Chase.] -^4:0 LApril 21, 



hydrogenic influence upon general atomicity, the mathematical probability 

 of the latter is satisfactorily established. I am not aware that the views 

 of Prout and Dalton have ever before been tested in any way like this. 



175. Combination of Harmonic Influences. 



In my studies of cosmical harmony I have often had occasion to speak 

 of the simultaneous operation of different dscillatory tendencies. Similar 

 tendencies, involving similar modifications of resulting rhythms, must 

 exist in the various forms of molecular activity. Dr. Thomas Hill, whose 

 participation in Peirce's investigations of planetary phyllotaxy have given 

 him an interest in other like researches, having suggested that the surd, 

 h (3-V/5), might be more closely represented in the atomic ratios than -its 

 phyllotactic approximations, I have tried it upon each of the foregoing 

 groups. I find some evidence of its influence, but the combinations of 

 phyllotactic ratios which are represented by my two divisors, .768 and 

 1.998, are much more satisfactory. Therefore it seems probable that, 

 although the differences of internal work may prevent any precise atomic 

 commensurability, there are as close approximations to precision in the 

 elementary atoms as there are in plants and in planets. 



176. Fourier's Doctrine of Elasticity. 



The early views of Rittenhouse and other American investigators,* are 

 corroborated by the following extract from Fourier's " Tlieorie analytique 

 de la chaleur," which is cited by Melsens in his report on Hirn's experi- 

 mental investigations of the relation which exists between the resistance 

 of the air and its temperature (Bull, de V Acad. Roy. de Belgique, [3] 2, 

 p. 253, 8 Octobre 1881). 



Art. 53. " La chaleur est le principe de toute elasticite ; c'est sa force 

 repulsive qui conserve la figure des masses solides et le volume des liquides. 

 Dans les substances solides, les molecules voisines cederaient a leur attrac- 

 tion mutuelle, si son efiet n'etait pas detruit par la chaleur qui les separe. 

 Cette force elastique est d'autant plus grande que la temperature est plus 

 elevea ; c'est pour cela que les coi'ps se dilatent ou se condensent, lorsqu'on 

 eleve ou lorsqu'on abaisse leur temperature." 



177. Test of Atomic Divisors by Arithmetical Means. 

 The superiority of the combined phyllotactic divisors, over the surd 

 divisors, Gerber's empirical divisors and the hydrogen unit, may be 

 further shown by comparing the mean percentages of difference from 

 exact multiples of the several divisors, in each of Gerber's groups : 



*See Proc. Amer. Phil. Soc, xvi, 298 seq. 



