Chase.j -oO lApril 21, 



reference to those laws, without introducing any new hypotheses. 1 have 

 already compared various phyllotactic harmonies with other cliemical 

 hypotheses, and Note 232 furuislies data for extending the tests of mathe- 

 matical probability. In my first paper on the harmonic interferences in 

 the spectra of chemical elements {Proc. A. P. 8., xoii, 297-301) I examined 

 the measured wave-lengths of 128 lines, in twenty-one different spectra. 

 The greatest mean deviation of the measured lines in either spectrum from 

 lines which are rigidly harmonic, is less than ^ of one per cent., the mean 

 deviation in the whole number of lines being less than ^V of one per cent. 

 The mean deviations in the several spectra are as follows : ^V- sV' f' oS- 

 0, t\. tV t7^. i't. t's. t^. i h tIj. jt \' tV. ^V. ^V. uV- tV of one per 

 cent. The greatest deviation in any single line is one per cent., and there 

 is only one line which has a deviation of more than ^ of one per cent., 

 which is only -^j as great as the greatest deviation in Perkin's set of crys- 

 talline measurements, or less than ^ as great as his mean variability. 

 Later comparisons, of which Notes 226 and 228 may be taken as examples, 

 show approximations which are still closer. The greatest deviation in 

 Tacchini's cometary measurements is ^V of .01, and the mean deviation 

 j}^ of .01 ; the greatest deviation in Thollon's measurements is -^-i^^-^, and 

 the mean deviation ^y^g ; the greatest deviation in the first lithium spec- 

 trum of Note 228 is ^^^^, and the mean deviation yJjy ; the greatest de- 

 viation in the second spectrum of the same note is x^'itj. and the mean 

 deviation ^jVct- 



235. Spectrum of the Great Nebula in Orion. 



On the 7th of March, 1882, Huggins {Am. Jour. ScL, [3] xxiii, 335) 

 obtained a photograph of the spectrum of the nebula in Orion, with an 

 exposure of 45 minutes. His former researches showed that the visible 

 spectrum of gaseous nebuliE contains four bright lines, 5005,. 4957, and 

 two of the hydrogen lines, [i and y. The photograph has also a strong 

 line in the ultra-violet, at the position of X 3730, or nearly so. Some of 

 the harmonic relations of the lines are given in the following table : 

 Harmonic. - Observed. 



525405 -^ 105 = 5003.86 5005 



525405 H- 106 — 4956.65 4957 



525405 -- 108 = 4864.86 4861 



525405 -4- 121 = 4342.19 4340 



525405 -f- 141 = 3726.28 3730 



The greatest deviation is -^^ of one per cent., and the mean deviation 

 ■^^ of one per cent. 



236. Magnetic Estimate of .Ethereal Density. 



Newton's aethereal hypothesis, Faraday's electric hypothesis and my 

 own numerical relations (See Note 200) are exemplified in the following 

 combined harmonies : Let «„ represent Earth's mean orbital velocity 



