420 wells: interpretation of mineral analyses 



some advantages possessed by a comparison of the atom numbers. 

 Residuals of the latter may be compared with one another with 

 respect to the possibility of their combination into simple mole- 

 cules. In objecting to this method of comparison on mathematical 

 grounds the authors of the second paper appear to have over- 

 looked an important distinction. In weighing out the mineral 

 for analysis as well as in all the analytical operations there are 

 the same atoms involved, atoms of different weights — here eleven 

 atoms of sulfur, two of arsenic and eight of silver — so that the 

 percentages of the different elements are already weighed, i.e., 

 ''weighted" according to these proportions and, in dividing, the 

 chemist simply tends to restore unit weight to each determina- 

 tion of the common divisor upon which the atomic theory depends. 

 When we compare percentages we compare data for eleven atoms 

 of silver, two of arsenic, and eight of silver; on the other hand, 

 when the comparison is between different values of the greatest 

 common divisor we are comparing numbers having a significance 

 common to all the atoms in the mineral. 



Now in view of the consideration on page 419 it appears in 

 general that (a) when percentages are compared the principal 

 constituents will contain the smallest relative errors while con- 

 stant errors will tend to compensate one another. The tptal 

 essential constituents expanded to 100 per cent will therefore be 

 the best basis of comparison with the theoretical percentages. 

 (b) When the atom numbers are to be compared the one obtained 

 from the minor constituent will be most affected by "constant er- 

 rors" such as those of weighing and measuring, the one obtained 

 from the major constituent will be most affected by "relative 

 errors," those proceeding from chemical transformations. Which 

 kind of error will predominate here will depend again upon the 

 mineral and the method of analysis. The plan has heretofore 

 been to base the value of the common divisor upon the minor 

 constituent. Schaller's proposal bases the divisor upon all the 

 constituents. Another plan would be to base the value of the 

 common divisor upon the chief constituent or the most accurately 

 determined one. A factor may be very simply obtained, however, 

 by taking 1 /100th of the molecular weight assumed for the mineral, 



