Coincidences betiveen the Lines of different Spectra. 5 



sources of error affecting the wave-length measurements. 

 The evidence afforded by the method appears then to supply 

 a substantial confirmation to the reality of the coincidences, 

 so far as the material for investigation goes. 



Professor Grunwald's Investigations. 

 The most important verification of his theory put forward 

 by Grunwald is that afforded by the close agreement between 

 the wave-lengths of the lines in the spectrum of water, as 

 deduced by him from those of the hydrogen spectrum, and 

 their values as obtained by observation. So far, 58 of the 

 predicted lines have been observed by Prof. Liveing; and 

 the remainder occur in a part of the spectrum not yet sub- 

 mitted to examination. The wave-lengths are given in 

 Grunwald's* paper ; the differences between the observed and 

 calculated values are given here : — 



Between 0*0 and 01 Xth metr< 



0-1 

 0-2 

 0-3 

 0-4 

 0-5 

 0-6 

 0-7 

 0-8 

 0-9 

 1-0 

 1-1 



0-2 

 0-3 

 0-4 

 0-5 

 0-6 

 0-7 

 0-8 

 0-9 

 1-0 

 1-1 

 1-2 



, 7 coincidences. 

 10 



8 



7 



2 



2 



^ 



5 



2 

 2 

 1 



1-5 



1-6 



1 



These when plotted give the curve fig. 7, which agrees almost 

 exactly with the formula for the Theoretical Curve of Error, 

 as tested by taking points. On the other hand, four of the 

 points do not agree so well with the smooth curve as those in 

 the cases already examined; and until further measurements 

 are obtained, the method only warrants us in asserting that 

 the balance of probability lies on the side of the reality of the 

 coincidences. 



The curve shown in fig. 8 is extremely interesting ; it is 

 plotted from the comparison, in Grunwald's paper, between 

 the spectrum of one of his hypothetical constituents of 

 hydrogen, termed by him " Z>," and the nearest solar lines, as 

 given in Angstrom's map. The number of lines included 

 is 41. The differences are as follows : — 



* Phil. Mag. [5] xxiv. p. 357, 1887. 



