352 



Molecules, Ultimates, Atorns, and Waves. [July, 



the unit being the ten-thousandth part of the millionth of a 

 millimetre. * 





Observed. 



Calculated. 



Differences + . 



Differences — , 



A. 



7,604,000 



7.604,017 



000,001,7 



— 



B. 



6,867,100 



6,867,098 



— 



000,000,2 



C. 



6,562,100 



6,562,093 



— 



000,000,7 



D. 



5,895^30 



5,895,H7 



— 



000,001,3 



E. 



5,268,670 



5,268,670 



— 



— 



F. 



4,860,740 



4,860,747 



000,000,7 



>. — 



G. 



4,307,250 



4,307,235 



— 



000,001,5 



H. 



3,933.000 



3,932,995 



— 



000,000,5 





000,002,4 



000,004,2 



Thus the sum of the differences plus and minus is only 

 66-tenths of the thousandth of the millionth of a millimetre ; 

 while the greatest difference is only 17 of those decimal parts. 

 This quantity would affect the position of the lines to an ex- 

 tent so minute as to be wholly inappreciable to the eye, 

 either on the atlas of M. Angstrom or on the map of M. 

 Kirchhoff. The following are the calculated wave-lengths 

 stated in billionths of an inch : — 



A. 



29,957,6oo 



B. 



27,o54,36o 



C. 25,852,720 



D. 



23,225,300 



E. 



20,757,000 



F. 19,149,930 



G. 



16,969,250 



H. 



i5,494, 8 5o 





The extreme smallness of the differences between M. 



o 



Angstrom's measurements and the values calculated from 

 the formulae seems to establish both the accuracy of his ob- 

 servations and the truth of the relations which the formulae 

 express. The wave-lengths, as calculated from those for- 

 mulae, may accordingly be regarded as approximating very 

 closely to the truth. 



The relations thus shown to subsist among the wave- 

 lengths, correspondingto the above eight principal fixed lines, 

 will appear all the more remarkable when it is borne in 

 mind that the waves themselves are due to the action of 

 diverse substances. The A and B waves are produced by 

 the action of atmospheric air ; the c and F waves by hydro- 

 gen gas ; the d wave by the vapour of sodium ; the e, g, 

 and H waves by the vapour of iron. 



The marvel of the double coincidence, moreover, — the cir- 

 cumstance that not only are the other seven capable of being 



* It is the longer of the two d waves, the shorter of the two e waves, and 

 the shorter of the two h waves that are given in the table. 



