253 [Chase. 



Relative Residuals, 



The "logarithms of probability " are deduced from the first four group- 

 ings of Note 180, by the method and with the phyllotactic values which 

 were adopted in Notes 171-4. They assign a greater degree of importance 

 to the strictly phyllotactic than to Gerber's approximately phyllotactic 

 divisors, in every instance ; a greater degree of importance to the hydro- 

 gen divisor than to either the strictly phyllotactic or the approximately 

 phyllotactic divisors, in the monatomic and metallic groups ; a greater de- 

 gree of importance both to the phyllotactic and to Gerber's divisors than 

 to the hydrogen divisor, in the 3 and 5, 2 and 4, aggregate and mean 

 groups. 



The "arithmetical residuals " are deduced from the first four groupings 

 of Note 180, by dividing the differences from exact multiples of the several 

 divisors by the respective divisors, by the method which was adopted in 

 Note 177. In this aspect of the question, as in Note 177, the hydrogen 

 unit is most important in the metallic group ; the phyllotactic divisors, in 

 each of the other groups ; Gerber's coinciding with the phyllotactic in the 

 tri- and pentavalent groups. 



The " relative probability " and "relative residuals" are found by tak- 

 ing the least value in each group as the unit. The indications are, of 

 course, the same as in the systems of grouping from which they were 

 derived. In the metallic group the probability of predominant hydrogen 

 influence is 89507.6 times as great as that of Gerber's divisors, or 1330.6 

 times as great as that of the phyllotactic divisors. In the di- and tetratomic 

 group the phyllotactic probability is more than 7780740 times as great as 

 that of the hydrogen divisor, or 1.4475 times as great as that of Gerber's 

 divisors. The aggregate phyllotactic probability is 15593.649 times as 

 great as that of the hydrogen divisor, or 119.918 times as great as that of 

 Gerber's divisors. 



182. Synopsis of Probable Errors. 



The following tables are computed on the hypothesis that the atomic 

 weights are exact multiples of the several divisors. The percentages of 

 the divisors which represent (T — O) -f- D,* are treated as errors of obser- 

 vation, and the probable errors are deduced in the usual way. Those per- 

 centages may evidently vary between and ± .5. 



* Seelvoteni. 



