Chase.J ^*-'t> [Nov. 4, 



of 2850 and 4570, respectively. These represent, approximately, the phyl- 

 lotactic numbers 5 and 8, viz. : 



Pliyllotactic. Observed. 



2854 2850 



4566 4570 



In the arc-spectrum and spark-spectrum, there is " a very striking group 

 of two very strong lines at wave-lengths about 2801 and 2794," and ' ' one 

 line common to the arc and spark at wave-length 4703 " which " does not 

 appear in Angstrom's table." The diflFerence between the "two very 

 strong lines " has modified the other lines, as shown below : — 

 Harmonic. Observed. 



7 X 399 = 2793 2794 



7 X 400 = 2800 2801 



7 X 407 =^ 2849 2850 



7 X 653 = 4571 4570 



7 X 672 = 4704 4703 



The greatest difference is ^ and the mean difference is g^ of the har- 

 monic divisor. If there were no law controlling the approximations, the 

 probable maximum difference would be ^ and the mean difference would 

 be .25 of the divisor. 



143. The Special Phyllotactic Elements. 

 The elements which cannot be simply grouped with O and H, within 

 the limits of probable error (Note 138), have the following phyllotactic 



144. Analysis of the Hydrogen Spectrum. 

 It seems reasonable to look for clearer evidence of undisturbed or 

 slightly modified harmonic influence in hydrogen, than in any of the heav- 

 ier elements. Accordingly Professor Johnstone Stoney has " shown that 

 three out of the four lines in the visible part of the spectrum have wave 

 lengths which, to a high degree of accuracy, are in the ratios of 20 : 27 : 

 32." I find, moreover, that three of the lines are in simple geometric 

 .ratio, as will be seen by the following comparison : 



Tlieoretical Harmonic Lines. Observed, 



a = (2 X 3)3 X 30.379 = 6561.8 6561.8 



^5= 5 X 2^ X 30.379 = 4860.6 4860.6 



y — ^S^a)^ =4340.1 4340. 



.8= 5x33 X 30.379 = 4101.1 4101.2 



