191 1.] HINRICHS— ATOMIC WEIGHT OF VANADIUM. 199 



serviceable and by far the most readily understood and easiest 

 applied. 



Our general deduction (really as indicated 1894 already: a 

 method of the variation of the constants) leads to the simple form 

 of the equation of condition 



100 (7 = 2A€, 



where the constant 100 presupposes that the analytical excess e and 

 the variation A are expressed in units of the fifth place while the 

 departure c is expressed in units of the third place or thousandths 

 of the unit of atomic weights. 



It may not be amiss here to insist on the fact that since in every 

 chemical reaction there are at least two elements present, the above 

 equation contains at least two unknown departures e. and is there' 

 fore really an indeterminate or a diophantic equation. 



Our practical solution ex sequo of this equation is as follows : 

 Let m be the number of elements involved in the chemical reaction, 

 used, then the number of terms Ac in the above sum 2 is m. 



Ascribing to all elements an equal influence on the error or excess 

 e, the part thereof due to each element will be e'^=e/m. 



Hence the actual departure e for each element in the reaction 

 will be determined by the simple relation 



100 e' 



If the value of A be above a certain limit, this determination will 

 be sharp; the corresponding reaction therefore may also be called 

 sharp. 



But if the value of the variation A for any element is small, 

 the reaction for that element zinll be dull and the determination of 

 the atomic weight will be impossible with any high degree of pre- 

 cision, as we have shown in Comptcs Rcndns, T. 148, p. 484, 1909, 

 in the attempted determination of the atomic weight of Tellurium by 

 a reaction quite dull for that element. 



This one attempt strikingly shows the real condition of the 

 work of the dominant school to be irrational. 



After having briefly explained the manner in which we have 

 tried to solve the great problem of the deduction of the true atomic 



