AND CERTAINTY. 287 



We may consider this number practically infinite, under 

 all ordinary human conditions.^ 



Hence, we can say, that the twenty-five chemical ele- 

 ments enumerated, for which the true atomic weight is 

 known with a degree of precision of at least o.oi of a unit, 

 are hereby proved to be compounds of one single material, 

 the atomic weight of which is one-half a unit, or $ of our 

 standard of matter, the diamond-carbon. 



The chance that this conclusion is an error is as one is 

 to the practically infinite number just given, namely, 5000 

 followed by ten times the million group of six ciphers. 



We can also state the same conclusion by saying its cer- 

 tainty is expressed by this same number, the chance of an 

 error being unity. 



Since now these twenty-five chemical elements were not 

 chosen or selected by us for any special reason other than 

 the accuracy or the degree of precision wherewith their 

 atomic weight has been determined, this conclusion applies 

 to any and every group of 25 chemical elements, that is, to 

 all chemical elements, even those not yet known to us. 



These 25 elements comprise fully one-third of all ele- 

 ments known to-day. They include nearly all the best 

 known and most important of these chemical elements. 



As soon as the atomic weight determinations shall be 

 carried on in a rational manner, in accordance with the 

 principles laid down in this work and in our True Atomic 

 Weights of 1894, the required precision will be obtained and 

 the elements will fall into line. 



It is easily determined that the certainty for all 38 ele- 

 ments now determined with a precision of o.i or more is 



800 followed by thirteen times the million-group of 



6 ciphers, 



which is 800 oooooo oooooo oooooo 



times the greatest number of antiquity of Archimedes. 



The thirteen additional elements here referred to are: 



V Al, Bi, Ur, precision 0.02 ; 

 VI Au, Be, In, Mn, Se, Wo, Zn, precfsion 0.05; 

 VII Sb, Sn, Ti, precision o.i. 



