I9I3.] HINRICHS— TRUE ATOMIC WEIGHT OF BROMINE. 549 



In fact I have communicated to prominent chemists in the United 

 States and in France first proofs of some of my new cuts repre- 

 senting quite a number of such chemical perturbations. All the 

 dominant elements^ and a number of the others have now been so 

 represented. These first proofs form already quite an atlas. One 

 of these cuts (no. JZl^ has been published in the Comptes Rendus 

 of the meeting of May 6, 1912.^° It covers work of Richards at 

 Harvard and of Guye at Geneva, on the dominant elements Ag, 

 CI and N, O, respectively. 



By this work we have also introduced into chemistry the method 

 of demonstration of the geometricians of ancient Greece known as 

 the " rediictio ad ahsiirdiim," which is just as decisive in modern 

 chemistry of precision as in geometry, the highest science of ancient 

 Greece. 



V. The Rational Method of Reduction. 



This was first published in the Comptes Rendus of March 27, 

 1893 and in my "True Atomic Weights" of 1894. It has been 

 extended and perfected during twenty years, but no complete ex- 

 position of all the steps involved having been published in one place 

 at one time, it is no doubt somewhat difficult to grasp and use the 

 same. It is for this reason that we here give, merely as an example, 

 its application to the laboratory work of Mr. Weber on bromine. 



The old way of successive substitution, producing of necessity 

 an accumulation of errors unknown in magnitude, is based upon the 

 elementary method of solving an algebraic equation with supposedly 

 one unknown only, when in fact it contains as many unknown as 

 there are elements present in the chemical reaction employed. 

 Since, however, in a chemical reaction it is impossible to accept any 

 one element as without error in its action, all these equations are 

 de facto indeterminate (or diophantic) and therefore insoluble. 

 The solutions given by the school are therefore erroneous and can- 

 not be in accord with the facts. 



But while the work of the school during the entire century has 



thus necessarily failed to give a true solution of the problem by that 



^Comptes Rcndiis, T. 153, p. 817; 30 Oct., 191 1. 

 1" T. 154, p. 1228. 



