MAGNITUDE AND MINUTENESS. 



divided, these surfaces^exhibit an intense polish which no effort 

 of art can equal. 



We must conclude, therefore, that these planes of cleavage are 

 parallel to the sides of the constituent atoms of the crystals, and 

 their directions therefore form so many conditions for the deter- 

 mination of the shape of these atoms. 



This shape being once determined, it is not difficult to assign 

 all the various ways in which they may be arranged, so as to 

 produce regular figures ; and we accordingly find that regular 

 figures thus indicated by mathematical reasoning correspond with 

 the forms assumed by the crystals of the same substances. 



34. It follows, therefore, from these effects, and the reasoning 

 established upon them, that the substances which are susceptible 

 of crystallization consist of ultimate atoms of different figure. 

 Now, all solid bodies whatever are included in this class, for they 

 have severally been found in, or are reducible to a crystallized form. 

 Liquids crystallize in freezing : several of the gases have been 

 already reduced to the liquid and solid forms, and analysis justifies 

 the conclusion that all are capable of being reduced to this form. 



Hence it appears reasonable to presume that all bodies whatever 

 are composed of ultimate atoms, having determinate shape and 

 magnitude ; that the different qualities with which we find dif- 

 ferent bodies endued, depend upon the shape and magnitude of 

 these atoms ; that these atoms cannot be disturbed or changed so 

 long as the body to which they belong is not decomposed into 

 other elements, as we find the qualities which depend on them 

 unchangeably the same under all the influences to which they 

 have been submitted. 



"We must conclude also that these atoms are so minute in their 

 magnitudes that they cannot be observed by any means which 

 human art has yet contrived, but nevertheless that such magni- 

 tudes still have limits. 



35. It is necessary, however, to observe that notwithstanding 

 the strong analogies which support these conclusions as to the 

 ultimate constitution of material substances, the principles of 

 mechanical science are quite independent of them, and do not 

 rest upon any hypothesis concerning such atomic constitution, and 

 therefore the truth of these principles would not be in any wise 

 disturbed even though it should be established that matter is in 

 the most literal sense infinitely divisible, and is not formed of 

 ultimate atoms. 



The basis of mechanical science is observed facts ; and since the 

 reasoning upon these observed facts is demonstrative, the conclu- 

 sions, when rightly deduced, have the same degree of certainty as 

 the facts from which they are inferred. 

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