the Abbe decides which 

 forms are possible and which are impossible. . It is thus by 

 his simple and general law of crystallization, " the number 

 of the ranges of the subtractive particles must always be a 

 commensurable quantity," that he has demonstrated the 

 regular dodecaedron and the regular icosaedron to be im- 

 possible forms in mineralogy. As the immortal Newton, 

 by having discovered the law of attraction to be " in the 

 inverse ratio of the squares of the distances," explained and 

 calculated every thing in the vast regions of the firmament ; 

 so at the other extremity of the creation the Abbe Haiiy, by 

 means of a single law which he has discovered, explains 

 the irregularities and calculates those problematic forma- 

 tions with which the mineral kingdom had hitherto asto- 

 nished the natural philosopher. 



Laws, sir, that result from the study of nature enjoy this 

 inestimable advantage, that they always lead to equations ; 

 and it is only by the help of equations (expressed or under- 

 stood) that questions can be solved which relate to objects 

 that can be either counted or measured. 



Of late, sir, the word nature has been so much abused, 

 that I must beg leave to state the precise sense in which I 



R 2 wish 



