1882.] ^*" [Chase. 



We find, therefore, that in this comparison tlie evidence of phyllotactic 

 influence upon valency is more striking than that of the hydrogen unit or 

 of Gerber's empirical divisors. In Gerber's special metallic group, how- 

 ever, the hydrogen unit furnishes the nearest, and Gerber's divisor the 

 most remote approximation. 



178. Probable Errors of Atomic Remainders. 



If the deviations from exact multiples of the several divisors are treated as 

 errors of observation, in order to determine the "jirobable erroi', " we get 

 the following results : 



Accidental. H. Gerber. Phyllotactic. 



For the perissads ±.0503 d= .0433 ±.0371 ±.0300 

 " artiads ± .0294 ± .0280 ± .0178 ± .0180 



For all the elements ± .0266 ± .0236 ± ,0163 ± .0154 

 The legitimacy of this treatment may be questioned, but it cannot be 

 charged with any unjust partiality. The artiads furnish an instance in 

 vFliich Gerber's empirical divisors give the nearest approximation. The 

 hydrogen unit is still the least satisfactory of all. 



179. Deduced Laics of Atomicity. 



Notes 171-8 seem to justify the following conclusions : 



1. If all the atomic weights were accurately determined, they would be 

 found to be exact multiples of the hydrogen unit. 



2. Chemical combinations are influenced by phyllotactic laws, or by 

 tendencies to division in extreme and mean ratio. 



3. Aj'tiad and perissad combining units are different, but connected by 

 phyllotactic ratios. 



4. Metallic structure is controlled by phyllotactic laws. 



180. Phyllotactic Relations to Oxygen. 



In Note 138 I showed that 37 of the elements, according to Clarke's table, 



may be more nearly measured by jV O, while 26 approximate more 



closely to exact multiples of H. If we take | O =: 1.995 H, we get Gerber's 



di- or tetratomic divisor, from which others may be deduced by simple 



phyllotactic ratios : 



PhylJotactic. 



a 1.995 



/?= i a .9975 



r=^^%a .7673 



^= I a 1.2469 



e= I S 1.5586 



The following comparative tables introduce all of Clarke's recalculated 

 atomic weights : 



