191 1.] HIXRICHS— ATOMIC WEIGHT OF VANADIUM. 195 



forming a volume of over 200 pp. 4to. The first, and in fact the 

 greater number of the " Xotes," were presented by Berthelot ; others 

 were presented by Messrs. Gautier, Lemoine, Haller, Gernez, and 

 other academicians. 



In the Monitcur Sciciitifiquc. from 1906 to 1909 more than a 

 dozen longer articles have appeared with many diagrams. The 

 first two tables above referred to are found in the November num- 

 ber for 1901. with discussions, pp. 731—744. 



The papers were originally written in four languages : Danish, 

 German, English and French. To these papers the reader may be 

 referred by the Cinquantenaire and the list in the Prox. Constit. 

 The results obtained, being in conflict with the dominant chemical 

 school, have not been widely circulated except as adopted children. 



For these reasons it is necessary here to give enough of the 

 details of the finally worked out practical method of reduction to 

 enable the reader to repeat all the calculations required, so that he 

 can verify the results given. 



It will then be seen that the final method is quite simple ; the 

 difficulty was to get this method. 



Let a represent the absolute atomic z^right of any chemical ele- 

 ment, that is the whole or round number (h or even ^) which the 

 experiments indicate to be near the true atomic zveight A, which 

 exactly to determine is the object of the reduction. The unit 

 adopted is exactly yV of carbon-diamond which is practically iden- 

 tical with iV of that of oxygen.' 



The departure of the true atomic weight from the absolute 

 atomic weight we designate by the Greek letter epsilon (e) ; that is: 

 A^a-\-e. This departure, as a matter of fact, is found to be a 

 small fraction of the unit ; we invariably express it in thousandths 

 of that unit. 



This departure — in units of the third decimal — is really our new 

 variable, the quantity to be determined. This apparently insignifi- 

 cant matter of form is really of the greatest importance. For this 

 new variable all products and powers become negligible quantities 



^Comptes Rendus, 117, p. 1075, 1893. 



PROC. AMER. PH[L. SOC. , L, I99 M, PRINTED JUNE 26, I9II. 



