1881.] o93 [Chase. 



The first six pliyllotactic numbers are 1, 2, 3, 5, 8, 13 ; the third does 

 not appear in the formation of the theoretical divisors, but the others are 

 all employed. The simple phjllotactic relation of all the divisors to H, 

 shows that they have "value in themselves." 



137. Mutual Phyllotaxy. 



Upon examining the mutual relations of the above pliyllotactic divisors, it 

 will be seen that D^ = ^V D.^ = 2 X | X A ^z = tV D^ ; D2 = 2 X | X 

 f Dg = 2^ X I D, ; D3 = f X ^ D^ ; D^ = i/HD~. These varied pro- 

 visions for the stability of cyclical equilibrium, in all possible varieties of 

 intra-molecular sethereal movement, show that the command, "Let there 

 be light, " manifested its formative power of organization as soon as ma- 

 terial atoms were set in motion. The appearance of the first five phyllo- 

 tactic numbers, 1, 2, 3, 5, 8, in crystallization, furnishes a step from inor- 

 ganic to organic morphology, giving new meaning to the landscapes on 

 our frosted window-panes, as well as to the protective mimicry of vege- 

 tables and animals, as illustrations of the "distributive ratio " which con- 

 trols alike light-waves, atomic inertia, crystalline structure, organic 

 growth, planetary configuration and interstellar action. 



138. Relations of the Water Molecules. 



The importance of oxygen and hydrogen, both in mutual combination 

 and in connection with other elements, suggests the following compara- 

 tive grouping of Clarke's table of atomic weights : 



