338 Dr. A. Schuster. [Jan. 27, 



o 



I have only taken such lines as are found on Angstrom's map, 

 and I have compared the ratios of any two lines with the ratios of 

 integer numbers smaller than 100. These latter ratios were calculated 

 out to six decimal places, and arranged in order of magnitude in a 

 table, to which I shall refer as the Auxiliary Table. I have adopted 

 two methods of comparison. The first is best explained by an 

 example. The wave-length of the less refrangible of the two yellow- 

 ish-green sodium lines divided by the wave-length of the less refran- 

 gible of the two yellow lines gave the ratio "964760 



•On referring to the Auxiliary Table we find that , this ratio 



lies between 55-^57= '964912 



and 82^85 = -964706 



The difference between these two fractions being "000206 



The difference of the fraction in the sodium spectrum with 



the nearest fraction of integer number is "000054 



The ratio of these two differences 54-^206 is found "262 



Similar ratios were formed for all possible fractions in the sodium 

 spectrum. Now, if the lines in spectra are distributed at random, we 

 should expect the ratio of the two differences to range indis- 

 criminately between and '5 ; the mean of all of them coming near 

 -25. If, on the other hand, the law of harmonic ratios is a true one, 

 we should expect a greater number of small fractions, and hence the 

 mean should be smaller than "25. The results are given in Table I. 

 The second column gives the numbers of fractions for each spectrum, 

 and the third the mean values obtained, which, as mentioned, ought 

 to be near "25, if the lines are distributed at random. 



Table I. 



Element. 



Number of 

 fractions. 



Mean value 

 of ratios. 



P=±. 



Mean 



18 

 40 

 101 

 303 

 10404 



"2626 

 •2399 

 •2430 

 •2592 

 •2513 



•0229 

 •0154 

 •0097 

 •0056 

 •0010 



10866 



"2514 





Nothing could be more decisive against the law of harmonic ratios 

 than this table ; three out of the five elements considered, including 

 the two containing the greatest number of lines, give a mean value 

 greater than "25. 



In order to see how near to this value we should expect the mean to 

 come if no law connects the different lines, I have given the probable 



