•466 Coincidences between the Lines of Different Spectra. 



of the differences, the second gives the expected number of 

 differences within these limits, the third the observed number 

 corresponding to the wave-lengths calculated from hydrogen, 

 the fourth the observed number corresponding to the said 

 mantissas of log sin and log tan. 



Limits of 



Expected 



Observed 



Limits of 



Expected 



Observed 



differences. 



numbers. 



numbers. 



differences. 



numbers. 



numbers. 



•00 to -05 



10-4 



12 



6 



2-05 to 2-] 5 



0-6 



2 



1 



•05 „ 15 



20-6 



16 



26 



215 „ 2-25 



0-5 







•15 „ -25 



20-2 



19 



16 



2-25 „ 2-35 



04 







•25 „ -35 



18-4 



21 



16 



2-35 „ 2-45 



1 







•35 „ -45 



16-0 



19 



15 



2-45 „ 2-55 



L 0-9 



1 





•45 „ -55 



13-8 



16 



16 



2-55 „ 2-65 



J 







•55 „ -65 



11-3 



11 



12 



2-65 „ 275 



"1 



1 





•65 „ -75 



9-3 



8 



9 



2-75 „ 2-85 



I 0-7 







•75 „ -85 



7-5 



7 



11 



2-85 „ 2-95 



1 







•85 „ -95 



5-9 



5 



12 



2-95 „ 305 



1 



1 





•95 „ 1-05 



4-9 



6 



1 



3-05 „ 345 



I 0-6 



1 



1 



1 05 „ 115 



3-8 



1 



5 



315 „ 325 



J 







115 „ 125 



31 





2 



3-25 „ 3-35 



| 



1 





1-25 „ 1-35 



2-2 



'*8 



3 



3-35 „ 3-45 



I 0-4 







1-35 „ 1-45 



1-8 



1 



2 



3-45 „ 3-55 



1 







1-45 ,. 1'55 



1-6 



3 



2 



3-55 „ 365 



1 







1-55 „ 1-65 



11 







3-65 „ 3-75 



0-4 







1-65 „ 1-75 



1-0 





1 



3-75 „ 3-85 



J 







1-75 „ 1-85 



09 



*2 



2 



3-85 „ 5-25 



10 



1 



1 



1-85 „ 1-95 



0-7 







5-25 „ 6-75 



0-7 



1 





1-95 „ 2-05 



07 



"2 



1 











As the distribution of the differences corresponding to the 

 wave-lengths calculated from hydrogen is in accordance with 

 the expected distribution, it follows either that the coincidences 

 are accidental or that their probable error is not smaller than 

 the one corresponding to c = 1*148. The probable error for 

 c = M48 is 0-42. That is to say, 0*42 x 10" 7 millim., as 10~ 7 

 millim. is the unit of the wave-lengths. It seems to me not im- 

 possible that the probable error of the difference between Liveing 

 and Dewar's measurements and the halves of Hasselberg's is as 

 much as 0*42. One cannot therefore, without more exact 

 measurements, safely infer that Griinwald's coincidences are 

 accidental. However, one can say that the distribution of 

 differences gives no more reason to believe the coincidences 

 real than to believe in a connexion between the mantissas of 

 log sin and the spectrum of water. 



