26^ 



This comparison shows that the general deviations from Dulong and 

 Petit's law, while they are of the same order of magnitude, are much 

 greater than the deviations from the perissad and artiad divisors. 



209. Secondary Character of Perissad Phyllotaxy. 



Although the fractions which are formed by successive approximations 

 to the surd divisors represent phyllotactic dextro- and Isevo-gyration, other 

 series of a higher order may spring from greater initial differences. If we 

 skip the first even number, we get the series 1, 3, 4, 7, 11, 18, etc. Hence 

 we see that the fundamental perissad and artiad divisors both start from 

 the phyllotactic number which most nearly represents the first surd 

 divisor, 3, and are formed by adding the next artiad number for the peris- 

 sad divisor, and the next perissad number for the artiad divisor. The co- 

 efficient of atomic heat is also formed from the same representative of 

 division in extreme and mean ratio by taking its simplest artiad multi- 

 ple, 2x3. 



210. Comparison of Probabilities. 



In looking more closely into the deviations which are given in Note 208, 

 we find the following indications of superiority in the perissad and artiad 

 divisors : 



1. The approximation of the observed values within .05 of the theoreti- 

 cal values occurs 19 times in my columns, and only 9 times in those of 

 Dulong and Petit. 



2. The average deviations are, d^ == .0642 ; 82 = .0344. 



PROC. AMER. PHILOS. SOC. XX. 111. 2h. PRINTED JUNE 3, 1882. 



