Chase.] 



254 



Probable Errors. 



[April 21, 



Groups. Surd I. 



Monatomic, ± .0529 



3 and 5, ± .0588 



2 and 4, ± .0438 



Metallic, 

 Aggregate, 



Surd II. Hydrogen. Gerber. Phyllotactic. 



± .0545 zb .0552 ± .0490 ± .0407 



d= .0556 zb .0445 ± .0253 ± .0253 



i .0497 ± .0439 ± .0357 rb .0218 



0375 zb .0385 zb .0358 zb .0358 dz .0361 



0232 ± -0242 zb .0222 db .0200 



.0181 



Relative Pi'obable Error». 



Surd. I. 

 1.3001 

 2.3211 

 2.0101 

 1.0473 

 1.2812 



Surd. II 

 1.3401 

 2.1933 

 2.2764 

 1.0752 

 1-3394 



. Hydrogen. Gerber. Phyllotactic. 



1.3571 

 1.7559 

 2.0109 

 1.0004 

 1.2274 



1.2038 

 1.0000 

 1.6361 

 1.0000 

 1.1079 



1.0000 

 1.0000 

 1.0000 

 1.0085 

 1.0000 



Groups. 

 Monatomic, 

 3 and 5, 

 2 and 4, 

 Metallic, 

 Aggregate, 



Surd I is i (3 — V^\ Surd II, \ (/S"— 1). 

 phj'llotactic divisors are the same as in the foregoing note. Phyllotactic 

 precedence is shown in eight of the groups ; Gerber's approximately^ phyl- 

 lotactic in four ; hydrogen in one. Surd divisors take precedence of hy- 

 drogen in four of the groups. They suggest the probability that dextro- 

 and Isevo-gyration may be phyllotactic phenomena, originating in tenden- 

 cies to division in extreme and mean ratio. 



The groupings and the 



183. Probabilities of the Surd Divisors. 



In order to show the character of the evidence to which I referred in 

 Note 175, and thus complete the comparative examination which I have 

 undertaken, I add the following tables. 



Logarithms of Probability. Arithmetical Residuals. 



The arithmetical residuals are so near Schuster's limit that they furnish 

 but slight evidence of harmonic influence. The mean probabilities, 1.304 

 and 1.147, are also comparatively small, but inasmuch as each of the 

 groups indicates a decided probability, while the aggregates are more than 

 24,500,000 and 6420 respectively, any hypothesis of accidental determina- 

 tion must be rejected. Perhaps the most important use which Ave can 

 make of the results is to extend the comparisons of the foregoing note, so 

 as to add further cogency to the proof of phyllotactic sway. 



