Q30 Parallel of Rome de V Isle's an 



will penetrate each other, while the particles will not only 

 not penetrate, but not even touch each other. All forms 

 would stand in the same predicament as the regular octae- 

 dron, which contains, as the Abbe Haiiy has demonstrated, 

 six regular octaedrons and eight regular tetraedrons, each 

 tetraedron containing one octaedron and four tetraedrons. 

 It will further follow, if the chemical elements can be looked 

 upon as particles which are not in contact with each other, 

 that we may from thence mathematically determine che- 

 mical affinities. 



I have now, sir, but one task left ; to speak of the appli- 

 cation our author has made of algebra and geometry to crys- 

 tallography. Many persons complain of the difficulty ne- 

 cessarily resulting from it in the study of mineralogy; and 

 dare not engage in it, uncertain whether they will find a 

 compensation for their trouble. Our author has therefore 

 adopted a double plan, and begins by exposing his theory 

 by a series of reasonings and arguments which will suffice 

 to make the reader understand it, or anv discoveries made 

 in consequence of it. He then exposes the theory in the 

 most, correct of all languages — mathematical analysis ; by 

 far the most interesting, and the only means of making dis- 

 coveries oneself: and who can be callous to the pleasure of 

 discovering an unknown truth ? If the solution of a problem 

 gives so much satisfaction, though the data be only ima- 

 ginary., what must be the sensations of those who are happy 

 enough to solve problems whose data are set by Him whom 

 the greatest of pagan philosophers calls the eternal .Geome- 

 trician? This recalls reflections to my mind which I cannot 

 suppress. Conversing one dav with the Abbe Haiiy, he 

 was taking a cursory view of all the modern discoveries ; 

 when he could not help remarking, that there was not one 

 of them but what furnished victorious arms to the cause of 

 religion. My answer was, that in future the name of God 

 would be as distinctly written on a crystal as it had hitherto 

 been in the heavens. The observation of this most religious 

 and ingenious man reminds me of the saying of lord Bacon : 

 " A little philosophy estranges us from religion, but a great 

 deal reclaims us again." Even d'Alembert could not help 

 saying: " An atheist in the Cartesian system is a philoso- 

 pher mistaken in the principles ; but an atheist in the New- 

 tonian svstem is something worse, an inconsequent philo- 

 sopher. " 



But to return to the mathematical part of our author's 

 theory : the branch of mathematics, and the manner in 

 which he treats it, are almost new. The theory of polye- 



drona 



