OUR METHOD OF DETERMINATION. 65 



We may also express this result by saying 



" Hg = 200.1 gives ratio 3 high " or " change of o.i gives 

 ratio 3 high " or " Chg. 3 high." 



Now, in the first determination by Erdmann and 

 Marchand, they found, as above stated, the analytical ratio 

 0.92 594 or " i high." 



Since o.i causes 3 high, this actual " i high " corresponds 

 to our one third of o.i or 0.03 on the atomic weight of 

 mercury. 



That is, by a mere glance at the analytical excess (here 

 i high) the calculated change (always for o.i) gives the 

 corresponding departure of the atomic weight from the 

 standard. 



In this case, for this first determination by Erdmann and 

 Marchand, departure is 0.03 from the standard 200, so that 

 the atomic weight of mercury exactly corresponding to that 

 first determination is 200.03. 



It is plain, that this method is the simplest possible for 

 use, calling for no calculation but such as can be instantly 

 made mentally, the changes for o.i having been given. 



It is the well known method of proportional parts, used in 

 all common tables of sines, tangents, logarithms we extend 

 it to the atomic weight calculations. 



Of course, the possibility of doing this depends upon the 

 fact that the true atomic weights differ very little from our 

 standard atomic "weights, as we have recognized it in all the 

 analyses of the nineteenth century so far as the chemists 

 were able, and therefore their methods used, reliable. 



Now, if absolutely reliable and practically concordant 

 analyses should give any appreciable analytical excess, not 

 due to errors of work or process, then we can instantly, by 

 the above proportional parts, mentally calculate the exact 

 departure d of the true atomic -weight t from our standard 

 atomic -weight s and obtain t = s -f- d (4) 



Standard and True Atomic Weights. 



I may already here remark, that we shall find this analyti- 

 cal excess e entirely within the limit of precision attained. 



