1873 •] in Experimental Research. 9 



and oxygen, and the weights in vacuo, the quantity of nitric 

 acid required to convert the thallium into nitrate is — 



(339-646066- 183790332 = )55'855834grs. 

 We have then the proportion — 



Weight of ' Weight of Atomic Weight ^v*? 1 ? 1 /"* f 



Nitric Acid. Thallium. of Nitric Acid. X^fv 



lhailium. 



55*855834 " 183790232 :: 61*889 : %', 

 .*. # = 203*642. 

 Substituting the old equivalents we obtain — 



55*855834 : 183790232 :: 62 : 204*007 

 as the atomic weight ; but I cannot admit this number to be 

 so nearly correct as 203*642. 



If we take the corrected weighings in air of ordinary 

 density, we have, with N9 3 = 61*889, 



203*738. 

 WithN0 6 =62, 



204*103. 



Accepting the uncorrected weights, observed in air, we 

 have, with N9 3 = 61*889, 



203*162. 

 WithN0 6 = 62, 



204*165. 



The error of the last deduction is +0*523, a sufficiently 

 large number to show the inutility of the application of the 

 theory of probability until every care has been taken to 

 eliminate the errors arising from inaccuracies. As I have 

 stated, in the paper to which I have referred, the largeness 

 of these errors has an immediate bearing upon quantitative 

 analysis, for it is shown that, from data ordinarily given, 

 very varying results may be obtained. Chemists have to 

 deal with much smaller quantities than a quarter per cent, 

 particularly in organic analysis, where so wide a difference 

 from the truth may lead to very erroneous reasoning. 



Pass we now to the application of the theory of proba- 

 bilities to ten results of the most trustworthy weighings. 

 These, with N0 3 = 61*889, are as H1 Table I. — 



Tabulating the results of the determinations, with the 

 view to ascertain severally their degree of approximation to 

 the arithmetic mean (Table II.) — 



The arithmetic mean of the ten observations is — 



^ 2036-424 ^6 



10 



VOL. III. (N.S.) C 



