DEGREE OF CERTAINTY. 285 



CONCLUDING REMARKS. 



I. THE DEGREE OF CERTAINTY ATTAINED. 



Having completed the exposition of the actual analytical 

 determinations made during the century just closed, and 

 having also given a final reductio ad absurdum of the system 

 of Stas, pp. 169-209, we must close the entire work with a 

 numerical summary of the evidence of the exact commen- 

 surability of the true atomic weights of the chemical elements 

 and of the unity of matter. 



The manner of procedure in this demonstration has been 

 fully explained on pp. 212-214. We may repeat the method 

 here in more general terms. . 



If the measure of precision of the true atomic weight be 

 p which is the n*h part of a unit, then the certainty is as n 

 to i for one, 2 to i for 2, > to i for m elements all termi- 

 nating their true atomic weight with the full natural number. 



Is p = 0.001 then zr:iooo; for 5 such elements, 5 is 

 one followed by 5 -x 3 =115 ciphers. 



\Ve shall now enumerate the elements in groups accord- 

 ing to this degree of precision. 



I. For the following eleven elements the precision of 

 determination of this absolute atomic weight reaches o.ooi ; 

 hence, one thousand divisions of the unit giving for all the 

 termination .000, represents one chance in 1000 raised to the 

 eleventh power, which is expressed by the number one fol- 

 lowed by 33 ciphers. 



The eleven elements here referred to are : Ag, As, Bo, 

 Br, C, Cd, Cu, N, O, P, Tl. 



We could also say, that this number 



IOOO OOOOOO OOOOOO OOOOOO OOOOOO OOOOOO 



compared to one represents the certainty that these eleven 

 elements are composed of but one primitive material, the 

 atomic weight of which is one twenty-fourth of that of car- 

 bon-diamond. We have called this primitive material 



PAXTOGEN. 



II. For the three elements, Fl, H, Li, the precision 

 does not exceed 0.002, of which 500 make one unit. Hence, 



