between the Lines of Different Spectra. 465 



of differences between certain limits equal to the area of our 

 curve of difference between the same limits multiplied by the 

 number of lines of the second spectrum. And if a curve is 

 plotted in the manner indicated by Love, it evidently must 

 resemble the curve given by the law of error, whatever the 

 second spectrum may be. In this case, therefore, the method 

 of Love cannot give us any information whether the coinci- 

 dences between the lines of the two spectra are real or 

 accidental. But we may derive some information by con- 

 sidering the value of the constant in the formula given by the 

 law of error. Supposing the coincidences to be real ones, the 

 differences between the lines compared must be distributed 



according to the formula y= —-=re~ c2x2 . If now we can make 



V 7T 



an estimate of c and find it considerably larger than 1*148, 

 the distribution of differences ought to show a divergence 

 from the distribution given above. If the divergence is not 

 shown, the coincidences must be accidental. Only when c is 

 not found considerably larger than 1*148 we are left without 

 an answer. The distribution of differences would then be the 

 one given above, and would afford no reason to think the coin- 

 cidences real ones. 



The most important verification of A. Grrtinwald's far- 

 reaching speculations on the composition of the elements 

 he believes to be afforded by the agreement between the 

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

 duced by him from those of the hydrogen spectrum, and 

 their values as obtained by observation. But I find that the 

 distribution of differences is in perfect accordance with the 

 one expected for an equal number of wave-lengths chosen at 

 random. To show this more clearly, I have taken the man- 

 tissas of log sin from 9° 43' to 12° 4', and of log tan from 

 19° 20' to 19° 38' for each minute abbreviated to five 

 figures. These numbers lie between the extreme wave- 

 lengths of the water-bands. The distribution of differences 

 between each of these numbers and the nearest wave-length 

 of the water-spectrum does not show any serious divergence 

 from the distribution corresponding to the wave-lengths 

 calculated according to Griinwald's theory by multiplying the 

 wave-lengths of hydrogen by i **• 



The first column of the following table contains the limits 



* I have taken Hasselberg's measurements, M6m. de VAcad. dc St. 

 Petersbourc/, 1882, as Grinwald has preferred these to the more complete 

 measurements of 1883. I have abbreviated the halves to rive figures, 

 adding- a unity to the fifth figure when it was even. 





